Abstract group data - 256.5742

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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': [2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 4, 8, 16, 64], [137, 164, 8, 16, 64], [33, 4, 8, 16, 96], [139, 4, 40, 176, 64], [131, 4, 8, 24, 204], [129, 4, 8, 48, 64], [173, 164, 136, 48, 192], [33, 4, 8, 48, 64]], 'aut_group': '1024.djx', 'aut_hash': 8067704780552372617, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 48, 'aut_perms': [7883571553475619328263613971454262416883203254844267432426818, 2514828213662867067637007159145925375062939643405140090531, 10134223258725961310696451357875748576117832909034043345832086, 10998749194541038850991990672841304066633020761461781281328563, 3067627582576359408964266471089512014727260036974760431302452, 9453764360818092641081474452939404213452510376075565573329139, 5851981582321694402000033009860938415857268596716488062266916], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 4], [2, 8, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 8, 1, 9], [4, 8, 4, 1], [4, 16, 2, 2], [8, 16, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6:C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '128.2163', 'autcentquo_hash': 2163, 'autcentquo_nilpotent': True, 'autcentquo_order': 128, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 4], [2, 8, 2], [4, 4, 4], [4, 8, 13], [4, 16, 4], [8, 16, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.522', 'commutator_count': 1, 'commutator_label': '16.11', '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', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5742, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 4], [2, 8, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 8, 1, 9], [4, 8, 2, 2], [4, 16, 2, 2], [8, 16, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 5376, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 0, 2]], 'familial': False, 'frattini_label': '32.46', 'frattini_quotient': '8.5', 'hash': 5742, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 2, 2, 4], 'inner_gens': [[1, 164, 8, 24, 236], [161, 4, 40, 176, 192], [1, 36, 8, 16, 192], [9, 164, 8, 16, 64], [141, 132, 136, 16, 64]], 'inner_hash': 522, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': None, 'inner_tex': 'C_2^4.D_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 2]], 'label': '256.5742', 'linC_count': 2, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 16, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 16, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^4.(C2*D4)', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 69, 'number_conjugacy_classes': 34, 'number_divisions': 28, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 379, 'number_subgroup_classes': 391, 'number_subgroups': 1159, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 184], [8, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[129, 4, 8, 48, 64], [139, 4, 40, 176, 64], [137, 164, 8, 16, 64]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 8, 'outer_perms': [23616, 11536, 5167], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 2], [8, 1], [16, 1]], 'representations': {'PC': {'code': 2733101103424306455807362887285405414737, 'gens': [1, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 16, 3938, 442, 339, 964, 1780, 116, 13222, 6286, 2710, 1374, 166, 10247]}, 'Perm': {'d': 32, 'gens': [152932197174750945594291294277632000, 101975790215895262428131543044149817, 84963054044187526724174007889857358, 67977995780968282257602718863923200, 33988952657447882563638486559363183, 16976205612381906363352243137194303, 1313941673647, 8231691320578226211046411712681647]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4.(C_2\\times D_4)', 'transitive_degree': 32, '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: 109466462
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 5742, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 109466473
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 5742, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 109466484
    {'aut_label': '2B', 'centralizer': '2.g1.a1', 'counter': 3, 'group_counter': 5742, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 138, 'size': 2}
  • id: 109466490
    {'aut_label': '2C', 'centralizer': '2.a1.a1', 'counter': 4, 'group_counter': 5742, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 128, 'size': 2}
  • id: 109466491
    {'aut_label': '2D', 'centralizer': '2.f1.a1', 'counter': 5, 'group_counter': 5742, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 42, 'size': 2}
  • id: 109466492
    {'aut_label': '2E', 'centralizer': '4.n1.a1', 'counter': 6, 'group_counter': 5742, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 8, 'size': 4}
  • id: 109466493
    {'aut_label': '2F', 'centralizer': '4.r1.a1', 'counter': 7, 'group_counter': 5742, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 4, 'size': 4}
  • id: 109466494
    {'aut_label': '2G', 'centralizer': '4.n1.a1', 'counter': 8, 'group_counter': 5742, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 2, 'size': 4}
  • id: 109466495
    {'aut_label': '2H', 'centralizer': '4.s1.a1', 'counter': 9, 'group_counter': 5742, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 46, 'size': 4}
  • id: 109466463
    {'aut_label': '2I', 'centralizer': '8.dh1.a1', 'counter': 10, 'group_counter': 5742, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 72, 'size': 8}
  • id: 109466464
    {'aut_label': '2J', 'centralizer': '8.ch1.a1', 'counter': 11, 'group_counter': 5742, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 82, 'size': 8}
  • id: 109466465
    {'aut_label': '4A', 'centralizer': '4.w1.a1', 'counter': 12, 'group_counter': 5742, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 12, 'size': 4}
  • id: 109466466
    {'aut_label': '4B', 'centralizer': '4.u1.a1', 'counter': 13, 'group_counter': 5742, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 134, 'size': 4}
  • id: 109466467
    {'aut_label': '4C1', 'centralizer': '4.l1.a1', 'counter': 14, 'group_counter': 5742, 'group_order': 256, 'label': '4C1', 'order': 4, 'powers': [2], 'representative': 16, 'size': 4}
  • id: 109466468
    {'aut_label': '4C1', 'centralizer': '4.l1.a1', 'counter': 15, 'group_counter': 5742, 'group_order': 256, 'label': '4C-1', 'order': 4, 'powers': [2], 'representative': 144, 'size': 4}
  • id: 109466469
    {'aut_label': '4D', 'centralizer': '8.dq1.a1', 'counter': 16, 'group_counter': 5742, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 64, 'size': 8}
  • id: 109466470
    {'aut_label': '4E', 'centralizer': '8.dd1.a1', 'counter': 17, 'group_counter': 5742, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [4], 'representative': 80, 'size': 8}
  • id: 109466471
    {'aut_label': '4F', 'centralizer': '8.bh1.a1', 'counter': 18, 'group_counter': 5742, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 20, 'size': 8}
  • id: 109466472
    {'aut_label': '4G', 'centralizer': '8.df1.a1', 'counter': 19, 'group_counter': 5742, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [2], 'representative': 66, 'size': 8}
  • id: 109466474
    {'aut_label': '4H', 'centralizer': '8.b1.a1', 'counter': 20, 'group_counter': 5742, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [2], 'representative': 18, 'size': 8}
  • id: 109466475
    {'aut_label': '4I', 'centralizer': '8.cf1.a1', 'counter': 21, 'group_counter': 5742, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [2], 'representative': 88, 'size': 8}
  • id: 109466476
    {'aut_label': '4J', 'centralizer': '8.dm1.a1', 'counter': 22, 'group_counter': 5742, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [4], 'representative': 74, 'size': 8}
  • id: 109466477
    {'aut_label': '4K', 'centralizer': '8.be1.a1', 'counter': 23, 'group_counter': 5742, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [4], 'representative': 22, 'size': 8}
  • id: 109466478
    {'aut_label': '4L', 'centralizer': '8.cz1.a1', 'counter': 24, 'group_counter': 5742, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 90, 'size': 8}
  • id: 109466479
    {'aut_label': '4M1', 'centralizer': '8.dv1.b1', 'counter': 25, 'group_counter': 5742, 'group_order': 256, 'label': '4M1', 'order': 4, 'powers': [5], 'representative': 17, 'size': 8}
  • id: 109466480
    {'aut_label': '4M1', 'centralizer': '8.dv1.b1', 'counter': 26, 'group_counter': 5742, 'group_order': 256, 'label': '4M-1', 'order': 4, 'powers': [5], 'representative': 19, 'size': 8}
  • id: 109466481
    {'aut_label': '4M1', 'centralizer': '8.dv1.a1', 'counter': 27, 'group_counter': 5742, 'group_order': 256, 'label': '4N1', 'order': 4, 'powers': [5], 'representative': 145, 'size': 8}
  • id: 109466482
    {'aut_label': '4M1', 'centralizer': '8.dv1.a1', 'counter': 28, 'group_counter': 5742, 'group_order': 256, 'label': '4N-1', 'order': 4, 'powers': [5], 'representative': 147, 'size': 8}
  • id: 109466483
    {'aut_label': '4O1', 'centralizer': '16.dy1.a1', 'counter': 29, 'group_counter': 5742, 'group_order': 256, 'label': '4O1', 'order': 4, 'powers': [8], 'representative': 1, 'size': 16}
  • id: 109466485
    {'aut_label': '4O1', 'centralizer': '16.dy1.a1', 'counter': 30, 'group_counter': 5742, 'group_order': 256, 'label': '4O-1', 'order': 4, 'powers': [8], 'representative': 3, 'size': 16}
  • id: 109466486
    {'aut_label': '4P1', 'centralizer': '16.be1.a1', 'counter': 31, 'group_counter': 5742, 'group_order': 256, 'label': '4P1', 'order': 4, 'powers': [9], 'representative': 65, 'size': 16}
  • id: 109466487
    {'aut_label': '4P1', 'centralizer': '16.be1.a1', 'counter': 32, 'group_counter': 5742, 'group_order': 256, 'label': '4P-1', 'order': 4, 'powers': [9], 'representative': 67, 'size': 16}
  • id: 109466488
    {'aut_label': '8A1', 'centralizer': '16.bh1.a1', 'counter': 33, 'group_counter': 5742, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [13], 'representative': 81, 'size': 16}
  • id: 109466489
    {'aut_label': '8A1', 'centralizer': '16.bh1.a1', 'counter': 34, 'group_counter': 5742, 'group_order': 256, 'label': '8A-1', 'order': 8, 'powers': [13], 'representative': 83, 'size': 16}
• 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: 4288290
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1a', '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], 'schur_index': 1}
  • id: 4288301
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1b', '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], 'schur_index': 1}
  • id: 4288311
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1c', '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], 'schur_index': 1}
  • id: 4288312
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1d', '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], 'schur_index': 1}
  • id: 4288313
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1e', '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], 'schur_index': 1}
  • id: 4288314
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1f', '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], 'schur_index': 1}
  • id: 4288315
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1g', '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], 'schur_index': 1}
  • id: 4288316
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1h', '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], 'schur_index': 1}
  • id: 4288317
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1i', '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, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288291
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1j', '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, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288292
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1k', '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, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288293
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.1l', '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, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288294
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, -2, 2, 2, -2, 0, 0, 2, -2, -2, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288295
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, -2, 2, 2, -2, 0, 0, 2, -2, 2, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288296
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 2, -2, -2, 2, 0, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288297
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 2, -2, -2, 2, 0, 2, 2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288298
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 2, 2, -2, -2, -2, 0, -2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288299
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 0, -2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288300
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 0, 2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288302
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288303
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, 2, -2, 2, 0, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288304
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, 2, -2, 2, 0, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288305
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, -2, -2, -2, -2, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288306
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, -2, -2, 2, 2, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288307
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.4a', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288308
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.4b', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4288309
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.4c', 'multiplicity': 2, 'nt': [16, 146], 'qdim': 8, 'qvalues': [8, 8, 8, -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, 0, 0, 0], 'schur_index': 1}
  • id: 4288310
    {'cdim': 8, 'counter': 28, 'faithful': True, 'group': '256.5742', 'group_order': 256, 'image': None, 'label': '256.5742.8a', 'multiplicity': 2, 'nt': [32, 6591], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 6374100
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.5742.1a', '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]]]}
  • id: 6374111
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.5742.1b', '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]]]}
  • id: 6374122
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.5742.1c', '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]]]}
  • id: 6374128
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.5742.1d', '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]]]}
  • id: 6374129
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.5742.1e', '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]]]}
  • id: 6374130
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.5742.1f', '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]]]}
  • id: 6374131
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.5742.1g', '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]]]}
  • id: 6374132
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.5742.1h', '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]]]}
  • id: 6374133
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.k1.a1', 'kernel_order': 64, 'label': '256.5742.1i1', '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, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6374101
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.k1.a1', 'kernel_order': 64, 'label': '256.5742.1i2', '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, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6374102
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1.a1', 'kernel_order': 64, 'label': '256.5742.1j1', '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, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6374103
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1.a1', 'kernel_order': 64, 'label': '256.5742.1j2', '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, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6374104
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.i1.a1', 'kernel_order': 64, 'label': '256.5742.1k1', '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, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6374105
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.i1.a1', 'kernel_order': 64, 'label': '256.5742.1k2', '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, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6374106
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1.a1', 'kernel_order': 64, 'label': '256.5742.1l1', '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, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6374107
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1.a1', 'kernel_order': 64, 'label': '256.5742.1l2', '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, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6374108
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.o1.a1', 'kernel_order': 32, 'label': '256.5742.2a', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 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]]]}
  • id: 6374109
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.n1.a1', 'kernel_order': 32, 'label': '256.5742.2b', '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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 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]]]}
  • id: 6374110
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.q1.a1', 'kernel_order': 32, 'label': '256.5742.2c', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374112
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.p1.a1', 'kernel_order': 32, 'label': '256.5742.2d', '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]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374113
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.s1.a1', 'kernel_order': 32, 'label': '256.5742.2e', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374114
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.r1.a1', 'kernel_order': 32, 'label': '256.5742.2f', '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]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374115
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.g1.a1', 'kernel_order': 32, 'label': '256.5742.2g', '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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374116
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 32, 'label': '256.5742.2h', '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]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374117
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 32, 'label': '256.5742.2i', '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]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374118
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 32, 'label': '256.5742.2j', '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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374119
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 32, 'label': '256.5742.2k', '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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 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]]]}
  • id: 6374120
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 32, 'label': '256.5742.2l', '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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 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]]]}
  • id: 6374121
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.c1.a1', 'kernel_order': 4, 'label': '256.5742.4a', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374123
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.c1.a1', 'kernel_order': 4, 'label': '256.5742.4b', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374124
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '64.139', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.5742.4c1', 'nt': [16, 146], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374125
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '64.139', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.5742.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374126
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 4, 'dim': 8, 'faithful': True, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '256.5742', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5742.8a1', 'nt': [32, 6591], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6374127
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 4, 'dim': 8, 'faithful': True, 'field': [1, 0, 1], 'group': '256.5742', 'group_counter': 5742, 'group_order': 256, 'image': None, 'image_isoclass': '256.5742', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5742.8a2', 'nt': [32, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 64593793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.5742.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '256.5742', 'subgroup_hash': 5742, 'subgroup_order': 256, 'subgroup_tex': 'C_2^4.(C_2\\times D_4)', 'supersolvable': True, 'sylow': 2}
  • id: 64593904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2265', 'subgroup_hash': 2265, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.643', 'subgroup_hash': 643, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.859', 'subgroup_hash': 859, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.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': '128.645', 'subgroup_hash': 645, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.853', 'subgroup_hash': 853, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.622', 'subgroup_hash': 622, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.851', 'subgroup_hash': 851, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.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': '4.2', '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': '64.215', 'subgroup_hash': 215, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.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': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.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': '4.2', '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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.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': '4.2', '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': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.241', 'subgroup_hash': 241, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.240', 'subgroup_hash': 240, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.244', 'subgroup_hash': 244, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.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': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.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': '64.62', 'subgroup_hash': 62, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.227', 'subgroup_hash': 227, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.232', 'subgroup_hash': 232, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.228', 'subgroup_hash': 228, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.u1.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': '64.102', 'subgroup_hash': 102, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.v1.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': '64.233', 'subgroup_hash': 233, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.w1.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': '64.18', 'subgroup_hash': 18, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.x1.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': '64.234', 'subgroup_hash': 234, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.y1.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': '64.243', 'subgroup_hash': 243, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.z1.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': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ba1.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': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bb1.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': '64.219', 'subgroup_hash': 219, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bc1.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': '64.220', 'subgroup_hash': 220, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bd1.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': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.be1.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': '64.33', 'subgroup_hash': 33, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bf1.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': '64.221', 'subgroup_hash': 221, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bg1.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': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bh1.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': '64.223', 'subgroup_hash': 223, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.4.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bi1.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': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.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': '8.5', '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', 'U1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.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': '8.3', '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.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': '8.3', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bh1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bi1.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bj1.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1.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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64594164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bp1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bq1.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.br1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bs1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bt1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bu1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bv1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bw1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bx1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.by1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bz1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ca1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cb1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cc1.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64594183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cd1.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ce1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cf1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cg1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ch1.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ci1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cj1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ck1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cl1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cm1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cn1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.co1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cp1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cq1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cr1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cs1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ct1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cu1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cv1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cw1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cx1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cy1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cz1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.da1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.db1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dc1.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dd1.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.de1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.df1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dg1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dh1.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.di1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dj1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dk1.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dl1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dm1.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dn1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.do1.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': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dp1.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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dq1.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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dr1.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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ds1.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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dt1.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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.du1.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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dv1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dv1.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dw1.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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dw1.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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dx1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dx1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dy1.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.8.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dy1.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.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': '16.11', '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64593852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64593853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 161, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 64593863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 164, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 165, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 166, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.q1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.r1.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 169, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.s1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cd1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ch1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ci1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cj1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ck1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cl1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cm1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cn1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.co1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cp1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cq1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cr1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ct1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cx1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.da1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.db1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dc1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64593941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dd1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.de1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dg1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dh1.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.di1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dk1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dm1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dn1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.do1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dp1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dq1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64593957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593958
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593964
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dx2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx2.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dx2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx2.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ea2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea2.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ea2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea2.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eb1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ec1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ed1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64593975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ee2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee2.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ee2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee2.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64593978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.16.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ef1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64593979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['U2'], '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: 64593980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.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': ['C5'], '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: 64593981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.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': [], '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: 64593983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', '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: 64593984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 271, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', '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: 64593985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.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': [], '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: 64593986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', '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: 64593987
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64593988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64593989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593992
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64593995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64593996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593997
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64593999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594008
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594031
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594032
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 318, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.32.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.by1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bz1.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ca1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cb1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594042
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cf1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cg1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ch1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64594047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594053
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594054
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64594056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594057
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cr1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.32.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cs1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64594062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 341, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.139', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 139, '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': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594063
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.60', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 60, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5742.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64594065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 64594066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594070
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594072
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 350, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594073
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594074
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 352, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594075
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 353, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594076
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594077
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594078
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594079
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': 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: 64594084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1.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': 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: 64594085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.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': 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: 64594086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.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': 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: 64594087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.w2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w2.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': 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: 64594088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1.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': 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: 64594089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.x2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x2.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': 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: 64594090
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1.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': 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: 64594091
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.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': 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: 64594092
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.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': 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: 64594094
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.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': 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: 64594095
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.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': 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: 64594096
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.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': 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: 64594097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.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': 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: 64594098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.be1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': 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: 64594099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bf1.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': 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: 64594100
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg1.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': 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: 64594101
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg1.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': 64, 'quotient_simple': 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: 64594102
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5742.64.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bh1.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': 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: 64594103
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi1.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': 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: 64594105
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.64.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bj1.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': 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: 64594106
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 381, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5742.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.522', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 522, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4.D_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U3', 'L3', 'D2', 'C7'], '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: 64594107
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 64594108
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 64594109
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594110
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594111
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594112
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594113
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594114
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594116
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5742.128.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, '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: 64594117
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5742', 'ambient_counter': 5742, 'ambient_order': 256, 'ambient_tex': 'C_2^4.(C_2\\times D_4)', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 391, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.5742.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.5742', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5742, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4.(C_2\\times D_4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D3', 'C8'], '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: 64594042
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1'], 'contains': ['64.r1.a1', '64.bj1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T7450', 'count': 16, 'diagramx': [1126, -1, 1507, -1, 1126, -1, 1507, -1], 'generators': [65, 164], 'label': '256.5742.32.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '32.cd1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64593846
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '64.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.dz1.a1', '16.ea2.a1', '16.eb1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [577, -1, 833, -1, 577, -1, 833, -1], 'generators': [225, 216], 'label': '256.5742.8.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '8.dx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593793
    {'ambient': '256.5742', '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': '128.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1377, 4579, 1626, 4463, 1377, 4595, 1626, 4533], 'generators': [1, 16, 64], 'label': '256.5742.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '128.522', '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': '128.522'}
  • id: 64593847
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '64.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.dz1.a1', '16.ea2.b1', '16.eb1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [577, -1, 905, -1, 577, -1, 906, -1], 'generators': [65, 216], 'label': '256.5742.8.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '8.dx1.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dx1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593794
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.i1.a1', '8.k1.a1', '8.p1.a1', '8.q1.a1', '8.u1.a1', '8.bf1.a1', '8.bo1.a1', '8.cl1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4008, 5618, 3432, 5527, 3995, 5637, 3433, 5613], 'generators': [80, 2, 172, 8], 'label': '256.5742.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.p1.a1', '8.q1.a1', '8.i1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64593795
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ce1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.q1.a1', '4.bb1.a1'], 'contains': ['16.l1.a1', '16.bm1.a1', '16.bn1.a1', '16.ch1.a1', '16.cj1.a1', '16.dd1.a1', '16.dh1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7989, -1, 9970, -1, 7989, -1, 9976, -1], 'generators': [16, 64, 164], 'label': '256.5742.8.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ce1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593796
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.p1.a1', '4.bc1.a1'], 'contains': ['16.m1.a1', '16.bm1.a1', '16.bn1.a1', '16.ci1.a1', '16.ck1.a1', '16.de1.a1', '16.di1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4401, -1, 7283, -1, 4401, -1, 7287, -1], 'generators': [24, 64, 164], 'label': '256.5742.8.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593797
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.q1.a1', '4.bc1.a1'], 'contains': ['16.n1.a1', '16.bm1.a1', '16.bp1.a1', '16.cl1.a1', '16.cm1.a1', '16.dj1.a1', '16.dk1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9714, -1, 9658, -1, 9713, -1, 9663, -1], 'generators': [26, 64, 164], 'label': '256.5742.8.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593798
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.p1.a1', '4.bb1.a1'], 'contains': ['16.k1.a1', '16.bn1.a1', '16.bo1.a1', '16.cp1.a1', '16.cq1.a1', '16.ct1.a1', '16.cu1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7728, -1, 5472, -1, 7727, -1, 5475, -1], 'generators': [16, 226, 164], 'label': '256.5742.8.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ch1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593799
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ci1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.q1.a1', '4.bc1.a1'], 'contains': ['16.n1.a1', '16.bn1.a1', '16.bo1.a1', '16.df1.a1', '16.dg1.a1', '16.dp1.a1', '16.dq1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8267, -1, 5716, -1, 8267, -1, 5719, -1], 'generators': [24, 226, 164], 'label': '256.5742.8.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ci1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593800
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.q1.a1', '4.bb1.a1'], 'contains': ['16.l1.a1', '16.bo1.a1', '16.bp1.a1', '16.dl1.a1', '16.dm1.a1', '16.dn1.a1', '16.do1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7920, -1, 6793, -1, 7920, -1, 6798, -1], 'generators': [18, 226, 164], 'label': '256.5742.8.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593801
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ck1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.p1.a1', '4.bc1.a1'], 'contains': ['16.m1.a1', '16.bo1.a1', '16.bp1.a1', '16.dr1.a1', '16.ds1.a1', '16.dt1.a1', '16.du1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3694, -1, 3984, -1, 3693, -1, 3987, -1], 'generators': [26, 226, 164], 'label': '256.5742.8.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ck1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593802
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bf1.a1', '4.bh1.a1'], 'contains': ['16.o1.a1', '16.br1.a1', '16.bv1.a1', '16.by1.a1', '16.cb1.a1', '16.cn1.a1', '16.cw1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6106, -1, 5642, -1, 6106, -1, 5646, -1], 'generators': [80, 2, 172], 'label': '256.5742.8.cl1.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.cl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593803
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bf1.a1', '4.bh1.a1'], 'contains': ['16.o1.a1', '16.bs1.a1', '16.bu1.a1', '16.bz1.a1', '16.cc1.a1', '16.cv1.a1', '16.cx1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5473, -1, 5219, -1, 5472, -1, 5223, -1], 'generators': [16, 2, 172], 'label': '256.5742.8.cm1.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.cm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593804
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bg1.a1', '4.bi1.a1'], 'contains': ['16.o1.a1', '16.bw1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [896, -1, 1836, -1, 897, -1, 1837, -1], 'generators': [1, 172], 'label': '256.5742.8.cn1.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.cn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64593805
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.j1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1', '8.y1.a1', '8.bi1.a1', '8.ca1.a1', '8.cm1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2957, 2494, 2764, 2441, 2956, 2502, 2765, 2479], 'generators': [16, 2, 172, 8], 'label': '256.5742.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.n1.a1', '8.o1.a1', '8.j1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593806
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.co1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.bg1.a1', '4.bi1.a1'], 'contains': ['16.o1.a1', '16.cd1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [972, -1, 1909, -1, 972, -1, 1910, -1], 'generators': [65, 172], 'label': '256.5742.8.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.co1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.co1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64593807
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bb1.a1', '4.bf1.a1'], 'contains': ['16.bq1.a1', '16.br1.a1', '16.bs1.a1', '16.ce1.a1', '16.ch1.a1', '16.cq1.a1', '16.dn1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7328, -1, 8353, -1, 7327, -1, 8358, -1], 'generators': [24, 200, 2], 'label': '256.5742.8.cp1.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': '8.cp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593808
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bb1.a1', '4.bf1.a1'], 'contains': ['16.bq1.a1', '16.br1.a1', '16.bu1.a1', '16.cf1.a1', '16.cj1.a1', '16.cu1.a1', '16.do1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9443, -1, 9903, -1, 9442, -1, 9910, -1], 'generators': [28, 200, 2], 'label': '256.5742.8.cq1.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': '8.cq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593809
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bc1.a1', '4.bf1.a1'], 'contains': ['16.bq1.a1', '16.bs1.a1', '16.bv1.a1', '16.ci1.a1', '16.cl1.a1', '16.dg1.a1', '16.dt1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4176, -1, 6874, -1, 4176, -1, 6878, -1], 'generators': [16, 200, 2], 'label': '256.5742.8.cr1.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': '8.cr1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593810
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bc1.a1', '4.bf1.a1'], 'contains': ['16.bq1.a1', '16.bu1.a1', '16.bv1.a1', '16.ck1.a1', '16.cm1.a1', '16.dq1.a1', '16.du1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6637, -1, 8627, -1, 6637, -1, 8633, -1], 'generators': [20, 200, 2], 'label': '256.5742.8.cs1.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': '8.cs1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593811
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ct1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bb1.a1', '4.bh1.a1'], 'contains': ['16.br1.a1', '16.bs1.a1', '16.bt1.a1', '16.cp1.a1', '16.cr1.a1', '16.dd1.a1', '16.dl1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7111, -1, 6713, -1, 7111, -1, 6717, -1], 'generators': [16, 64, 2], 'label': '256.5742.8.ct1.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': '8.ct1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593812
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bb1.a1', '4.bh1.a1'], 'contains': ['16.br1.a1', '16.bt1.a1', '16.bu1.a1', '16.cs1.a1', '16.ct1.a1', '16.dh1.a1', '16.dm1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8604, -1, 8534, -1, 8604, -1, 8539, -1], 'generators': [20, 64, 2], 'label': '256.5742.8.cu1.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': '8.cu1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593813
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bc1.a1', '4.bh1.a1'], 'contains': ['16.bs1.a1', '16.bt1.a1', '16.bv1.a1', '16.de1.a1', '16.df1.a1', '16.dj1.a1', '16.dr1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4093, -1, 5118, -1, 4093, -1, 5122, -1], 'generators': [24, 64, 2], 'label': '256.5742.8.cv1.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': '8.cv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593814
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bc1.a1', '4.bh1.a1'], 'contains': ['16.bt1.a1', '16.bu1.a1', '16.bv1.a1', '16.di1.a1', '16.dk1.a1', '16.dp1.a1', '16.ds1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6472, -1, 6954, -1, 6472, -1, 6959, -1], 'generators': [28, 64, 2], 'label': '256.5742.8.cw1.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': '8.cw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593815
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.x1.a1', '4.bf1.a1'], 'contains': ['16.bx1.a1', '16.by1.a1', '16.bz1.a1', '16.cf1.a1', '16.ci1.a1', '16.cq1.a1', '16.du1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7027, -1, 7202, -1, 7027, -1, 7206, -1], 'generators': [16, 200, 174], 'label': '256.5742.8.cx1.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': '8.cx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593816
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '64.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.v1.a1', '8.z1.a1', '8.bj1.a1', '8.dv1.a1', '8.dv1.b1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [476, 3865, 739, 4997, 476, 3878, 740, 5075], 'generators': [17, 172, 8, 160], 'label': '256.5742.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 64593817
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.y1.a1', '4.bf1.a1'], 'contains': ['16.bx1.a1', '16.by1.a1', '16.cc1.a1', '16.ce1.a1', '16.ck1.a1', '16.cu1.a1', '16.dt1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6181, -1, 7452, -1, 6181, -1, 7456, -1], 'generators': [20, 200, 174], 'label': '256.5742.8.cy1.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': '8.cy1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593818
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.a1', '4.bf1.a1'], 'contains': ['16.bx1.a1', '16.bz1.a1', '16.cb1.a1', '16.ch1.a1', '16.cm1.a1', '16.dg1.a1', '16.do1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9526, -1, 9030, -1, 9525, -1, 9035, -1], 'generators': [24, 200, 174], 'label': '256.5742.8.cz1.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': '8.cz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593819
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.da1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.y1.a1', '4.bf1.a1'], 'contains': ['16.bx1.a1', '16.cb1.a1', '16.cc1.a1', '16.cj1.a1', '16.cl1.a1', '16.dn1.a1', '16.dq1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9220, -1, 9139, -1, 9220, -1, 9144, -1], 'generators': [28, 200, 174], 'label': '256.5742.8.da1.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': '8.da1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.da1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593820
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.db1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.x1.a1', '4.bh1.a1'], 'contains': ['16.by1.a1', '16.bz1.a1', '16.ca1.a1', '16.cp1.a1', '16.cs1.a1', '16.de1.a1', '16.ds1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6832, -1, 5815, -1, 6831, -1, 5819, -1], 'generators': [24, 64, 174], 'label': '256.5742.8.db1.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': '8.db1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.db1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593821
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.y1.a1', '4.bh1.a1'], 'contains': ['16.by1.a1', '16.ca1.a1', '16.cc1.a1', '16.cr1.a1', '16.ct1.a1', '16.di1.a1', '16.dr1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6250, -1, 6110, -1, 6250, -1, 6114, -1], 'generators': [28, 64, 174], 'label': '256.5742.8.dc1.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': '8.dc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593822
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.a1', '4.bh1.a1'], 'contains': ['16.bz1.a1', '16.ca1.a1', '16.cb1.a1', '16.dd1.a1', '16.df1.a1', '16.dk1.a1', '16.dm1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9095, -1, 7722, -1, 9094, -1, 7727, -1], 'generators': [16, 64, 174], 'label': '256.5742.8.dd1.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': '8.dd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593823
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.de1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.y1.a1', '4.bh1.a1'], 'contains': ['16.ca1.a1', '16.cb1.a1', '16.cc1.a1', '16.dh1.a1', '16.dj1.a1', '16.dl1.a1', '16.dp1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8535, -1, 8071, -1, 8535, -1, 8077, -1], 'generators': [20, 64, 174], 'label': '256.5742.8.de1.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': '8.de1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.de1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593824
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.df1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.cf1.a1', '16.cg1.a1', '16.ch1.a1', '16.co1.a1', '16.cp1.a1', '16.cy1.a1', '16.dm1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7837, -1, 7371, -1, 7837, -1, 7376, -1], 'generators': [16, 100, 166], 'label': '256.5742.8.df1.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': '8.df1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.df1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593825
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.y1.a1', '4.bb1.a1'], 'contains': ['16.ce1.a1', '16.cg1.a1', '16.cj1.a1', '16.co1.a1', '16.ct1.a1', '16.da1.a1', '16.dl1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7431, -1, 7844, -1, 7431, -1, 7848, -1], 'generators': [20, 100, 166], 'label': '256.5742.8.dg1.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': '8.dg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593826
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.x1.a1', '4.bc1.a1'], 'contains': ['16.cg1.a1', '16.ci1.a1', '16.cm1.a1', '16.cy1.a1', '16.db1.a1', '16.df1.a1', '16.ds1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5350, -1, 6195, -1, 5350, -1, 6199, -1], 'generators': [24, 100, 166], 'label': '256.5742.8.dh1.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': '8.dh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593827
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '64.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.w1.a1', '8.cb1.a1', '8.cn1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [827, 5097, 1501, 3179, 827, 5114, 1502, 3228], 'generators': [1, 172, 8], 'label': '256.5742.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '128.522', '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': '64.138'}
  • id: 64593828
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.di1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.cg1.a1', '16.ck1.a1', '16.cl1.a1', '16.da1.a1', '16.db1.a1', '16.dp1.a1', '16.dr1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5256, -1, 6504, -1, 5256, -1, 6508, -1], 'generators': [28, 100, 166], 'label': '256.5742.8.di1.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': '8.di1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593829
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.t1.a1', '4.bf1.a1'], 'contains': ['16.p1.a1', '16.ce1.a1', '16.cf1.a1', '16.cl1.a1', '16.cm1.a1', '16.cn1.a1', '16.cx1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9610, -1, 8861, -1, 9609, -1, 8867, -1], 'generators': [18, 200, 172], 'label': '256.5742.8.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593830
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.t1.a1', '4.bf1.a1'], 'contains': ['16.p1.a1', '16.ch1.a1', '16.ci1.a1', '16.cj1.a1', '16.ck1.a1', '16.cv1.a1', '16.cw1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5152, -1, 7971, -1, 5152, -1, 7976, -1], 'generators': [16, 200, 172], 'label': '256.5742.8.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dk1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593831
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.t1.a1', '4.bh1.a1'], 'contains': ['16.r1.a1', '16.cn1.a1', '16.cp1.a1', '16.ct1.a1', '16.cv1.a1', '16.df1.a1', '16.dp1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7535, -1, 4391, -1, 7535, -1, 4394, -1], 'generators': [16, 226, 172], 'label': '256.5742.8.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593832
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.v1.a1', '4.bf1.a1'], 'contains': ['16.s1.a1', '16.cn1.a1', '16.cq1.a1', '16.cu1.a1', '16.cv1.a1', '16.dg1.a1', '16.dq1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9346, -1, 7048, -1, 9345, -1, 7053, -1], 'generators': [16, 106, 172], 'label': '256.5742.8.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593833
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.v1.a1', '4.bh1.a1'], 'contains': ['16.q1.a1', '16.cn1.a1', '16.cr1.a1', '16.cs1.a1', '16.cx1.a1', '16.dj1.a1', '16.dk1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9818, -1, 9557, -1, 9817, -1, 9563, -1], 'generators': [18, 64, 172], 'label': '256.5742.8.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593834
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.do1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.co1.a1', '16.cq1.a1', '16.cs1.a1', '16.cy1.a1', '16.cz1.a1', '16.dd1.a1', '16.do1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8880, -1, 9411, -1, 8880, -1, 9417, -1], 'generators': [16, 64, 166], 'label': '256.5742.8.do1.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': '8.do1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.do1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593835
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.y1.a1', '4.bb1.a1'], 'contains': ['16.co1.a1', '16.cr1.a1', '16.cu1.a1', '16.cz1.a1', '16.da1.a1', '16.dh1.a1', '16.dn1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8804, -1, 9483, -1, 8805, -1, 9490, -1], 'generators': [20, 64, 166], 'label': '256.5742.8.dp1.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': '8.dp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593836
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.v1.a1', '4.bh1.a1'], 'contains': ['16.q1.a1', '16.cv1.a1', '16.cw1.a1', '16.dd1.a1', '16.de1.a1', '16.dh1.a1', '16.di1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6388, -1, 8941, -1, 6388, -1, 8947, -1], 'generators': [16, 64, 172], 'label': '256.5742.8.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593837
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.t1.a1', '4.bh1.a1'], 'contains': ['16.r1.a1', '16.cw1.a1', '16.cx1.a1', '16.dl1.a1', '16.dm1.a1', '16.dr1.a1', '16.ds1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4923, -1, 4164, -1, 4923, -1, 4166, -1], 'generators': [18, 226, 172], 'label': '256.5742.8.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dr1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593838
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.ba1.a1', '8.bp1.a1', '8.co1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [952, 3240, 1849, 3780, 952, 3252, 1850, 3838], 'generators': [65, 172, 8], 'label': '256.5742.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '128.522', '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': '64.139'}
  • id: 64593839
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ds1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.v1.a1', '4.bf1.a1'], 'contains': ['16.s1.a1', '16.cw1.a1', '16.cx1.a1', '16.dn1.a1', '16.do1.a1', '16.dt1.a1', '16.du1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6312, -1, 7136, -1, 6312, -1, 7140, -1], 'generators': [18, 106, 172], 'label': '256.5742.8.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ds1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593840
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.x1.a1', '4.bc1.a1'], 'contains': ['16.cy1.a1', '16.cz1.a1', '16.db1.a1', '16.de1.a1', '16.dg1.a1', '16.dk1.a1', '16.du1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6735, -1, 8138, -1, 6734, -1, 8143, -1], 'generators': [24, 64, 166], 'label': '256.5742.8.dt1.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': '8.dt1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593841
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.du1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.cz1.a1', '16.da1.a1', '16.db1.a1', '16.di1.a1', '16.dj1.a1', '16.dq1.a1', '16.dt1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6541, -1, 8287, -1, 6541, -1, 8291, -1], 'generators': [28, 64, 166], 'label': '256.5742.8.du1.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': '8.du1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.du1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593842
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.bf1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.dv1.a1', '16.dx1.a1', '16.dx2.b1', '16.ea1.a1', '16.ea2.b1', '16.ee1.a1', '16.ee2.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [367, -1, 395, -1, 367, -1, 395, -1], 'generators': [177, 172, 8], 'label': '256.5742.8.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.dv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593843
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.dv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.dv1.a1', '16.dx1.a1', '16.dx2.a1', '16.ea1.a1', '16.ea2.a1', '16.ee1.a1', '16.ee2.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [367, -1, 306, -1, 367, -1, 306, -1], 'generators': [17, 172, 8], 'label': '256.5742.8.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.dv1.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593844
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.dw1.a1', '16.dx2.a1', '16.dy1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [31, -1, 30, -1, 32, -1, 31, -1], 'generators': [1, 16], 'label': '256.5742.8.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '8.dw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593845
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.dw1.a1', '16.dx2.b1', '16.dy1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [31, -1, 104, -1, 32, -1, 104, -1], 'generators': [161, 16], 'label': '256.5742.8.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '8.dw1.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593848
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dy1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '64.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1'], 'contains': ['16.ed1.a1', '16.ee2.a1', '16.ef1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1060, -1, 991, -1, 1061, -1, 992, -1], 'generators': [17, 200], 'label': '256.5742.8.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '8.dy1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64593849
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.bk1.a1', '8.bq1.a1', '8.cc1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1763, 4489, 1380, 4381, 1763, 4504, 1380, 4448], 'generators': [81, 172, 8], 'label': '256.5742.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '128.522', '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': '64.139'}
  • id: 64593850
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '8.dy1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '64.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1'], 'contains': ['16.ed1.a1', '16.ee2.b1', '16.ef1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1060, -1, 1090, -1, 1061, -1, 1091, -1], 'generators': [177, 200], 'label': '256.5742.8.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '8.dy1.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dy1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64593851
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.t1.a1', '8.u1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.d1.a1', '32.h1.a1', '32.z1.a1', '32.ca1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2211, 3351, 2630, 3409, 2210, 3362, 2632, 3517], 'generators': [2, 8, 160, 32], 'label': '256.5742.16.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', '32.d1.a1', '32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593852
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.x1.a1', '8.y1.a1', '8.z1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.e1.a1', '32.i1.a1', '32.ba1.a1', '32.cb1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2265, 4411, 2742, 4473, 2265, 4426, 2744, 4542], 'generators': [10, 164, 160, 32], 'label': '256.5742.16.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.e1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64593853
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.bf1.a1', '8.bi1.a1', '8.bj1.a1', '8.bk1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '32.l1.a1', '32.bd1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2346, 7193, 2820, 7333, 2345, 7217, 2821, 7453], 'generators': [10, 172, 160], 'label': '256.5742.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1'], 'normal_contains': ['32.a1.a1', '32.g1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64593854
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': 96, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.f1.a1', '32.bg1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3038, 6717, 3281, 6498, 3038, 6740, 3283, 6600], 'generators': [172, 8, 160], 'label': '256.5742.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1'], 'normal_contains': ['32.c1.a1', '32.b1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64593855
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.e1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.n1.a1', '8.o1.a1', '8.bn1.a1', '8.bo1.a1', '8.bp1.a1', '8.bq1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '32.bh1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2750, 3839, 3003, 3828, 2750, 3852, 3005, 3903], 'generators': [174, 8, 160], 'label': '256.5742.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.a1', '8.n1.a1', '8.o1.a1'], 'normal_contains': ['32.e1.a1', '32.b1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64593856
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.j1.a1', '8.n1.a1', '8.bt1.a1', '8.bv1.a1'], 'contains': ['32.b1.a1', '32.p1.a1', '32.bi1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3136, 2082, 3376, 2125, 3136, 2090, 3378, 2440], 'generators': [16, 8, 160], 'label': '256.5742.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.b1.a1', '8.n1.a1', '8.j1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593857
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.g1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.j1.a1', '8.o1.a1', '8.bu1.a1', '8.bw1.a1'], 'contains': ['32.b1.a1', '32.s1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3821, 1013, 4058, 1112, 3820, 980, 4060, 918], 'generators': [28, 8], 'label': '256.5742.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1', '8.o1.a1', '8.j1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64593858
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.m1.a1', '8.o1.a1', '8.br1.a1', '8.bx1.a1'], 'contains': ['32.b1.a1', '32.u1.a1', '32.bj1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3241, 1543, 3187, 2891, 3241, 1512, 3188, 3069], 'generators': [18, 8, 160], 'label': '256.5742.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.b1.a1', '8.o1.a1', '8.m1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593859
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.i1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.m1.a1', '8.n1.a1', '8.bs1.a1', '8.by1.a1'], 'contains': ['32.b1.a1', '32.x1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3896, 2785, 3984, 1607, 3896, 2794, 3987, 1762], 'generators': [30, 8], 'label': '256.5742.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.c1.a1', '8.n1.a1', '8.m1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593860
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': ['64.bi1.a1', '64.bg1.a1', '64.bg1.b1', '64.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.m1.a1', '8.br1.a1', '8.bs1.a1', '8.cd1.a1', '8.cg1.a1', '8.dj1.a1', '8.dn1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8719, 7717, 8829, 6716, 8718, 7743, 8833, 6820], 'generators': [18, 64, 172, 8], 'label': '256.5742.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.h1.a1', '8.i1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '128.522', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64593861
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.j1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.bz1.a1', '8.ca1.a1', '8.cb1.a1', '8.cc1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '32.bk1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2658, 4766, 2915, 4933, 2658, 4783, 2916, 5010], 'generators': [2, 164, 160], 'label': '256.5742.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1'], 'normal_contains': ['32.d1.a1', '32.c1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593878
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.z1.a1', '8.bj1.a1'], 'contains': ['32.a1.a1', '32.bf1.a1', '32.bf1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [693, -1, 1080, -1, 693, -1, 1081, -1], 'generators': [17, 160], 'label': '256.5742.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.z1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593862
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.i1.a1', '8.p1.a1', '8.cd1.a1', '8.ch1.a1'], 'contains': ['32.c1.a1', '32.o1.a1', '32.bl1.a1', '32.ch1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6888, 5630, 3745, 5285, 6888, 5650, 3747, 5367], 'generators': [242, 164, 160, 32], 'label': '256.5742.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.d1.a1', '8.p1.a1', '8.i1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593863
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.k1.a1', '8.p1.a1', '8.ce1.a1', '8.cj1.a1'], 'contains': ['32.c1.a1', '32.r1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5534, 6313, 4203, 6898, 5534, 6334, 4206, 7005], 'generators': [80, 164], 'label': '256.5742.16.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': ['8.e1.a1', '8.p1.a1', '8.k1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.l1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593864
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.k1.a1', '8.q1.a1', '8.cf1.a1', '8.ck1.a1'], 'contains': ['32.c1.a1', '32.v1.a1', '32.bm1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2848, 5243, 3478, 5668, 2848, 5260, 3479, 5756], 'generators': [216, 164, 160], 'label': '256.5742.16.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': ['8.d1.a1', '8.q1.a1', '8.k1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.m1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593865
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.n1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.i1.a1', '8.q1.a1', '8.cg1.a1', '8.ci1.a1'], 'contains': ['32.c1.a1', '32.y1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7334, 5948, 4130, 6099, 7334, 5968, 4133, 6194], 'generators': [122, 164], 'label': '256.5742.16.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': ['8.e1.a1', '8.q1.a1', '8.i1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.n1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593866
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.o1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.r1.a1', '8.s1.a1', '8.cl1.a1', '8.cm1.a1', '8.cn1.a1', '8.co1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1', '32.bn1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2567, 7668, 3091, 7809, 2567, 7694, 3093, 7936], 'generators': [2, 172, 160], 'label': '256.5742.16.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': ['8.a1.a1', '8.r1.a1', '8.s1.a1'], 'normal_contains': ['32.e1.a1', '32.d1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.o1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593867
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.p1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.h1.a1', '8.r1.a1', '8.dj1.a1', '8.dk1.a1'], 'contains': ['32.f1.a1', '32.n1.a1', '32.bv1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3535, 8554, 6715, 9265, 3535, 8583, 6719, 9445], 'generators': [200, 172, 160], 'label': '256.5742.16.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': ['8.f1.a1', '8.r1.a1', '8.h1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.p1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593868
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.q1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.q1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.h1.a1', '8.s1.a1', '8.dn1.a1', '8.dq1.a1'], 'contains': ['32.f1.a1', '32.q1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3755, 9240, 7891, 8438, 3755, 9271, 7896, 8608], 'generators': [64, 172], 'label': '256.5742.16.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': ['8.g1.a1', '8.s1.a1', '8.h1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.q1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593869
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.r1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.l1.a1', '8.s1.a1', '8.dl1.a1', '8.dr1.a1'], 'contains': ['32.f1.a1', '32.t1.a1', '32.bx1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2947, 8111, 3572, 8815, 2946, 8139, 3574, 8988], 'generators': [226, 172, 160], 'label': '256.5742.16.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': ['8.f1.a1', '8.s1.a1', '8.l1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.r1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64593870
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.s1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.s1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.l1.a1', '8.r1.a1', '8.dm1.a1', '8.ds1.a1'], 'contains': ['32.f1.a1', '32.w1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3701, 8943, 4602, 8164, 3700, 8973, 4605, 8297], 'generators': [106, 172], 'label': '256.5742.16.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': ['8.g1.a1', '8.r1.a1', '8.l1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.s1.a1', 'projective_image': '128.522', 'quotient_action_image': '16.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 64593871
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': ['64.bi1.a1', '64.bg1.a1', '64.bg1.b1', '64.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.h1.a1', '8.j1.a1', '8.k1.a1', '8.bt1.a1', '8.bu1.a1', '8.ce1.a1', '8.cf1.a1', '8.dk1.a1', '8.dq1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4425, 7179, 7573, 7706, 4426, 7204, 7537, 7826], 'generators': [16, 64, 172, 8], 'label': '256.5742.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.h1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '128.522', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64593872
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.cy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.t1.a1', '8.x1.a1', '8.bb1.a1', '8.bc1.a1', '8.bd1.a1', '8.be1.a1'], 'contains': ['32.a1.a1', '32.j1.a1', '32.n1.a1', '32.t1.a1', '32.bb1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3627, -1, 3904, -1, 3627, -1, 3906, -1], 'generators': [200, 10, 160], 'label': '256.5742.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.t1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593873
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.u1.a1', '8.bb1.a1', '8.bc1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1'], 'contains': ['32.a1.a1', '32.k1.a1', '32.o1.a1', '32.v1.a1', '32.bc1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3339, -1, 3815, -1, 3339, -1, 3818, -1], 'generators': [92, 10, 160], 'label': '256.5742.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.u1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593874
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.y1.a1', '8.bb1.a1', '8.bd1.a1', '8.bg1.a1', '8.bi1.a1', '8.bl1.a1'], 'contains': ['32.a1.a1', '32.m1.a1', '32.p1.a1', '32.u1.a1', '32.be1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3438, -1, 3667, -1, 3437, -1, 3669, -1], 'generators': [16, 10, 160], 'label': '256.5742.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.v1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593875
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.cv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.t1.a1', '8.x1.a1', '8.bg1.a1', '8.bh1.a1', '8.bl1.a1', '8.bm1.a1'], 'contains': ['32.a1.a1', '32.q1.a1', '32.w1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4909, -1, 6884, -1, 4909, -1, 6888, -1], 'generators': [64, 10], 'label': '256.5742.16.w1.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.w1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593876
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.u1.a1', '8.bd1.a1', '8.be1.a1', '8.bf1.a1', '8.bl1.a1', '8.bm1.a1'], 'contains': ['32.a1.a1', '32.r1.a1', '32.y1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7121, -1, 6400, -1, 7121, -1, 6404, -1], 'generators': [80, 10], 'label': '256.5742.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.x1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593877
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.y1.a1', '8.bc1.a1', '8.be1.a1', '8.bh1.a1', '8.bi1.a1', '8.bm1.a1'], 'contains': ['32.a1.a1', '32.s1.a1', '32.x1.a1', '32.cc1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6428, -1, 4913, -1, 6429, -1, 4916, -1], 'generators': [28, 10, 32], 'label': '256.5742.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.y1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593879
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.h1.a1', '32.i1.a1', '32.l1.a1', '32.bg1.a1', '32.bh1.a1', '32.bk1.a1', '32.bn1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1593, -1, 1953, -1, 1593, -1, 1954, -1], 'generators': [162, 172, 8], 'label': '256.5742.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.ba1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593880
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.h1.a1', '32.m1.a1', '32.bi1.a1', '32.bj1.a1', '32.bo1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1850, -1, 2158, -1, 1850, -1, 2160, -1], 'generators': [16, 162, 8], 'label': '256.5742.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.bb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64593881
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1'], 'contains': ['32.h1.a1', '32.bp1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [257, -1, 744, -1, 257, -1, 745, -1], 'generators': [1, 168], 'label': '256.5742.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.a1', 'old_label': '16.bc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593882
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': ['64.bi1.a1', '64.bg1.a1', '64.bg1.b1', '64.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.i1.a1', '8.j1.a1', '8.l1.a1', '8.bv1.a1', '8.bw1.a1', '8.ch1.a1', '8.ci1.a1', '8.dl1.a1', '8.dm1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7644, 6634, 4918, 6071, 7644, 6656, 5152, 6165], 'generators': [16, 226, 172, 8], 'label': '256.5742.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.i1.a1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '128.522', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64593883
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.i1.a1', '32.k1.a1', '32.bl1.a1', '32.bm1.a1', '32.bq1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1752, -1, 2440, -1, 1751, -1, 2442, -1], 'generators': [216, 170, 164], 'label': '256.5742.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.bd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 64593884
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1'], 'contains': ['32.i1.a1', '32.br1.a1', '32.cd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [980, -1, 1419, -1, 980, -1, 1420, -1], 'generators': [65, 164, 32], 'label': '256.5742.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '16.be1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64593885
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1'], 'contains': ['32.j1.a1', '32.k1.a1', '32.m1.a1', '32.bs1.a1', '32.bu1.a1', '32.bw1.a1', '32.bz1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2490, -1, 2686, -1, 2490, -1, 2688, -1], 'generators': [16, 200, 170], 'label': '256.5742.16.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '16.bf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593886
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.j1.a1', '32.l1.a1', '32.bt1.a1', '32.bv1.a1', '32.bx1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2152, -1, 2515, -1, 2152, -1, 2516, -1], 'generators': [200, 170, 172], 'label': '256.5742.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '16.bg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593887
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1'], 'contains': ['32.l1.a1', '32.by1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1948, -1, 1579, -1, 1948, -1, 1580, -1], 'generators': [81, 12], 'label': '256.5742.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '16.bh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64593888
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.t1.a1', '8.bn1.a1', '8.br1.a1', '8.bs1.a1', '8.bt1.a1', '8.bu1.a1'], 'contains': ['32.b1.a1', '32.n1.a1', '32.q1.a1', '32.ce1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4992, -1, 8514, -1, 4992, -1, 8520, -1], 'generators': [64, 8, 32], 'label': '256.5742.16.bi1.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.bi1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593889
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.u1.a1', '8.bo1.a1', '8.br1.a1', '8.bs1.a1', '8.bv1.a1', '8.bw1.a1'], 'contains': ['32.b1.a1', '32.o1.a1', '32.y1.a1', '32.cf1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8024, -1, 6126, -1, 8024, -1, 6131, -1], 'generators': [242, 8, 32], 'label': '256.5742.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593890
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.u1.a1', '8.bo1.a1', '8.bt1.a1', '8.bu1.a1', '8.bx1.a1', '8.by1.a1'], 'contains': ['32.b1.a1', '32.r1.a1', '32.v1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4064, -1, 5560, -1, 4063, -1, 5563, -1], 'generators': [80, 8], 'label': '256.5742.16.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bk1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593891
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.t1.a1', '8.bn1.a1', '8.bv1.a1', '8.bw1.a1', '8.bx1.a1', '8.by1.a1'], 'contains': ['32.b1.a1', '32.t1.a1', '32.w1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4696, -1, 4365, -1, 4695, -1, 4367, -1], 'generators': [226, 8], 'label': '256.5742.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593892
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.x1.a1', '8.bz1.a1', '8.cd1.a1', '8.ce1.a1', '8.cf1.a1', '8.cg1.a1'], 'contains': ['32.c1.a1', '32.n1.a1', '32.q1.a1', '32.cg1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5618, -1, 8603, -1, 5618, -1, 8608, -1], 'generators': [64, 164, 32], 'label': '256.5742.16.bm1.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.bm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593893
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': ['64.bi1.a1', '64.bg1.a1', '64.bg1.b1', '64.bj1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.k1.a1', '8.l1.a1', '8.m1.a1', '8.bx1.a1', '8.by1.a1', '8.cj1.a1', '8.ck1.a1', '8.dr1.a1', '8.ds1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4129, 6067, 4196, 7262, 4243, 6088, 4199, 7375], 'generators': [18, 226, 172, 8], 'label': '256.5742.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.k1.a1', '8.l1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '128.522', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64593894
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.y1.a1', '8.ca1.a1', '8.ce1.a1', '8.cf1.a1', '8.ch1.a1', '8.ci1.a1'], 'contains': ['32.c1.a1', '32.p1.a1', '32.s1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5383, -1, 5487, -1, 5383, -1, 5490, -1], 'generators': [16, 164], 'label': '256.5742.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593895
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.x1.a1', '8.bz1.a1', '8.ch1.a1', '8.ci1.a1', '8.cj1.a1', '8.ck1.a1'], 'contains': ['32.c1.a1', '32.t1.a1', '32.w1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4771, -1, 4438, -1, 4771, -1, 4440, -1], 'generators': [226, 164], 'label': '256.5742.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bo1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593896
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.y1.a1', '8.ca1.a1', '8.cd1.a1', '8.cg1.a1', '8.cj1.a1', '8.ck1.a1'], 'contains': ['32.c1.a1', '32.u1.a1', '32.x1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5459, -1, 5354, -1, 5459, -1, 5358, -1], 'generators': [18, 164], 'label': '256.5742.16.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593897
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.t1.a1', '8.bz1.a1', '8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.cs1.a1'], 'contains': ['32.d1.a1', '32.n1.a1', '32.w1.a1', '32.ci1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4612, -1, 7511, -1, 4612, -1, 7516, -1], 'generators': [200, 2, 32], 'label': '256.5742.16.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593898
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.u1.a1', '8.cl1.a1', '8.cp1.a1', '8.cq1.a1', '8.ct1.a1', '8.cu1.a1'], 'contains': ['32.d1.a1', '32.o1.a1', '32.r1.a1', '32.cj1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6962, -1, 6804, -1, 6961, -1, 6808, -1], 'generators': [80, 2, 32], 'label': '256.5742.16.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.br1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593899
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.ca1.a1', '8.cm1.a1', '8.cp1.a1', '8.cr1.a1', '8.ct1.a1', '8.cv1.a1'], 'contains': ['32.d1.a1', '32.p1.a1', '32.u1.a1', '32.bo1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4409, -1, 4739, -1, 4409, -1, 4742, -1], 'generators': [16, 2, 160], 'label': '256.5742.16.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bs1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593900
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.t1.a1', '8.bz1.a1', '8.ct1.a1', '8.cu1.a1', '8.cv1.a1', '8.cw1.a1'], 'contains': ['32.d1.a1', '32.q1.a1', '32.t1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4138, -1, 5060, -1, 4138, -1, 5063, -1], 'generators': [64, 2], 'label': '256.5742.16.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bt1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593901
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.ca1.a1', '8.cm1.a1', '8.cq1.a1', '8.cs1.a1', '8.cu1.a1', '8.cw1.a1'], 'contains': ['32.d1.a1', '32.s1.a1', '32.x1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6519, -1, 6957, -1, 6519, -1, 6961, -1], 'generators': [28, 2], 'label': '256.5742.16.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bu1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593902
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.u1.a1', '8.cl1.a1', '8.cr1.a1', '8.cs1.a1', '8.cv1.a1', '8.cw1.a1'], 'contains': ['32.d1.a1', '32.v1.a1', '32.y1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4214, -1, 4826, -1, 4214, -1, 4829, -1], 'generators': [92, 2], 'label': '256.5742.16.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593903
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '8.cb1.a1', '8.cn1.a1'], 'contains': ['32.d1.a1', '32.bp1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1146, -1, 1660, -1, 1146, -1, 1660, -1], 'generators': [1, 160], 'label': '256.5742.16.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '16.bw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593904
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.7540510', 'aut_weyl_index': 2, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1', '4.p1.a1', '4.q1.a1', '4.t1.a1', '4.v1.a1', '4.x1.a1', '4.y1.a1', '4.bb1.a1', '4.bc1.a1', '4.bf1.a1', '4.bh1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6076, 6430, 6366, 6393, 6075, 6451, 6224, 6493], 'generators': [16, 64, 2, 8, 172], 'label': '256.5742.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64593905
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.t1.a1', '8.u1.a1', '8.bb1.a1', '8.bd1.a1', '8.bg1.a1', '8.bl1.a1', '8.br1.a1', '8.bt1.a1', '8.bv1.a1', '8.bx1.a1', '8.cp1.a1', '8.cr1.a1', '8.ct1.a1', '8.cv1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4540, -1, 5446, -1, 4564, -1, 5487, -1], 'generators': [16, 64, 2, 8], 'label': '256.5742.4.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': '128.522', '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': '16.14'}
  • id: 64593906
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.x1.a1', '8.bn1.a1', '8.cx1.a1', '8.cy1.a1', '8.cz1.a1', '8.da1.a1'], 'contains': ['32.e1.a1', '32.n1.a1', '32.w1.a1', '32.ck1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6138, -1, 7599, -1, 6138, -1, 7604, -1], 'generators': [200, 174, 32], 'label': '256.5742.16.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593907
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.bo1.a1', '8.cl1.a1', '8.cx1.a1', '8.cy1.a1', '8.db1.a1', '8.dc1.a1'], 'contains': ['32.e1.a1', '32.o1.a1', '32.v1.a1', '32.bq1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5847, -1, 5140, -1, 5847, -1, 5144, -1], 'generators': [92, 174, 160], 'label': '256.5742.16.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.by1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593908
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.y1.a1', '8.cm1.a1', '8.cx1.a1', '8.cz1.a1', '8.db1.a1', '8.dd1.a1'], 'contains': ['32.e1.a1', '32.p1.a1', '32.x1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6656, -1, 5221, -1, 6656, -1, 5225, -1], 'generators': [16, 174], 'label': '256.5742.16.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593909
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.x1.a1', '8.bn1.a1', '8.db1.a1', '8.dc1.a1', '8.dd1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.q1.a1', '32.t1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5993, -1, 5693, -1, 5992, -1, 5696, -1], 'generators': [64, 174], 'label': '256.5742.16.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ca1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593910
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.bo1.a1', '8.cl1.a1', '8.cz1.a1', '8.da1.a1', '8.dd1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.r1.a1', '32.y1.a1', '32.cl1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8273, -1, 7284, -1, 8273, -1, 7288, -1], 'generators': [80, 174, 32], 'label': '256.5742.16.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593911
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.y1.a1', '8.cm1.a1', '8.cy1.a1', '8.da1.a1', '8.dc1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.s1.a1', '32.u1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6222, -1, 5868, -1, 6221, -1, 5871, -1], 'generators': [28, 174], 'label': '256.5742.16.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593912
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.bp1.a1', '8.co1.a1'], 'contains': ['32.e1.a1', '32.br1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1509, -1, 2033, -1, 1509, -1, 2035, -1], 'generators': [65, 160], 'label': '256.5742.16.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.cd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593913
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.br1.a1', '8.cd1.a1', '8.cp1.a1', '8.cy1.a1', '8.dg1.a1', '8.dj1.a1'], 'contains': ['32.n1.a1', '32.o1.a1', '32.u1.a1', '32.bs1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7417, -1, 7760, -1, 7417, -1, 7765, -1], 'generators': [26, 200, 160], 'label': '256.5742.16.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ce1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593914
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.bs1.a1', '8.cd1.a1', '8.cq1.a1', '8.cx1.a1', '8.df1.a1', '8.dj1.a1'], 'contains': ['32.n1.a1', '32.o1.a1', '32.x1.a1', '32.cm1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8904, -1, 8691, -1, 8904, -1, 8696, -1], 'generators': [30, 200, 32], 'label': '256.5742.16.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593915
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.bn1.a1', '8.bz1.a1', '8.df1.a1', '8.dg1.a1', '8.dh1.a1', '8.di1.a1'], 'contains': ['32.g1.a1', '32.n1.a1', '32.t1.a1', '32.bt1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4514, -1, 5780, -1, 4514, -1, 5784, -1], 'generators': [100, 166, 160], 'label': '256.5742.16.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593916
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.t1.a1', '8.u1.a1', '8.bc1.a1', '8.be1.a1', '8.bh1.a1', '8.bm1.a1', '8.bs1.a1', '8.bu1.a1', '8.bw1.a1', '8.by1.a1', '8.cq1.a1', '8.cs1.a1', '8.cu1.a1', '8.cw1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6479, -1, 7097, -1, 6478, -1, 7101, -1], 'generators': [28, 64, 2, 8], 'label': '256.5742.4.m1.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.m1.a1', 'projective_image': '128.522', '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': '32.51'}
  • id: 64593917
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.df1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.bt1.a1', '8.ce1.a1', '8.cp1.a1', '8.cz1.a1', '8.df1.a1', '8.dk1.a1'], 'contains': ['32.n1.a1', '32.p1.a1', '32.r1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7045, -1, 8140, -1, 7045, -1, 8145, -1], 'generators': [24, 200], 'label': '256.5742.16.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ch1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593918
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ci1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.bt1.a1', '8.cf1.a1', '8.cr1.a1', '8.cx1.a1', '8.dh1.a1', '8.dk1.a1'], 'contains': ['32.n1.a1', '32.p1.a1', '32.v1.a1', '32.bu1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4304, -1, 6620, -1, 4304, -1, 6624, -1], 'generators': [16, 200, 160], 'label': '256.5742.16.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ci1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593919
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.bu1.a1', '8.ce1.a1', '8.cq1.a1', '8.da1.a1', '8.dg1.a1', '8.dk1.a1'], 'contains': ['32.n1.a1', '32.r1.a1', '32.s1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7824, -1, 9119, -1, 7824, -1, 9125, -1], 'generators': [28, 200], 'label': '256.5742.16.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593920
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ck1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.bu1.a1', '8.cf1.a1', '8.cs1.a1', '8.cy1.a1', '8.di1.a1', '8.dk1.a1'], 'contains': ['32.n1.a1', '32.s1.a1', '32.v1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5702, -1, 7681, -1, 5701, -1, 7685, -1], 'generators': [20, 200], 'label': '256.5742.16.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ck1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593921
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.br1.a1', '8.cg1.a1', '8.cr1.a1', '8.da1.a1', '8.di1.a1', '8.dj1.a1'], 'contains': ['32.n1.a1', '32.u1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8183, -1, 8007, -1, 8183, -1, 8012, -1], 'generators': [18, 200], 'label': '256.5742.16.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593922
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.bs1.a1', '8.cg1.a1', '8.cs1.a1', '8.cz1.a1', '8.dh1.a1', '8.dj1.a1'], 'contains': ['32.n1.a1', '32.x1.a1', '32.y1.a1', '32.cn1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9003, -1, 8912, -1, 9003, -1, 8918, -1], 'generators': [22, 200, 32], 'label': '256.5742.16.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593923
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bf1.a1', '8.cl1.a1', '8.dj1.a1', '8.dl1.a1', '8.dm1.a1', '8.dn1.a1'], 'contains': ['32.f1.a1', '32.o1.a1', '32.y1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8364, -1, 6267, -1, 8363, -1, 6272, -1], 'generators': [242, 172], 'label': '256.5742.16.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593924
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.bf1.a1', '8.bo1.a1', '8.df1.a1', '8.dg1.a1', '8.do1.a1', '8.dp1.a1'], 'contains': ['32.g1.a1', '32.o1.a1', '32.r1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7258, -1, 7370, -1, 7258, -1, 7375, -1], 'generators': [80, 166], 'label': '256.5742.16.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.co1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593925
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.bv1.a1', '8.ch1.a1', '8.ct1.a1', '8.db1.a1', '8.df1.a1', '8.dl1.a1'], 'contains': ['32.o1.a1', '32.p1.a1', '32.t1.a1', '32.bw1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6747, -1, 4524, -1, 6746, -1, 4527, -1], 'generators': [16, 226, 160], 'label': '256.5742.16.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593926
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.bv1.a1', '8.ch1.a1', '8.cp1.a1', '8.cx1.a1', '8.dm1.a1', '8.do1.a1'], 'contains': ['32.o1.a1', '32.p1.a1', '32.w1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7694, -1, 7030, -1, 7693, -1, 7034, -1], 'generators': [24, 106], 'label': '256.5742.16.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593927
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2323', 'aut_weyl_index': 8, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.b1.a1', '8.v1.a1', '8.w1.a1', '8.dw1.a1', '8.dw1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [247, -1, 440, -1, 247, -1, 360, -1], 'generators': [1, 16, 160], 'label': '256.5742.4.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.n1.a1', 'projective_image': '128.522', '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': '16.11'}
  • id: 64593928
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.br1.a1', '8.cd1.a1', '8.ct1.a1', '8.dc1.a1', '8.dn1.a1', '8.dp1.a1'], 'contains': ['32.o1.a1', '32.q1.a1', '32.u1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8108, -1, 8213, -1, 8107, -1, 8218, -1], 'generators': [18, 64], 'label': '256.5742.16.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cr1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593929
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.bs1.a1', '8.cd1.a1', '8.cu1.a1', '8.db1.a1', '8.dn1.a1', '8.do1.a1'], 'contains': ['32.o1.a1', '32.q1.a1', '32.x1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8822, -1, 8826, -1, 8821, -1, 8831, -1], 'generators': [22, 64], 'label': '256.5742.16.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cs1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593930
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.bw1.a1', '8.ch1.a1', '8.cu1.a1', '8.dc1.a1', '8.dg1.a1', '8.dl1.a1'], 'contains': ['32.o1.a1', '32.s1.a1', '32.t1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7501, -1, 6474, -1, 7500, -1, 6477, -1], 'generators': [20, 226], 'label': '256.5742.16.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ct1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593931
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.cu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.bw1.a1', '8.ch1.a1', '8.cq1.a1', '8.cy1.a1', '8.dm1.a1', '8.dp1.a1'], 'contains': ['32.o1.a1', '32.s1.a1', '32.w1.a1', '32.co1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8607, -1, 8300, -1, 8607, -1, 8305, -1], 'generators': [28, 106, 32], 'label': '256.5742.16.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cu1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593932
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.bi1.a1', '8.cm1.a1', '8.dk1.a1', '8.dl1.a1', '8.dm1.a1', '8.dq1.a1'], 'contains': ['32.f1.a1', '32.p1.a1', '32.s1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6061, -1, 5288, -1, 6061, -1, 5291, -1], 'generators': [16, 172], 'label': '256.5742.16.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593933
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.bf1.a1', '8.cl1.a1', '8.dk1.a1', '8.dq1.a1', '8.dr1.a1', '8.ds1.a1'], 'contains': ['32.f1.a1', '32.r1.a1', '32.v1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5069, -1, 5627, -1, 5069, -1, 5630, -1], 'generators': [80, 172], 'label': '256.5742.16.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593934
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.bi1.a1', '8.cm1.a1', '8.dj1.a1', '8.dn1.a1', '8.dr1.a1', '8.ds1.a1'], 'contains': ['32.f1.a1', '32.u1.a1', '32.x1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6290, -1, 5420, -1, 6290, -1, 5424, -1], 'generators': [18, 172], 'label': '256.5742.16.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593935
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.bi1.a1', '8.ca1.a1', '8.df1.a1', '8.dh1.a1', '8.do1.a1', '8.dt1.a1'], 'contains': ['32.g1.a1', '32.p1.a1', '32.x1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5315, -1, 5934, -1, 5314, -1, 5938, -1], 'generators': [16, 166], 'label': '256.5742.16.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cy1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593936
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.bn1.a1', '8.bz1.a1', '8.do1.a1', '8.dp1.a1', '8.dt1.a1', '8.du1.a1'], 'contains': ['32.g1.a1', '32.q1.a1', '32.w1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5924, -1, 7835, -1, 5924, -1, 7840, -1], 'generators': [64, 166], 'label': '256.5742.16.cz1.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.cz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593937
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.da1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.bi1.a1', '8.ca1.a1', '8.dg1.a1', '8.di1.a1', '8.dp1.a1', '8.du1.a1'], 'contains': ['32.g1.a1', '32.s1.a1', '32.u1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5253, -1, 6053, -1, 5253, -1, 6056, -1], 'generators': [20, 166], 'label': '256.5742.16.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.da1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.da1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593938
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.c1.a1', '8.v1.a1', '8.w1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [362, -1, 560, -1, 362, -1, 565, -1], 'generators': [1, 28], 'label': '256.5742.4.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.o1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64593939
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.db1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.bf1.a1', '8.bo1.a1', '8.dh1.a1', '8.di1.a1', '8.dt1.a1', '8.du1.a1'], 'contains': ['32.g1.a1', '32.v1.a1', '32.y1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5193, -1, 5994, -1, 5192, -1, 5997, -1], 'generators': [216, 166], 'label': '256.5742.16.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.db1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.db1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593940
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.bq1.a1', '8.cc1.a1'], 'contains': ['32.g1.a1', '32.by1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2088, -1, 1876, -1, 2088, -1, 1877, -1], 'generators': [81, 160], 'label': '256.5742.16.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.dc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593941
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.dd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.bt1.a1', '8.ce1.a1', '8.ct1.a1', '8.dd1.a1', '8.do1.a1', '8.dq1.a1'], 'contains': ['32.p1.a1', '32.q1.a1', '32.r1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7628, -1, 8762, -1, 7627, -1, 8768, -1], 'generators': [16, 64], 'label': '256.5742.16.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593942
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.de1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.de1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.bt1.a1', '8.cf1.a1', '8.cv1.a1', '8.db1.a1', '8.dq1.a1', '8.dt1.a1'], 'contains': ['32.p1.a1', '32.q1.a1', '32.v1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5130, -1, 7096, -1, 5130, -1, 7101, -1], 'generators': [24, 64], 'label': '256.5742.16.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.de1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.de1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593943
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.df1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.bv1.a1', '8.ci1.a1', '8.cv1.a1', '8.dd1.a1', '8.dh1.a1', '8.dl1.a1'], 'contains': ['32.p1.a1', '32.t1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7190, -1, 4658, -1, 7189, -1, 4661, -1], 'generators': [24, 226], 'label': '256.5742.16.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.df1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593944
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.dg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.bv1.a1', '8.ci1.a1', '8.cr1.a1', '8.cz1.a1', '8.dm1.a1', '8.dt1.a1'], 'contains': ['32.p1.a1', '32.w1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7951, -1, 7206, -1, 7951, -1, 7210, -1], 'generators': [16, 106], 'label': '256.5742.16.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593945
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bm1.a1', '8.bu1.a1', '8.ce1.a1', '8.cu1.a1', '8.de1.a1', '8.dp1.a1', '8.dq1.a1'], 'contains': ['32.q1.a1', '32.r1.a1', '32.s1.a1', '32.cp1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8509, -1, 9200, -1, 8509, -1, 9205, -1], 'generators': [20, 64, 32], 'label': '256.5742.16.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593946
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.di1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.di1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.bu1.a1', '8.cf1.a1', '8.cw1.a1', '8.dc1.a1', '8.dq1.a1', '8.du1.a1'], 'contains': ['32.q1.a1', '32.s1.a1', '32.v1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6349, -1, 7944, -1, 6348, -1, 7949, -1], 'generators': [28, 64], 'label': '256.5742.16.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.di1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.di1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593947
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.br1.a1', '8.cg1.a1', '8.cv1.a1', '8.de1.a1', '8.dn1.a1', '8.du1.a1'], 'contains': ['32.q1.a1', '32.u1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8432, -1, 8440, -1, 8432, -1, 8445, -1], 'generators': [26, 64], 'label': '256.5742.16.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593948
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bm1.a1', '8.bs1.a1', '8.cg1.a1', '8.cw1.a1', '8.dd1.a1', '8.dn1.a1', '8.dt1.a1'], 'contains': ['32.q1.a1', '32.x1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9090, -1, 9052, -1, 9090, -1, 9058, -1], 'generators': [30, 64], 'label': '256.5742.16.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dk1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593949
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.x1.a1', '8.y1.a1', '8.bb1.a1', '8.bc1.a1', '8.bg1.a1', '8.bh1.a1', '8.cd1.a1', '8.cf1.a1', '8.ch1.a1', '8.ck1.a1', '8.cx1.a1', '8.cy1.a1', '8.db1.a1', '8.dc1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5825, -1, 5880, -1, 5823, -1, 5859, -1], 'generators': [24, 64, 10, 164], 'label': '256.5742.4.p1.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.p1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593950
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.bx1.a1', '8.cj1.a1', '8.ct1.a1', '8.de1.a1', '8.dg1.a1', '8.dr1.a1'], 'contains': ['32.r1.a1', '32.t1.a1', '32.u1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6830, -1, 6201, -1, 6830, -1, 6205, -1], 'generators': [18, 226], 'label': '256.5742.16.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593951
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.dm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.by1.a1', '8.cj1.a1', '8.cu1.a1', '8.dd1.a1', '8.df1.a1', '8.dr1.a1'], 'contains': ['32.r1.a1', '32.t1.a1', '32.x1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7758, -1, 7153, -1, 7758, -1, 7157, -1], 'generators': [22, 226], 'label': '256.5742.16.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64593952
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.bx1.a1', '8.cj1.a1', '8.cp1.a1', '8.da1.a1', '8.dp1.a1', '8.ds1.a1'], 'contains': ['32.r1.a1', '32.u1.a1', '32.w1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7570, -1, 8381, -1, 7569, -1, 8386, -1], 'generators': [26, 106], 'label': '256.5742.16.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593953
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.do1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bm1.a1', '8.by1.a1', '8.cj1.a1', '8.cq1.a1', '8.cz1.a1', '8.do1.a1', '8.ds1.a1'], 'contains': ['32.r1.a1', '32.w1.a1', '32.x1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8691, -1, 8993, -1, 8691, -1, 8999, -1], 'generators': [30, 106], 'label': '256.5742.16.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.do1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.do1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593954
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.bw1.a1', '8.ci1.a1', '8.cw1.a1', '8.de1.a1', '8.di1.a1', '8.dl1.a1'], 'contains': ['32.s1.a1', '32.t1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7893, -1, 6540, -1, 7892, -1, 6544, -1], 'generators': [28, 226], 'label': '256.5742.16.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593955
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bm1.a1', '8.bw1.a1', '8.ci1.a1', '8.cs1.a1', '8.da1.a1', '8.dm1.a1', '8.du1.a1'], 'contains': ['32.s1.a1', '32.w1.a1', '32.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8752, -1, 8073, -1, 8752, -1, 8079, -1], 'generators': [20, 106], 'label': '256.5742.16.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593956
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.bx1.a1', '8.ck1.a1', '8.cv1.a1', '8.dc1.a1', '8.di1.a1', '8.dr1.a1'], 'contains': ['32.t1.a1', '32.u1.a1', '32.v1.a1', '32.bz1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3980, -1, 4283, -1, 3979, -1, 4286, -1], 'generators': [26, 226, 160], 'label': '256.5742.16.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dr1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593957
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.by1.a1', '8.ck1.a1', '8.cw1.a1', '8.db1.a1', '8.dh1.a1', '8.dr1.a1'], 'contains': ['32.t1.a1', '32.v1.a1', '32.x1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5770, -1, 4993, -1, 5770, -1, 4997, -1], 'generators': [30, 226], 'label': '256.5742.16.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ds1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593958
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.bx1.a1', '8.ck1.a1', '8.cr1.a1', '8.cy1.a1', '8.ds1.a1', '8.du1.a1'], 'contains': ['32.u1.a1', '32.v1.a1', '32.w1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4840, -1, 6334, -1, 4840, -1, 6338, -1], 'generators': [18, 106], 'label': '256.5742.16.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dt1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593959
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.by1.a1', '8.ck1.a1', '8.cs1.a1', '8.cx1.a1', '8.ds1.a1', '8.dt1.a1'], 'contains': ['32.v1.a1', '32.w1.a1', '32.x1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6588, -1, 7437, -1, 6587, -1, 7441, -1], 'generators': [22, 106], 'label': '256.5742.16.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.du1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64593960
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.x1.a1', '8.y1.a1', '8.bd1.a1', '8.be1.a1', '8.bl1.a1', '8.bm1.a1', '8.ce1.a1', '8.cg1.a1', '8.ci1.a1', '8.cj1.a1', '8.cz1.a1', '8.da1.a1', '8.dd1.a1', '8.de1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8132, -1, 7702, -1, 8131, -1, 7687, -1], 'generators': [16, 64, 10, 164], 'label': '256.5742.4.q1.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.q1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593961
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.dv1.a1', '8.dv1.b1'], 'contains': ['32.z1.a1', '32.ba1.a1', '32.bd1.a1', '32.bg1.a1', '32.bh1.a1', '32.bk1.a1', '32.bn1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1229, -1, 898, -1, 1229, -1, 898, -1], 'generators': [2, 172, 8], 'label': '256.5742.16.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.dv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593962
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.dw1.a1', '8.dw1.b1'], 'contains': ['32.z1.a1', '32.be1.a1', '32.bi1.a1', '32.bj1.a1', '32.bo1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1419, -1, 993, -1, 1419, -1, 993, -1], 'generators': [16, 2, 8], 'label': '256.5742.16.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.dw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64593963
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.dx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.dv1.a1', '8.dv1.b1'], 'contains': ['32.z1.a1', '32.bf1.a1', '32.bf1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [438, -1, 510, -1, 437, -1, 510, -1], 'generators': [17, 168], 'label': '256.5742.16.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.dx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593964
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dx2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.dx2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.dv1.b1', '8.dw1.a1'], 'contains': ['32.z1.a1', '32.bf1.a1', '32.cq1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [347, -1, 321, -1, 347, -1, 322, -1], 'generators': [17, 8, 32], 'label': '256.5742.16.dx2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.dx2.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx2.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593965
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dx2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.dx2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.dv1.a1', '8.dw1.b1'], 'contains': ['32.z1.a1', '32.bf1.b1', '32.cq1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [347, -1, 423, -1, 347, -1, 423, -1], 'generators': [177, 8, 32], 'label': '256.5742.16.dx2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.dx2.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx2.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593966
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.dy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '8.dw1.a1', '8.dw1.b1'], 'contains': ['32.z1.a1', '32.bp1.a1', '32.cr1.a1', '32.cr1.a2'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [166, -1, 221, -1, 167, -1, 221, -1], 'generators': [1, 8, 32], 'label': '256.5742.16.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.dy1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593967
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.dx1.a1', '8.dx1.b1'], 'contains': ['32.ba1.a1', '32.bc1.a1', '32.bl1.a1', '32.bm1.a1', '32.bq1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1321, -1, 1740, -1, 1321, -1, 1741, -1], 'generators': [216, 10, 164], 'label': '256.5742.16.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.dz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 64593968
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ea1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dv1.a1', '8.dv1.b1'], 'contains': ['32.ba1.a1', '32.bf1.a1', '32.bf1.b1', '32.cs1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [527, -1, 597, -1, 527, -1, 598, -1], 'generators': [17, 4, 32], 'label': '256.5742.16.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.ea1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593969
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ea2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ea2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dv1.b1', '8.dx1.a1'], 'contains': ['32.ba1.a1', '32.bf1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [618, -1, 817, -1, 617, -1, 818, -1], 'generators': [17, 164], 'label': '256.5742.16.ea2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.ea2.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea2.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593970
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ea2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ea2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dv1.a1', '8.dx1.b1'], 'contains': ['32.ba1.a1', '32.bf1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [618, -1, 1153, -1, 617, -1, 1154, -1], 'generators': [177, 164], 'label': '256.5742.16.ea2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.ea2.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea2.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593971
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '64.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.z1.a1', '8.ba1.a1', '8.dx1.a1', '8.dx1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [605, -1, 896, -1, 605, -1, 897, -1], 'generators': [65, 216, 160], 'label': '256.5742.4.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.r1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.25'}
  • id: 64593972
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.eb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.dx1.a1', '8.dx1.b1'], 'contains': ['32.ba1.a1', '32.br1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1071, -1, 1332, -1, 1070, -1, 1333, -1], 'generators': [65, 4], 'label': '256.5742.16.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.eb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593973
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ec1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1'], 'contains': ['32.bb1.a1', '32.bc1.a1', '32.be1.a1', '32.bs1.a1', '32.bu1.a1', '32.bw1.a1', '32.bz1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2428, -1, 2574, -1, 2429, -1, 2575, -1], 'generators': [16, 200, 10], 'label': '256.5742.16.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '16.ec1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593974
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ed1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.dy1.a1', '8.dy1.b1'], 'contains': ['32.bb1.a1', '32.bd1.a1', '32.bt1.a1', '32.bv1.a1', '32.bx1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2024, -1, 1814, -1, 2024, -1, 1815, -1], 'generators': [200, 10, 172], 'label': '256.5742.16.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '16.ed1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593975
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ee1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ee1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.dv1.a1', '8.dv1.b1'], 'contains': ['32.bd1.a1', '32.bf1.a1', '32.bf1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [762, -1, 678, -1, 762, -1, 678, -1], 'generators': [17, 172], 'label': '256.5742.16.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.ee1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593976
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ee2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ee2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.dv1.b1', '8.dy1.a1'], 'contains': ['32.bd1.a1', '32.bf1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [820, -1, 1216, -1, 820, -1, 1217, -1], 'generators': [17, 12], 'label': '256.5742.16.ee2.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.ee2.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee2.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593977
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ee2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.ee2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.dv1.a1', '8.dy1.b1'], 'contains': ['32.bd1.a1', '32.bf1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [820, -1, 1269, -1, 820, -1, 1270, -1], 'generators': [177, 12], 'label': '256.5742.16.ee2.b1', '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.ee2.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee2.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593978
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '16.ef1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.dy1.a1', '8.dy1.b1'], 'contains': ['32.bd1.a1', '32.by1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1672, -1, 1503, -1, 1672, -1, 1503, -1], 'generators': [81, 172], 'label': '256.5742.16.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '16.ef1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593979
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '32.a1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.t1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1', '16.z1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.p1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3068, 4395, 3554, 4323, 3068, 4410, 3572, 4390], 'generators': [10, 160, 32], 'label': '256.5742.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.a1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '64.c1.a1', '64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '128.522', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593980
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.b1', 'aut_quo_index': 64, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.bi1.a1', '16.bj1.a1', '16.bk1.a1', '16.bl1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.s1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3980, 3315, 4021, 3150, 3979, 3326, 4024, 3293], 'generators': [8, 160, 32], 'label': '256.5742.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.e1.a1', '16.d1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593981
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.c1', 'aut_quo_index': 64, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1', '16.n1.a1', '16.bm1.a1', '16.bn1.a1', '16.bo1.a1', '16.bp1.a1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.t1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5057, 5630, 4167, 5607, 5057, 5650, 4170, 5694], 'generators': [164, 160, 32], 'label': '256.5742.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.b1.a1', '16.j1.a1', '16.d1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1', '16.n1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593982
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '64.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.e1.a1', '8.z1.a1', '8.ba1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [716, -1, 1004, -1, 716, -1, 1004, -1], 'generators': [65, 80], 'label': '256.5742.4.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.s1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 64593983
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.d1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.o1.a1', '16.bq1.a1', '16.br1.a1', '16.bs1.a1', '16.bt1.a1', '16.bu1.a1', '16.bv1.a1', '16.bw1.a1'], 'contains': ['64.b1.a1', '64.f1.a1', '64.u1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3924, 5365, 4826, 5281, 3925, 5384, 4829, 5363], 'generators': [2, 160, 32], 'label': '256.5742.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.a1.a1', '16.o1.a1', '16.j1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593984
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.o1.a1', '16.bx1.a1', '16.by1.a1', '16.bz1.a1', '16.ca1.a1', '16.cb1.a1', '16.cc1.a1', '16.cd1.a1'], 'contains': ['64.b1.a1', '64.g1.a1', '64.v1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5238, 5100, 5065, 4585, 5238, 5118, 5068, 4656], 'generators': [174, 160, 32], 'label': '256.5742.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.b1.a1', '16.o1.a1', '16.e1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593985
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': 64, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.o1.a1', '16.p1.a1', '16.q1.a1', '16.r1.a1', '16.s1.a1', '16.cn1.a1', '16.cv1.a1', '16.cw1.a1', '16.cx1.a1'], 'contains': ['64.b1.a1', '64.j1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4143, 7888, 5223, 7985, 4143, 7915, 5226, 8115], 'generators': [172, 160], 'label': '256.5742.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.c1.a1', '16.o1.a1', '16.d1.a1', '16.p1.a1', '16.r1.a1', '16.s1.a1', '16.q1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593986
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.e1.a1', '16.j1.a1', '16.cg1.a1', '16.co1.a1', '16.cy1.a1', '16.cz1.a1', '16.da1.a1', '16.db1.a1', '16.dc1.a1'], 'contains': ['64.b1.a1', '64.k1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4052, 4748, 5134, 4933, 4052, 4764, 5138, 5010], 'generators': [166, 160], 'label': '256.5742.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.c1.a1', '16.e1.a1', '16.j1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64593987
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.f1.a1', '64.q1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1550, -1, 1850, -1, 1550, -1, 1852, -1], 'generators': [162, 8, 32], 'label': '256.5742.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.h1.a1', 'projective_image': '128.522', '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': '4.2'}
  • id: 64593988
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.ba1.a1', '16.bd1.a1', '16.be1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.g1.a1', '64.r1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1448, -1, 1904, -1, 1448, -1, 1904, -1], 'generators': [170, 164, 32], 'label': '256.5742.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.i1.a1', 'projective_image': '128.522', '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': '4.2'}
  • id: 64593989
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.bf1.a1', '16.bg1.a1'], 'contains': ['64.a1.a1', '64.h1.a1', '64.m1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3016, -1, 3220, -1, 3016, -1, 3222, -1], 'generators': [200, 170], 'label': '256.5742.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.j1.a1', 'projective_image': '128.522', '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': '4.2'}
  • id: 64593990
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.bd1.a1', '16.bf1.a1'], 'contains': ['64.a1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2490, -1, 3040, -1, 2490, -1, 3042, -1], 'generators': [92, 170], 'label': '256.5742.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '32.k1.a1', 'projective_image': '128.522', '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': '4.2'}
  • id: 64593991
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.ba1.a1', '16.bg1.a1', '16.bh1.a1'], 'contains': ['64.a1.a1', '64.j1.a1', '64.k1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2234, -1, 2020, -1, 2234, -1, 2021, -1], 'generators': [170, 172], 'label': '256.5742.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.l1.a1', 'projective_image': '128.522', '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': '4.2'}
  • id: 64593992
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bb1.a1', '16.bf1.a1'], 'contains': ['64.a1.a1', '64.l1.a1', '64.n1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2650, -1, 2972, -1, 2650, -1, 2974, -1], 'generators': [16, 170], 'label': '256.5742.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.m1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64593993
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.a1', '8.bb1.a1', '8.bc1.a1', '8.bd1.a1', '8.be1.a1', '8.bf1.a1', '8.bi1.a1', '8.df1.a1', '8.dg1.a1', '8.dh1.a1', '8.di1.a1', '8.dj1.a1', '8.dk1.a1', '8.dl1.a1', '8.dr1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5935, -1, 6054, -1, 5935, -1, 6015, -1], 'generators': [16, 200, 10, 172], 'label': '256.5742.4.t1.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.t1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64593994
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.t1.a1', '16.bi1.a1', '16.bm1.a1', '16.bq1.a1', '16.bx1.a1', '16.ce1.a1', '16.cf1.a1', '16.cg1.a1', '16.ch1.a1', '16.ci1.a1', '16.cj1.a1', '16.ck1.a1', '16.cl1.a1', '16.cm1.a1'], 'contains': ['64.b1.a1', '64.h1.a1', '64.w1.a1', '64.w2.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5710, -1, 7487, -1, 5709, -1, 7492, -1], 'generators': [200, 160, 32], 'label': '256.5742.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.n1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593995
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.u1.a1', '16.bj1.a1', '16.br1.a1', '16.by1.a1', '16.ce1.a1', '16.cf1.a1', '16.cn1.a1', '16.co1.a1', '16.cp1.a1', '16.cq1.a1', '16.cr1.a1', '16.cs1.a1', '16.ct1.a1', '16.cu1.a1'], 'contains': ['64.b1.a1', '64.i1.a1', '64.x1.a1', '64.x2.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7118, -1, 6267, -1, 7117, -1, 6272, -1], 'generators': [242, 160, 32], 'label': '256.5742.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.o1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593996
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.v1.a1', '16.bn1.a1', '16.bs1.a1', '16.bz1.a1', '16.ch1.a1', '16.ci1.a1', '16.cp1.a1', '16.cq1.a1', '16.cv1.a1', '16.cy1.a1', '16.dd1.a1', '16.de1.a1', '16.df1.a1', '16.dg1.a1'], 'contains': ['64.b1.a1', '64.l1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5450, -1, 5539, -1, 5450, -1, 5543, -1], 'generators': [16, 160], 'label': '256.5742.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.p1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64593997
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.w1.a1', '16.bi1.a1', '16.bm1.a1', '16.bt1.a1', '16.ca1.a1', '16.cr1.a1', '16.cs1.a1', '16.cz1.a1', '16.dd1.a1', '16.de1.a1', '16.dh1.a1', '16.di1.a1', '16.dj1.a1', '16.dk1.a1'], 'contains': ['64.b1.a1', '64.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5924, -1, 7558, -1, 5924, -1, 7562, -1], 'generators': [64, 32], 'label': '256.5742.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.q1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593998
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.x1.a1', '16.bk1.a1', '16.br1.a1', '16.cb1.a1', '16.ch1.a1', '16.cj1.a1', '16.co1.a1', '16.cw1.a1', '16.dd1.a1', '16.dh1.a1', '16.dl1.a1', '16.dm1.a1', '16.dn1.a1', '16.do1.a1'], 'contains': ['64.b1.a1', '64.z1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7044, -1, 7289, -1, 7044, -1, 7293, -1], 'generators': [80, 32], 'label': '256.5742.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64593999
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.y1.a1', '16.bn1.a1', '16.bu1.a1', '16.cc1.a1', '16.cj1.a1', '16.ck1.a1', '16.ct1.a1', '16.cu1.a1', '16.cv1.a1', '16.da1.a1', '16.dh1.a1', '16.di1.a1', '16.dp1.a1', '16.dq1.a1'], 'contains': ['64.b1.a1', '64.ba1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6392, -1, 6560, -1, 6392, -1, 6564, -1], 'generators': [28, 32], 'label': '256.5742.32.s1.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.s1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594000
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.df1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.t1.a1', '16.bl1.a1', '16.bo1.a1', '16.bt1.a1', '16.ca1.a1', '16.cg1.a1', '16.cp1.a1', '16.ct1.a1', '16.df1.a1', '16.dl1.a1', '16.dm1.a1', '16.dp1.a1', '16.dr1.a1', '16.ds1.a1'], 'contains': ['64.b1.a1', '64.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5359, -1, 5363, -1, 5359, -1, 5367, -1], 'generators': [226, 160], 'label': '256.5742.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.t1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594001
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.v1.a1', '16.bp1.a1', '16.bs1.a1', '16.cc1.a1', '16.ce1.a1', '16.cl1.a1', '16.cr1.a1', '16.cx1.a1', '16.da1.a1', '16.dj1.a1', '16.dl1.a1', '16.dn1.a1', '16.dr1.a1', '16.dt1.a1'], 'contains': ['64.b1.a1', '64.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5540, -1, 5868, -1, 5540, -1, 5871, -1], 'generators': [18, 160], 'label': '256.5742.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.u1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594002
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.u1.a1', '16.bk1.a1', '16.bv1.a1', '16.by1.a1', '16.ci1.a1', '16.ck1.a1', '16.cw1.a1', '16.db1.a1', '16.de1.a1', '16.di1.a1', '16.dr1.a1', '16.ds1.a1', '16.dt1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.o1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5130, -1, 5627, -1, 5130, -1, 5630, -1], 'generators': [92, 160], 'label': '256.5742.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.v1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594003
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.w1.a1', '16.bl1.a1', '16.bo1.a1', '16.bq1.a1', '16.bx1.a1', '16.cq1.a1', '16.cu1.a1', '16.cz1.a1', '16.dg1.a1', '16.dn1.a1', '16.do1.a1', '16.dq1.a1', '16.dt1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.bb1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5833, -1, 7201, -1, 5833, -1, 7205, -1], 'generators': [106, 32], 'label': '256.5742.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.w1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594004
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '64.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.f1.a1', '8.bj1.a1', '8.bk1.a1', '8.dy1.a1', '8.dy1.b1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1238, -1, 1099, -1, 1238, -1, 1100, -1], 'generators': [17, 200, 160], 'label': '256.5742.4.u1.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.u1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 64594005
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.y1.a1', '16.bp1.a1', '16.bu1.a1', '16.bz1.a1', '16.cf1.a1', '16.cm1.a1', '16.cs1.a1', '16.cx1.a1', '16.cy1.a1', '16.dk1.a1', '16.dm1.a1', '16.do1.a1', '16.ds1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.bc1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6622, -1, 6472, -1, 6621, -1, 6476, -1], 'generators': [30, 32], 'label': '256.5742.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.x1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594006
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.cz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.x1.a1', '16.bj1.a1', '16.bv1.a1', '16.cb1.a1', '16.cl1.a1', '16.cm1.a1', '16.cn1.a1', '16.db1.a1', '16.df1.a1', '16.dg1.a1', '16.dj1.a1', '16.dk1.a1', '16.dp1.a1', '16.dq1.a1'], 'contains': ['64.b1.a1', '64.bd1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7191, -1, 6338, -1, 7190, -1, 6342, -1], 'generators': [254, 32], 'label': '256.5742.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.y1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594007
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.dv1.a1', '16.dw1.a1', '16.dx1.a1', '16.dx2.a1', '16.dx2.b1', '16.dy1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.f1.a1', '64.be1.a1', '64.be1.a2'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1200, -1, 994, -1, 1199, -1, 994, -1], 'generators': [2, 8, 32], 'label': '256.5742.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.z1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594008
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.dv1.a1', '16.dz1.a1', '16.ea1.a1', '16.ea2.a1', '16.ea2.b1', '16.eb1.a1'], 'contains': ['64.c1.a1', '64.e1.a1', '64.g1.a1', '64.bf1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1345, -1, 1349, -1, 1345, -1, 1349, -1], 'generators': [10, 164, 32], 'label': '256.5742.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.ba1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594009
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.ec1.a1', '16.ed1.a1'], 'contains': ['64.c1.a1', '64.h1.a1', '64.m1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2878, -1, 2718, -1, 2877, -1, 2720, -1], 'generators': [200, 10], 'label': '256.5742.32.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.bb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594010
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.dz1.a1', '16.ec1.a1'], 'contains': ['64.c1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2303, -1, 2526, -1, 2303, -1, 2528, -1], 'generators': [92, 10], 'label': '256.5742.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '32.bc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594011
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.dv1.a1', '16.ed1.a1', '16.ee1.a1', '16.ee2.a1', '16.ee2.b1', '16.ef1.a1'], 'contains': ['64.c1.a1', '64.j1.a1', '64.k1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1623, -1, 1594, -1, 1623, -1, 1595, -1], 'generators': [10, 172], 'label': '256.5742.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594012
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.dw1.a1', '16.ec1.a1'], 'contains': ['64.c1.a1', '64.l1.a1', '64.n1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2559, -1, 2371, -1, 2560, -1, 2373, -1], 'generators': [16, 10], 'label': '256.5742.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.be1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594013
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dv1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.dx1.a1', '16.dx2.a1', '16.ea1.a1', '16.ea2.a1', '16.ee1.a1', '16.ee2.a1'], 'contains': ['64.c1.a1', '64.bg1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [727, -1, 1065, -1, 727, -1, 1064, -1], 'generators': [17, 32], 'label': '256.5742.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594014
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.dx1.a1', '16.dx2.b1', '16.ea1.a1', '16.ea2.b1', '16.ee1.a1', '16.ee2.b1'], 'contains': ['64.c1.a1', '64.bg1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [727, -1, 1152, -1, 727, -1, 1152, -1], 'generators': [177, 32], 'label': '256.5742.32.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bf1.b1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594015
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.g1.a1', '4.u1.a1', '4.w1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1377, 4579, 1325, 5460, 1377, 4595, 1310, 5545], 'generators': [17, 64, 8], 'label': '256.5742.2.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.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '128.522'}
  • id: 64594016
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.g1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1', '8.bi1.a1', '8.bl1.a1', '8.bm1.a1', '8.dm1.a1', '8.dn1.a1', '8.do1.a1', '8.dp1.a1', '8.dq1.a1', '8.ds1.a1', '8.dt1.a1', '8.du1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6743, -1, 7976, -1, 6743, -1, 7798, -1], 'generators': [16, 64, 10, 172], 'label': '256.5742.4.v1.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.v1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594017
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.ba1.a1', '16.dv1.a1'], 'contains': ['64.d1.a1', '64.e1.a1', '64.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1741, -1, 1953, -1, 1741, -1, 1954, -1], 'generators': [172, 8], 'label': '256.5742.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594018
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.ba1.a1', '16.dv1.a1'], 'contains': ['64.d1.a1', '64.g1.a1', '64.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1693, -1, 1801, -1, 1693, -1, 1802, -1], 'generators': [174, 8], 'label': '256.5742.32.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594019
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.bb1.a1', '16.dw1.a1'], 'contains': ['64.d1.a1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2004, -1, 2283, -1, 2004, -1, 2285, -1], 'generators': [16, 8], 'label': '256.5742.32.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '32.bi1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594020
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.bb1.a1', '16.dw1.a1'], 'contains': ['64.d1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2095, -1, 2108, -1, 2095, -1, 2109, -1], 'generators': [18, 8], 'label': '256.5742.32.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '32.bj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594021
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.ba1.a1', '16.dv1.a1'], 'contains': ['64.e1.a1', '64.f1.a1', '64.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1499, -1, 1708, -1, 1499, -1, 1709, -1], 'generators': [2, 164], 'label': '256.5742.32.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bk1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594022
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.bd1.a1', '16.dz1.a1'], 'contains': ['64.e1.a1', '64.i1.a1', '64.bh1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1931, -1, 2623, -1, 1931, -1, 2624, -1], 'generators': [242, 164, 32], 'label': '256.5742.32.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '32.bl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64594023
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.bd1.a1', '16.dz1.a1'], 'contains': ['64.e1.a1', '64.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1810, -1, 2458, -1, 1810, -1, 2460, -1], 'generators': [216, 164], 'label': '256.5742.32.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '32.bm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 64594024
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.ba1.a1', '16.dv1.a1'], 'contains': ['64.f1.a1', '64.g1.a1', '64.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1396, -1, 1754, -1, 1396, -1, 1755, -1], 'generators': [2, 172], 'label': '256.5742.32.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.bn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594025
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bs1.a1', '16.dw1.a1'], 'contains': ['64.f1.a1', '64.l1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2373, -1, 2196, -1, 2373, -1, 2197, -1], 'generators': [16, 2], 'label': '256.5742.32.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '32.bo1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594026
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.dy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.bw1.a1', '16.dy1.a1'], 'contains': ['64.f1.a1', '64.bi1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [455, -1, 924, -1, 454, -1, 924, -1], 'generators': [1, 32], 'label': '256.5742.32.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.w1.a1', 'old_label': '32.bp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594027
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '64.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.g1.a1', '8.bj1.a1', '8.bk1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1377, -1, 1234, -1, 1377, -1, 1234, -1], 'generators': [17, 64], 'label': '256.5742.4.w1.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.w1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': '32.25'}
  • id: 64594028
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.by1.a1', '16.dz1.a1'], 'contains': ['64.g1.a1', '64.i1.a1', '64.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1880, -1, 2572, -1, 1880, -1, 2574, -1], 'generators': [92, 174], 'label': '256.5742.32.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.d1.a1', 'old_label': '32.bq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594029
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cd1.a1', '16.eb1.a1'], 'contains': ['64.g1.a1', '64.bj1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1272, -1, 1419, -1, 1272, -1, 1420, -1], 'generators': [65, 32], 'label': '256.5742.32.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '32.br1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594030
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.ce1.a1', '16.ec1.a1'], 'contains': ['64.h1.a1', '64.i1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3349, -1, 3355, -1, 3349, -1, 3357, -1], 'generators': [26, 200], 'label': '256.5742.32.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.bs1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594031
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cg1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.cg1.a1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.k1.a1', '64.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2947, -1, 2786, -1, 2947, -1, 2787, -1], 'generators': [100, 166], 'label': '256.5742.32.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.bt1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594032
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.ci1.a1', '16.ec1.a1'], 'contains': ['64.h1.a1', '64.l1.a1', '64.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3189, -1, 3287, -1, 3189, -1, 3289, -1], 'generators': [16, 200], 'label': '256.5742.32.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.bu1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594033
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bg1.a1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2720, -1, 2852, -1, 2720, -1, 2854, -1], 'generators': [200, 172], 'label': '256.5742.32.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '32.bv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64594034
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.cp1.a1', '16.ec1.a1'], 'contains': ['64.i1.a1', '64.l1.a1', '64.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3279, -1, 3153, -1, 3280, -1, 3155, -1], 'generators': [16, 226], 'label': '256.5742.32.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.bw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594035
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.bg1.a1', '16.ed1.a1'], 'contains': ['64.j1.a1', '64.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2443, -1, 2672, -1, 2442, -1, 2674, -1], 'generators': [226, 172], 'label': '256.5742.32.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.u1.a1', 'old_label': '32.bx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64594036
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.dc1.a1', '16.ef1.a1'], 'contains': ['64.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2164, -1, 1662, -1, 2164, -1, 1662, -1], 'generators': [81], 'label': '256.5742.32.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bk1.a1', 'old_label': '32.by1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594037
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.dr1.a1', '16.ec1.a1'], 'contains': ['64.m1.a1', '64.n1.a1', '64.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3119, -1, 3086, -1, 3119, -1, 3088, -1], 'generators': [26, 226], 'label': '256.5742.32.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.bz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594038
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.n1.a1', '8.bn1.a1', '8.bo1.a1', '8.bs1.a1', '8.bt1.a1', '8.bv1.a1', '8.by1.a1', '8.cx1.a1', '8.cz1.a1', '8.db1.a1', '8.dd1.a1', '8.df1.a1', '8.dh1.a1', '8.do1.a1', '8.dt1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6572, -1, 6653, -1, 6571, -1, 6477, -1], 'generators': [16, 64, 174, 8], 'label': '256.5742.4.x1.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.x1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594039
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1'], 'contains': ['64.p1.a1', '64.q1.a1', '64.s1.a1', '64.u1.a1', '64.be1.a1', '64.be1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T9228', 'count': 8, 'diagramx': [2771, -1, 2903, -1, 2771, -1, 2904, -1], 'generators': [2, 8, 160], 'label': '256.5742.32.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '32.ca1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594040
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1'], 'contains': ['64.p1.a1', '64.r1.a1', '64.t1.a1', '64.v1.a1', '64.bf1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T9267', 'count': 8, 'diagramx': [2827, -1, 3404, -1, 2826, -1, 3406, -1], 'generators': [10, 164, 160], 'label': '256.5742.32.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.y1.a1', 'old_label': '32.cb1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594041
    {'ambient': '256.5742', 'aut_centralizer_order': 64, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1'], 'contains': ['64.p1.a1', '64.ba1.a1', '64.bc1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8151', 'count': 8, 'diagramx': [6531, -1, 5452, -1, 6531, -1, 5455, -1], 'generators': [28, 10], 'label': '256.5742.32.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bi1.a1', 'old_label': '32.cc1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594043
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1'], 'contains': ['64.s1.a1', '64.w1.a1', '64.y1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8494', 'count': 8, 'diagramx': [5658, -1, 7847, -1, 5658, -1, 7851, -1], 'generators': [64, 8], 'label': '256.5742.32.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bt1.a1', 'old_label': '32.ce1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594044
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1'], 'contains': ['64.s1.a1', '64.x1.a1', '64.bd1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8495', 'count': 8, 'diagramx': [7537, -1, 6149, -1, 7537, -1, 6152, -1], 'generators': [242, 8], 'label': '256.5742.32.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bv1.a1', 'old_label': '32.cf1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594045
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1'], 'contains': ['64.t1.a1', '64.w2.a1', '64.y1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8496', 'count': 8, 'diagramx': [5610, -1, 7893, -1, 5610, -1, 7898, -1], 'generators': [64, 164], 'label': '256.5742.32.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cf1.a1', 'old_label': '32.cg1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594046
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.ch1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1'], 'contains': ['64.t1.a1', '64.x1.a1', '64.x2.a1', '64.bh1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T9305', 'count': 8, 'diagramx': [6695, -1, 5293, -1, 6695, -1, 5296, -1], 'generators': [242, 164, 160], 'label': '256.5742.32.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ch1.a1', 'old_label': '32.ch1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594047
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1'], 'contains': ['64.u1.a1', '64.w2.a1', '64.bb1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8790', 'count': 8, 'diagramx': [5289, -1, 7385, -1, 5289, -1, 7391, -1], 'generators': [200, 2], 'label': '256.5742.32.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cr1.a1', 'old_label': '32.ci1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594048
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.br1.a1'], 'contains': ['64.u1.a1', '64.x2.a1', '64.z1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8763', 'count': 8, 'diagramx': [6462, -1, 6404, -1, 6461, -1, 6409, -1], 'generators': [80, 2], 'label': '256.5742.32.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ct1.a1', 'old_label': '32.cj1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594049
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.o1.a1', '8.bn1.a1', '8.bo1.a1', '8.br1.a1', '8.bu1.a1', '8.bw1.a1', '8.bx1.a1', '8.cy1.a1', '8.da1.a1', '8.dc1.a1', '8.de1.a1', '8.dg1.a1', '8.di1.a1', '8.dp1.a1', '8.du1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6217, -1, 6877, -1, 6216, -1, 6737, -1], 'generators': [28, 64, 174, 8], 'label': '256.5742.4.y1.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.y1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594050
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1'], 'contains': ['64.v1.a1', '64.w1.a1', '64.bb1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8764', 'count': 8, 'diagramx': [5993, -1, 7433, -1, 5993, -1, 7438, -1], 'generators': [200, 174], 'label': '256.5742.32.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cz1.a1', 'old_label': '32.ck1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594051
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cb1.a1'], 'contains': ['64.v1.a1', '64.z1.a1', '64.bd1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T8572', 'count': 8, 'diagramx': [7281, -1, 6648, -1, 7281, -1, 6652, -1], 'generators': [80, 174], 'label': '256.5742.32.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dd1.a1', 'old_label': '32.cl1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594052
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cf1.a1'], 'contains': ['64.w1.a1', '64.x2.a1', '64.bc1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T6606', 'count': 8, 'diagramx': [7398, -1, 7712, -1, 7398, -1, 7717, -1], 'generators': [30, 200], 'label': '256.5742.32.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.df1.a1', 'old_label': '32.cm1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594053
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cm1.a1'], 'contains': ['64.w2.a1', '64.bc1.a1', '64.bd1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T6603', 'count': 8, 'diagramx': [7607, -1, 7779, -1, 7607, -1, 7784, -1], 'generators': [22, 200], 'label': '256.5742.32.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dh1.a1', 'old_label': '32.cn1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594054
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.cu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cu1.a1'], 'contains': ['64.x1.a1', '64.ba1.a1', '64.bb1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T6604', 'count': 8, 'diagramx': [7468, -1, 7645, -1, 7468, -1, 7650, -1], 'generators': [28, 106], 'label': '256.5742.32.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dm1.a1', 'old_label': '32.co1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594055
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dh1.a1'], 'contains': ['64.y1.a1', '64.z1.a1', '64.ba1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T6591', 'count': 8, 'diagramx': [7350, -1, 7939, -1, 7350, -1, 7944, -1], 'generators': [20, 64], 'label': '256.5742.32.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dq1.a1', 'old_label': '32.cp1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64594056
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.dx2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx2.a1'], 'contains': ['64.be1.a1', '64.bg1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T7341', 'count': 8, 'diagramx': [545, -1, 661, -1, 545, -1, 660, -1], 'generators': [17, 8], 'label': '256.5742.32.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dw1.a1', 'old_label': '32.cq1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594057
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.dx2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx2.b1'], 'contains': ['64.be1.a2', '64.bg1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T7341', 'count': 8, 'diagramx': [545, -1, 748, -1, 545, -1, 748, -1], 'generators': [177, 8], 'label': '256.5742.32.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dw1.b1', 'old_label': '32.cq1.b1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594058
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.dy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1'], 'contains': ['64.be1.a2', '64.bi1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T7359', 'count': 8, 'diagramx': [364, -1, 573, -1, 364, -1, 572, -1], 'generators': [1, 8], 'label': '256.5742.32.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dw1.a1', 'old_label': '32.cr1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594059
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.dy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1'], 'contains': ['64.be1.a1', '64.bi1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T7359', 'count': 8, 'diagramx': [364, -1, 485, -1, 364, -1, 485, -1], 'generators': [1, 40], 'label': '256.5742.32.cr1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dw1.b1', 'old_label': '32.cr1.a2', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594060
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['8.n1.a1', '8.bp1.a1', '8.bq1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2024, -1, 1974, -1, 2024, -1, 1975, -1], 'generators': [65, 16], 'label': '256.5742.4.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '4.z1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594061
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '32.cs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.ea1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ea1.a1'], 'contains': ['64.bf1.a1', '64.bg1.a1', '64.bg1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T7430', 'count': 16, 'diagramx': [636, -1, 836, -1, 636, -1, 836, -1], 'generators': [17, 4], 'label': '256.5742.32.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.ea1.a1', 'old_label': '32.cs1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594062
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '64.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.h1.a1', '32.i1.a1', '32.j1.a1', '32.k1.a1', '32.l1.a1', '32.m1.a1'], 'contains': ['128.a1.a1', '128.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2285, 4395, 2240, 4323, 2285, 4410, 2241, 4390], 'generators': [170, 32], 'label': '256.5742.64.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.6', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594081
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.ca1.a1', '32.ce1.a1', '32.cf1.a1'], 'contains': ['128.c1.a1', '128.e1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5250, -1, 4414, -1, 5322, -1, 4625, -1], 'generators': [8, 160], 'label': '256.5742.64.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.s1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594063
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '64.b1', 'aut_quo_index': 768, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.n1.a1', '32.o1.a1', '32.p1.a1', '32.q1.a1', '32.r1.a1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.v1.a1', '32.w1.a1', '32.x1.a1', '32.y1.a1'], 'contains': ['128.a1.a1', '128.c1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5450, 5013, 5627, 4892, 5450, 5030, 5630, 4964], 'generators': [160, 32], 'label': '256.5742.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.e1.a1', '32.d1.a1', '32.c1.a1', '32.b1.a1', '32.g1.a1', '32.f1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594064
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '64.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.z1.a1', '32.ba1.a1', '32.bb1.a1', '32.bc1.a1', '32.bd1.a1', '32.be1.a1', '32.bf1.a1', '32.bf1.b1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1752, 4660, 1807, 4585, 1751, 4676, 1808, 4656], 'generators': [10, 32], 'label': '256.5742.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594065
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.h1.a1', '32.z1.a1', '32.bg1.a1', '32.bh1.a1', '32.bi1.a1', '32.bj1.a1'], 'contains': ['128.a1.a1', '128.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1962, -1, 2034, -1, 1962, -1, 2036, -1], 'generators': [8, 32], 'label': '256.5742.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.522', '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': '2.1'}
  • id: 64594066
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.i1.a1', '32.ba1.a1', '32.bg1.a1', '32.bk1.a1', '32.bl1.a1', '32.bm1.a1'], 'contains': ['128.a1.a1', '128.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1810, -1, 2140, -1, 1810, -1, 2141, -1], 'generators': [164, 32], 'label': '256.5742.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594067
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.h1.a1', '32.z1.a1', '32.bk1.a1', '32.bn1.a1', '32.bo1.a1', '32.bp1.a1'], 'contains': ['128.a1.a1', '128.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1640, -1, 1754, -1, 1640, -1, 1755, -1], 'generators': [2, 32], 'label': '256.5742.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594068
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.i1.a1', '32.ba1.a1', '32.bh1.a1', '32.bn1.a1', '32.bq1.a1', '32.br1.a1'], 'contains': ['128.a1.a1', '128.h1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1695, -1, 1882, -1, 1695, -1, 1883, -1], 'generators': [174, 32], 'label': '256.5742.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594069
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.n1.a1', '32.bb1.a1', '32.bs1.a1', '32.bt1.a1', '32.bu1.a1', '32.bv1.a1'], 'contains': ['128.a1.a1', '128.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3012, -1, 3220, -1, 3008, -1, 3222, -1], 'generators': [200, 32], 'label': '256.5742.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594070
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.o1.a1', '32.bc1.a1', '32.bl1.a1', '32.bq1.a1', '32.bs1.a1', '32.bw1.a1'], 'contains': ['128.a1.a1', '128.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2490, -1, 2667, -1, 2490, -1, 2805, -1], 'generators': [242, 32], 'label': '256.5742.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '64.i1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594071
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['8.o1.a1', '8.bp1.a1', '8.bq1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1892, -1, 2101, -1, 1892, -1, 2103, -1], 'generators': [65, 28], 'label': '256.5742.4.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '4.ba1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594072
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.l1.a1', '32.bd1.a1', '32.bg1.a1', '32.bn1.a1', '32.bv1.a1', '32.bx1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2234, -1, 2190, -1, 2234, -1, 2191, -1], 'generators': [172], 'label': '256.5742.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.j1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594073
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.l1.a1', '32.bd1.a1', '32.bh1.a1', '32.bk1.a1', '32.bt1.a1', '32.by1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2175, -1, 1985, -1, 2175, -1, 1986, -1], 'generators': [166], 'label': '256.5742.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.k1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594074
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.p1.a1', '32.be1.a1', '32.bi1.a1', '32.bo1.a1', '32.bu1.a1', '32.bw1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2581, -1, 2499, -1, 2570, -1, 2587, -1], 'generators': [16], 'label': '256.5742.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.l1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594075
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.df1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.t1.a1', '32.bb1.a1', '32.bt1.a1', '32.bw1.a1', '32.bx1.a1', '32.bz1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2956, -1, 2936, -1, 2953, -1, 2938, -1], 'generators': [226], 'label': '256.5742.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.m1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594076
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.u1.a1', '32.be1.a1', '32.bj1.a1', '32.bo1.a1', '32.bs1.a1', '32.bz1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2640, -1, 2398, -1, 2629, -1, 2435, -1], 'generators': [18], 'label': '256.5742.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.n1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594077
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.cf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.v1.a1', '32.bc1.a1', '32.bm1.a1', '32.bq1.a1', '32.bu1.a1', '32.bz1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2387, -1, 2587, -1, 2388, -1, 2740, -1], 'generators': [92], 'label': '256.5742.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '64.o1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594078
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.ca1.a1', '32.cb1.a1', '32.cc1.a1'], 'contains': ['128.b1.a1', '128.c1.a1', '128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2827, -1, 3404, -1, 2826, -1, 3406, -1], 'generators': [10, 160], 'label': '256.5742.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '64.p1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594079
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.ca1.a1'], 'contains': ['128.b1.a1', '128.e1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1907, -1, 2087, -1, 1907, -1, 2089, -1], 'generators': [162, 8], 'label': '256.5742.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '64.q1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594080
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.cb1.a1', '32.cd1.a1'], 'contains': ['128.b1.a1', '128.f1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1586, -1, 1935, -1, 1585, -1, 1936, -1], 'generators': [170, 164], 'label': '256.5742.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '64.r1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594082
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.p1.a1', '8.bz1.a1', '8.ca1.a1', '8.cd1.a1', '8.ce1.a1', '8.ch1.a1', '8.cj1.a1', '8.cp1.a1', '8.cq1.a1', '8.ct1.a1', '8.cu1.a1', '8.df1.a1', '8.dg1.a1', '8.do1.a1', '8.dp1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7811, -1, 8065, -1, 7811, -1, 7887, -1], 'generators': [16, 64, 2, 164], 'label': '256.5742.4.bb1.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.bb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594083
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.cb1.a1', '32.cg1.a1', '32.ch1.a1'], 'contains': ['128.c1.a1', '128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5126, -1, 5189, -1, 5122, -1, 5193, -1], 'generators': [164, 160], 'label': '256.5742.64.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '64.t1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594084
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.ca1.a1', '32.ci1.a1', '32.cj1.a1'], 'contains': ['128.c1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4429, -1, 4929, -1, 4425, -1, 5036, -1], 'generators': [2, 160], 'label': '256.5742.64.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '64.u1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594085
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.cb1.a1', '32.ck1.a1', '32.cl1.a1'], 'contains': ['128.c1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5528, -1, 5408, -1, 5528, -1, 5464, -1], 'generators': [174, 160], 'label': '256.5742.64.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1.a1', 'old_label': '64.v1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594086
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '32.ce1.a1', '32.ck1.a1', '32.cm1.a1'], 'contains': ['128.c1.a1', '128.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5712, -1, 7435, -1, 5711, -1, 7439, -1], 'generators': [200, 128], 'label': '256.5742.64.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '64.w1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594087
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.w2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '32.cg1.a1', '32.ci1.a1', '32.cn1.a1'], 'contains': ['128.c1.a1', '128.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5609, -1, 7487, -1, 5608, -1, 7492, -1], 'generators': [200, 160], 'label': '256.5742.64.w2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bc1.a1', 'old_label': '64.w2.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594088
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.cf1.a1', '32.ch1.a1', '32.co1.a1'], 'contains': ['128.c1.a1', '128.j1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6906, -1, 6171, -1, 6905, -1, 6174, -1], 'generators': [242, 128], 'label': '256.5742.64.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.x1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594089
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.x2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.ch1.a1', '32.cj1.a1', '32.cm1.a1'], 'contains': ['128.c1.a1', '128.j1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6465, -1, 6267, -1, 6465, -1, 6272, -1], 'generators': [242, 160], 'label': '256.5742.64.x2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '64.x2.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594090
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1.a1', '32.ce1.a1', '32.cg1.a1', '32.cp1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5660, -1, 7847, -1, 5660, -1, 7851, -1], 'generators': [64], 'label': '256.5742.64.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '64.y1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594091
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.a1', '32.cj1.a1', '32.cl1.a1', '32.cp1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6522, -1, 6648, -1, 6520, -1, 6652, -1], 'generators': [80], 'label': '256.5742.64.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bh1.a1', 'old_label': '64.z1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594092
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.cc1.a1', '32.co1.a1', '32.cp1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6571, -1, 6560, -1, 6568, -1, 6564, -1], 'generators': [28], 'label': '256.5742.64.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '64.ba1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594093
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '4.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.q1.a1', '8.bz1.a1', '8.ca1.a1', '8.cf1.a1', '8.cg1.a1', '8.ci1.a1', '8.ck1.a1', '8.cr1.a1', '8.cs1.a1', '8.cv1.a1', '8.cw1.a1', '8.dh1.a1', '8.di1.a1', '8.dt1.a1', '8.du1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5303, -1, 6418, -1, 5303, -1, 6305, -1], 'generators': [24, 64, 2, 164], 'label': '256.5742.4.bc1.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.bc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594094
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.w1.a1', '32.ci1.a1', '32.ck1.a1', '32.co1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5833, -1, 7384, -1, 5833, -1, 7389, -1], 'generators': [106], 'label': '256.5742.64.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf1.a1', 'old_label': '64.bb1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594095
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.a1', '32.cc1.a1', '32.cm1.a1', '32.cn1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6622, -1, 6472, -1, 6621, -1, 6476, -1], 'generators': [30], 'label': '256.5742.64.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.bc1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594096
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.cz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.y1.a1', '32.cf1.a1', '32.cl1.a1', '32.cn1.a1'], 'contains': ['128.c1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7281, -1, 6338, -1, 7281, -1, 6342, -1], 'generators': [254], 'label': '256.5742.64.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '64.bd1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64594097
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.z1.a1', '32.ca1.a1', '32.cq1.a1', '32.cr1.a2'], 'contains': ['128.d1.a1', '128.e1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1327, -1, 1103, -1, 1325, -1, 1103, -1], 'generators': [34, 8], 'label': '256.5742.64.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '64.be1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594098
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.z1.a1', '32.ca1.a1', '32.cq1.b1', '32.cr1.a1'], 'contains': ['128.d1.a1', '128.e1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1327, -1, 1504, -1, 1325, -1, 1504, -1], 'generators': [2, 8], 'label': '256.5742.64.be1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '64.be1.a2', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594099
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '64.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ba1.a1', '32.cb1.a1', '32.cs1.a1'], 'contains': ['128.d1.a1', '128.f1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1530, -1, 1556, -1, 1530, -1, 1557, -1], 'generators': [10, 164], 'label': '256.5742.64.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1.a1', 'old_label': '64.bf1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594100
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dv1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bf1.a1', '32.cq1.a1', '32.cs1.a1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [681, -1, 945, -1, 682, -1, 944, -1], 'generators': [17], 'label': '256.5742.64.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dv1.b1', 'old_label': '64.bg1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594101
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bf1.b1', '32.cq1.b1', '32.cs1.a1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [681, -1, 1152, -1, 682, -1, 1152, -1], 'generators': [177], 'label': '256.5742.64.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dv1.a1', 'old_label': '64.bg1.b1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594102
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bl1.a1', '32.ch1.a1'], 'contains': ['128.f1.a1', '128.j1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2893, -1, 2720, -1, 2886, -1, 2858, -1], 'generators': [242, 164], 'label': '256.5742.64.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1.a1', 'old_label': '64.bh1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594103
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '16.dy1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bp1.a1', '32.cr1.a1', '32.cr1.a2'], 'contains': ['128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [455, -1, 790, -1, 454, -1, 789, -1], 'generators': [1], 'label': '256.5742.64.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.dy1.a1', 'old_label': '64.bi1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594104
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.p1.a1', '8.cb1.a1', '8.cc1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1649, -1, 1738, -1, 1649, -1, 1740, -1], 'generators': [1, 80], 'label': '256.5742.4.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.bd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64594105
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '64.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.br1.a1', '32.cd1.a1'], 'contains': ['128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1378, -1, 1605, -1, 1376, -1, 1607, -1], 'generators': [65], 'label': '256.5742.64.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.bj1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594106
    {'ambient': '256.5742', 'aut_centralizer_order': 1024, 'aut_label': '128.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.h1.a1', '64.i1.a1', '64.j1.a1', '64.k1.a1', '64.l1.a1', '64.m1.a1', '64.n1.a1', '64.o1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2259, 4660, 2236, 4585, 2259, 4676, 2238, 4656], 'generators': [32], 'label': '256.5742.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.c1.a1', '64.b1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.522', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.522', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594107
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.p1.a1', '64.q1.a1', '64.r1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1984, -1, 2187, -1, 1983, -1, 2188, -1], 'generators': [170], 'label': '256.5742.128.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '128.b1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594108
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.p1.a1', '64.s1.a1', '64.t1.a1', '64.u1.a1', '64.v1.a1', '64.w1.a1', '64.w2.a1', '64.x1.a1', '64.x2.a1', '64.y1.a1', '64.z1.a1', '64.ba1.a1', '64.bb1.a1', '64.bc1.a1', '64.bd1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5660, -1, 6267, -1, 5660, -1, 6272, -1], 'generators': [160], 'label': '256.5742.128.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '128.c1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594109
    {'ambient': '256.5742', 'aut_centralizer_order': 512, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.p1.a1', '64.be1.a1', '64.be1.a2', '64.bf1.a1', '64.bg1.a1', '64.bg1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1559, -1, 1530, -1, 1560, -1, 1531, -1], 'generators': [10], 'label': '256.5742.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '128.d1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594110
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '64.q1.a1', '64.s1.a1', '64.be1.a1', '64.be1.a2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1935, -1, 1961, -1, 1934, -1, 1963, -1], 'generators': [8], 'label': '256.5742.128.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '128.e1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594111
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.r1.a1', '64.t1.a1', '64.bf1.a1', '64.bh1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1837, -1, 2140, -1, 1862, -1, 2141, -1], 'generators': [164], 'label': '256.5742.128.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '128.f1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594112
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.f1.a1', '64.q1.a1', '64.u1.a1', '64.be1.a1', '64.be1.a2', '64.bi1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1642, -1, 1754, -1, 1642, -1, 1755, -1], 'generators': [2], 'label': '256.5742.128.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '128.g1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594113
    {'ambient': '256.5742', 'aut_centralizer_order': 256, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.g1.a1', '64.r1.a1', '64.v1.a1', '64.bf1.a1', '64.bj1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1694, -1, 2008, -1, 1693, -1, 2009, -1], 'generators': [174], 'label': '256.5742.128.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '128.h1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594114
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.dh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.w1.a1', '64.w2.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3012, -1, 6874, -1, 3008, -1, 6875, -1], 'generators': [200], 'label': '256.5742.128.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dh1.a1', 'old_label': '128.i1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594115
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.q1.a1', '8.cb1.a1', '8.cc1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1531, -1, 1626, -1, 1531, -1, 1626, -1], 'generators': [1, 216], 'label': '256.5742.4.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.be1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64594116
    {'ambient': '256.5742', 'aut_centralizer_order': 128, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.x1.a1', '64.x2.a1', '64.bh1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3059, -1, 2720, -1, 3056, -1, 2858, -1], 'generators': [242], 'label': '256.5742.128.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ch1.a1', 'old_label': '128.j1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594117
    {'ambient': '256.5742', 'aut_centralizer_order': None, 'aut_label': '256.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': ['128.a1.a1', '128.b1.a1', '128.c1.a1', '128.d1.a1', '128.e1.a1', '128.f1.a1', '128.g1.a1', '128.h1.a1', '128.i1.a1', '128.j1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1960, 4660, 2163, 4585, 1959, 4676, 2165, 4656], 'generators': [], 'label': '256.5742.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.5742', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64594118
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.f1.a1', '4.bg1.a1', '4.bi1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1107, 5686, 2153, 4463, 1106, 5705, 2154, 4533], 'generators': [1, 64, 8], 'label': '256.5742.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '128.522'}
  • id: 64594119
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '4.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.r1.a1', '8.cl1.a1', '8.cm1.a1', '8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.cs1.a1', '8.cx1.a1', '8.cy1.a1', '8.cz1.a1', '8.da1.a1', '8.dj1.a1', '8.dk1.a1', '8.dm1.a1', '8.ds1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6657, -1, 7327, -1, 6657, -1, 7330, -1], 'generators': [16, 200, 2, 172], 'label': '256.5742.4.bf1.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.bf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594120
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.r1.a1', '8.cn1.a1', '8.co1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1149, -1, 2295, -1, 1149, -1, 2296, -1], 'generators': [1, 200], 'label': '256.5742.4.bg1.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.bg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64594121
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '4.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56092', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.s1.a1', '8.cl1.a1', '8.cm1.a1', '8.ct1.a1', '8.cu1.a1', '8.cv1.a1', '8.cw1.a1', '8.db1.a1', '8.dc1.a1', '8.dd1.a1', '8.de1.a1', '8.dl1.a1', '8.dn1.a1', '8.dq1.a1', '8.dr1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6382, -1, 6212, -1, 6382, -1, 6144, -1], 'generators': [16, 64, 2, 172], 'label': '256.5742.4.bh1.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.bh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594122
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.s1.a1', '8.cn1.a1', '8.co1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1062, -1, 2212, -1, 1063, -1, 2213, -1], 'generators': [1, 64], 'label': '256.5742.4.bi1.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.bi1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '64.90'}
  • id: 64594123
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.j1.a1', '16.o1.a1', '16.ba1.a1', '16.dv1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1540, 3907, 1675, 3860, 1540, 3920, 1676, 3920], 'generators': [2, 172, 8, 160], 'label': '256.5742.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1', '4.e1.a1', '4.g1.a1'], 'normal_contains': ['16.b1.a1', '16.a1.a1', '16.c1.a1', '16.o1.a1', '16.e1.a1', '16.j1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64594124
    {'ambient': '256.5742', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.h1.a1', '16.v1.a1', '16.bb1.a1', '16.bs1.a1', '16.dw1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1722, 1475, 1995, 2090, 1721, 1480, 1997, 2122], 'generators': [16, 2, 8, 160], 'label': '256.5742.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '128.522', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64594125
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.m1.a1', '4.o1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.i1.a1', '16.y1.a1', '16.bu1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3325, 915, 2701, 271, 3325, 918, 2703, 276], 'generators': [28, 2, 8], 'label': '256.5742.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64594126
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.p1.a1', '4.r1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.m1.a1', '16.u1.a1', '16.bd1.a1', '16.by1.a1', '16.dz1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1827, 4418, 2098, 4364, 1827, 4433, 2099, 4432], 'generators': [216, 10, 164, 160], 'label': '256.5742.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.k1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.22'}
  • id: 64594127
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.q1.a1', '4.s1.a1'], 'contains': ['16.b1.a1', '16.l1.a1', '16.n1.a1', '16.x1.a1', '16.cb1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5718, 5618, 3373, 6105, 5717, 5637, 3375, 6201], 'generators': [80, 10, 164], 'label': '256.5742.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.l1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64594128
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.t1.a1', '4.u1.a1'], 'contains': ['16.c1.a1', '16.p1.a1', '16.r1.a1', '16.t1.a1', '16.bg1.a1', '16.cg1.a1', '16.ed1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1935, 8554, 2203, 9314, 1936, 8583, 2204, 9458], 'generators': [200, 10, 172, 160], 'label': '256.5742.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '16.p1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 64594129
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.r1.a1', '4.s1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [834, 4111, 1114, 4997, 847, 4125, 1075, 5075], 'generators': [65, 80, 8], 'label': '256.5742.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '128.522', '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': '128.522'}
  • id: 64594130
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.c1.a1', '16.q1.a1', '16.s1.a1', '16.w1.a1', '16.cz1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2368, 9709, 4897, 8173, 2368, 9742, 4900, 8300], 'generators': [64, 10, 172], 'label': '256.5742.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '16.s1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '128.522', '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': '32.22'}
  • id: 64594131
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.h1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.d1.a1', '16.p1.a1', '16.q1.a1', '16.bi1.a1', '16.bm1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3232, 8134, 8794, 8605, 3231, 8162, 8800, 8738], 'generators': [64, 172, 8], 'label': '256.5742.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'normal_contains': ['16.d1.a1', '16.p1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594132
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.n1.a1', '16.bj1.a1', '16.cn1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8364, 7406, 3892, 6684, 8363, 7431, 3894, 6788], 'generators': [242, 172, 8], 'label': '256.5742.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'normal_contains': ['16.d1.a1', '16.k1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64594133
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.j1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1', '16.bn1.a1', '16.cv1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2890, 2691, 3012, 2659, 2890, 2700, 3014, 2700], 'generators': [16, 172, 8], 'label': '256.5742.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.j1.a1'], 'normal_contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64594134
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.k1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '16.m1.a1', '16.bk1.a1', '16.cw1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2758, 6804, 3140, 7279, 2758, 6828, 3142, 7391], 'generators': [80, 172, 8], 'label': '256.5742.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1', '4.i1.a1', '4.k1.a1'], 'normal_contains': ['16.d1.a1', '16.l1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594169
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.e1.a1', '16.dc1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1631, -1, 1587, -1, 1631, -1, 1588, -1], 'generators': [81, 8], 'label': '256.5742.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.bq1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594135
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.l1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.r1.a1', '16.s1.a1', '16.bl1.a1', '16.bo1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2278, 7836, 2919, 7741, 2278, 7863, 2921, 7862], 'generators': [226, 172, 8], 'label': '256.5742.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'normal_contains': ['16.d1.a1', '16.r1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594136
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.i1.a1', '16.bp1.a1', '16.cx1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3022, 3331, 2825, 3291, 3022, 3343, 2827, 3342], 'generators': [18, 172, 8], 'label': '256.5742.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.c1.a1', '4.h1.a1', '4.k1.a1'], 'normal_contains': ['16.d1.a1', '16.h1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64594137
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.i1.a1', '16.bz1.a1', '16.cy1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2626, 2050, 2320, 1521, 2626, 2057, 2322, 1544], 'generators': [16, 174, 8], 'label': '256.5742.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.e1.a1', '16.f1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64594138
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.h1.a1', '16.cc1.a1', '16.da1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2494, 291, 2576, 888, 2493, 292, 2578, 902], 'generators': [28, 174, 8], 'label': '256.5742.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.e1.a1', '16.g1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '128.522', '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': '32.27'}
  • id: 64594139
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bb1.a1', '4.bd1.a1'], 'contains': ['16.j1.a1', '16.k1.a1', '16.l1.a1', '16.br1.a1', '16.co1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5597, 6203, 3490, 5527, 5596, 6224, 3492, 5613], 'generators': [80, 2, 164], 'label': '256.5742.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.a1', '16.k1.a1', '16.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594140
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6536092', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '4.bd1.a1', '4.be1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1590, 5097, 1626, 3882, 1590, 5114, 1626, 3942], 'generators': [1, 80, 8], 'label': '256.5742.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '128.522'}
  • id: 64594141
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.q1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bc1.a1', '4.be1.a1'], 'contains': ['16.j1.a1', '16.m1.a1', '16.n1.a1', '16.bv1.a1', '16.db1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2181, 4993, 2448, 4933, 2181, 5010, 2450, 5010], 'generators': [216, 2, 164], 'label': '256.5742.8.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.j1.a1', '16.m1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.q1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594142
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.r1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bf1.a1', '4.bg1.a1'], 'contains': ['16.o1.a1', '16.p1.a1', '16.s1.a1', '16.bq1.a1', '16.bx1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2084, 8975, 4697, 9729, 2084, 9005, 4700, 9880], 'generators': [200, 2, 172], 'label': '256.5742.8.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.o1.a1', '16.p1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594143
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.s1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bh1.a1', '4.bi1.a1'], 'contains': ['16.o1.a1', '16.q1.a1', '16.r1.a1', '16.bt1.a1', '16.ca1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2022, 9272, 3576, 8898, 2023, 9304, 3578, 9036], 'generators': [64, 2, 172], 'label': '256.5742.8.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.o1.a1', '16.r1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.s1.a1', 'projective_image': '128.522', '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': '64.60'}
  • id: 64594144
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.a1.a1', '16.t1.a1', '16.w1.a1', '16.bi1.a1', '16.bl1.a1', '16.bq1.a1', '16.bt1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3446, -1, 4612, -1, 3446, -1, 4614, -1], 'generators': [64, 2, 8], 'label': '256.5742.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.t1.a1', 'projective_image': '128.522', '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': '16.14'}
  • id: 64594145
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.a1.a1', '16.u1.a1', '16.x1.a1', '16.bj1.a1', '16.bk1.a1', '16.br1.a1', '16.bv1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3905, -1, 4077, -1, 3905, -1, 4080, -1], 'generators': [80, 2, 8], 'label': '256.5742.8.u1.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.u1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594146
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.n1.a1', '4.o1.a1'], 'contains': ['16.a1.a1', '16.z1.a1', '16.dx1.a1', '16.dx2.a1', '16.dx2.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [258, -1, 201, -1, 258, -1, 201, -1], 'generators': [17, 8, 160], 'label': '256.5742.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.v1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64594147
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.n1.a1', '4.o1.a1'], 'contains': ['16.a1.a1', '16.bc1.a1', '16.bw1.a1', '16.dy1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [133, -1, 500, -1, 133, -1, 500, -1], 'generators': [1, 8, 160], 'label': '256.5742.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.w1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64594148
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.p1.a1', '4.q1.a1'], 'contains': ['16.b1.a1', '16.t1.a1', '16.w1.a1', '16.bm1.a1', '16.bo1.a1', '16.bx1.a1', '16.ca1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3789, -1, 4783, -1, 3789, -1, 4786, -1], 'generators': [64, 10, 164], 'label': '256.5742.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.x1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594149
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.p1.a1', '4.q1.a1'], 'contains': ['16.b1.a1', '16.v1.a1', '16.y1.a1', '16.bn1.a1', '16.bp1.a1', '16.bz1.a1', '16.cc1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4830, -1, 3666, -1, 4830, -1, 3669, -1], 'generators': [16, 10, 164], 'label': '256.5742.8.y1.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.y1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594150
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.b1.a1', '16.z1.a1', '16.ea1.a1', '16.ea2.a1', '16.ea2.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [476, -1, 621, -1, 476, -1, 621, -1], 'generators': [17, 164, 160], 'label': '256.5742.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.z1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64594151
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10482067', 'aut_weyl_index': 2, 'centralizer': '64.c1.a1', 'complements': ['128.i1.a1', '128.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.n1.a1', '4.o1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [669, 3677, 794, 3406, 651, 3690, 834, 3459], 'generators': [1, 16, 172], 'label': '256.5742.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 64594152
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.b1.a1', '16.be1.a1', '16.cd1.a1', '16.eb1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [795, -1, 1201, -1, 796, -1, 1201, -1], 'generators': [65, 164, 160], 'label': '256.5742.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.ba1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 64594153
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.p1.a1', '4.t1.a1'], 'contains': ['16.t1.a1', '16.u1.a1', '16.v1.a1', '16.bf1.a1', '16.ce1.a1', '16.ci1.a1', '16.cp1.a1', '16.dr1.a1', '16.ec1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3145, -1, 3258, -1, 3145, -1, 3260, -1], 'generators': [16, 200, 10, 160], 'label': '256.5742.8.bb1.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': '8.bb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594154
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.p1.a1', '4.t1.a1'], 'contains': ['16.t1.a1', '16.u1.a1', '16.y1.a1', '16.cf1.a1', '16.ck1.a1', '16.ct1.a1', '16.ds1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5880, -1, 5570, -1, 5879, -1, 5573, -1], 'generators': [20, 200, 10], 'label': '256.5742.8.bc1.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': '8.bc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594155
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.q1.a1', '4.t1.a1'], 'contains': ['16.t1.a1', '16.v1.a1', '16.x1.a1', '16.ch1.a1', '16.cl1.a1', '16.df1.a1', '16.dl1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7223, -1, 5019, -1, 7223, -1, 5021, -1], 'generators': [24, 200, 10], 'label': '256.5742.8.bd1.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': '8.bd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594156
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.a1', '4.t1.a1'], 'contains': ['16.t1.a1', '16.x1.a1', '16.y1.a1', '16.cj1.a1', '16.cm1.a1', '16.dm1.a1', '16.dp1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8184, -1, 7621, -1, 8184, -1, 7625, -1], 'generators': [28, 200, 10], 'label': '256.5742.8.be1.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': '8.be1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594157
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.t1.a1', '4.v1.a1'], 'contains': ['16.c1.a1', '16.u1.a1', '16.x1.a1', '16.cn1.a1', '16.co1.a1', '16.cw1.a1', '16.db1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5020, -1, 4492, -1, 5020, -1, 4494, -1], 'generators': [80, 10, 172], 'label': '256.5742.8.bf1.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.bf1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594158
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.p1.a1', '4.v1.a1'], 'contains': ['16.u1.a1', '16.v1.a1', '16.w1.a1', '16.cq1.a1', '16.cr1.a1', '16.de1.a1', '16.dt1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4589, -1, 5943, -1, 4589, -1, 5947, -1], 'generators': [24, 64, 10], 'label': '256.5742.8.bg1.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': '8.bg1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594159
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.p1.a1', '4.v1.a1'], 'contains': ['16.u1.a1', '16.w1.a1', '16.y1.a1', '16.cs1.a1', '16.cu1.a1', '16.di1.a1', '16.du1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6944, -1, 8212, -1, 6944, -1, 8218, -1], 'generators': [28, 64, 10], 'label': '256.5742.8.bh1.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': '8.bh1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594160
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.t1.a1', '4.v1.a1'], 'contains': ['16.c1.a1', '16.v1.a1', '16.y1.a1', '16.cv1.a1', '16.cx1.a1', '16.cy1.a1', '16.da1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4711, -1, 3781, -1, 4711, -1, 3783, -1], 'generators': [16, 10, 172], 'label': '256.5742.8.bi1.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.bi1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594161
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.u1.a1', '4.w1.a1'], 'contains': ['16.c1.a1', '16.z1.a1', '16.ee1.a1', '16.ee2.a1', '16.ee2.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [673, -1, 739, -1, 674, -1, 740, -1], 'generators': [17, 172, 160], 'label': '256.5742.8.bj1.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.bj1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 64594162
    {'ambient': '256.5742', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10482067', 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['128.i1.a1', '128.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '4.z1.a1', '4.ba1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1827, 3137, 1908, 2873, 1827, 3148, 1909, 2917], 'generators': [65, 16, 172], 'label': '256.5742.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '128.522', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.139'}
  • id: 64594163
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.u1.a1', '4.w1.a1'], 'contains': ['16.c1.a1', '16.bh1.a1', '16.dc1.a1', '16.ef1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1262, -1, 1332, -1, 1262, -1, 1334, -1], 'generators': [81, 172, 160], 'label': '256.5742.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bk1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 64594164
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.q1.a1', '4.v1.a1'], 'contains': ['16.v1.a1', '16.w1.a1', '16.x1.a1', '16.dd1.a1', '16.dg1.a1', '16.dj1.a1', '16.dn1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8080, -1, 8447, -1, 8079, -1, 8452, -1], 'generators': [16, 64, 10], 'label': '256.5742.8.bl1.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': '8.bl1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594165
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.a1', '4.v1.a1'], 'contains': ['16.w1.a1', '16.x1.a1', '16.y1.a1', '16.dh1.a1', '16.dk1.a1', '16.do1.a1', '16.dq1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9893, -1, 9831, -1, 9893, -1, 9837, -1], 'generators': [20, 64, 10], 'label': '256.5742.8.bm1.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': '8.bm1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594166
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.y1.a1'], 'contains': ['16.e1.a1', '16.bi1.a1', '16.bl1.a1', '16.bx1.a1', '16.ca1.a1', '16.cg1.a1', '16.cz1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4485, -1, 6431, -1, 4484, -1, 6435, -1], 'generators': [64, 174, 8], 'label': '256.5742.8.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bn1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594167
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.x1.a1', '4.y1.a1'], 'contains': ['16.e1.a1', '16.bj1.a1', '16.bk1.a1', '16.by1.a1', '16.cb1.a1', '16.co1.a1', '16.db1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6030, -1, 6285, -1, 6030, -1, 6289, -1], 'generators': [80, 174, 8], 'label': '256.5742.8.bo1.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.bo1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594168
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.z1.a1', '4.ba1.a1'], 'contains': ['16.e1.a1', '16.cd1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1450, -1, 1763, -1, 1450, -1, 1764, -1], 'generators': [65, 8], 'label': '256.5742.8.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.bp1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594170
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.a1', '4.y1.a1'], 'contains': ['16.h1.a1', '16.bi1.a1', '16.bj1.a1', '16.ce1.a1', '16.cl1.a1', '16.cr1.a1', '16.dj1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8460, -1, 8728, -1, 8459, -1, 8733, -1], 'generators': [18, 64, 8], 'label': '256.5742.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.br1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594171
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.m1.a1', '4.x1.a1'], 'contains': ['16.i1.a1', '16.bi1.a1', '16.bj1.a1', '16.cf1.a1', '16.cm1.a1', '16.cs1.a1', '16.dk1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9969, -1, 9758, -1, 9968, -1, 9764, -1], 'generators': [30, 64, 8], 'label': '256.5742.8.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bs1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594172
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.l1.a1', '4.x1.a1'], 'contains': ['16.f1.a1', '16.bi1.a1', '16.bk1.a1', '16.ch1.a1', '16.ci1.a1', '16.dd1.a1', '16.de1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4010, -1, 7532, -1, 4010, -1, 7537, -1], 'generators': [16, 64, 8], 'label': '256.5742.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bt1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594173
    {'ambient': '256.5742', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 4, 'centralizer': '64.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.l1.a1', '8.r1.a1', '8.s1.a1', '8.t1.a1', '8.x1.a1', '8.bn1.a1', '8.bz1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2324, 8360, 4654, 8239, 2323, 8389, 4657, 8368], 'generators': [64, 2, 172, 8], 'label': '256.5742.4.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.f1.a1', '8.g1.a1', '8.r1.a1', '8.s1.a1', '8.h1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.60'}
  • id: 64594174
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.m1.a1', '4.y1.a1'], 'contains': ['16.g1.a1', '16.bi1.a1', '16.bk1.a1', '16.cj1.a1', '16.ck1.a1', '16.dh1.a1', '16.di1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5810, -1, 9344, -1, 5811, -1, 9350, -1], 'generators': [28, 64, 8], 'label': '256.5742.8.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bu1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594175
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.a1', '4.x1.a1'], 'contains': ['16.f1.a1', '16.bj1.a1', '16.bl1.a1', '16.cp1.a1', '16.cq1.a1', '16.df1.a1', '16.dg1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7619, -1, 4311, -1, 7619, -1, 4313, -1], 'generators': [16, 226, 8], 'label': '256.5742.8.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bv1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594176
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.m1.a1', '4.y1.a1'], 'contains': ['16.g1.a1', '16.bj1.a1', '16.bl1.a1', '16.ct1.a1', '16.cu1.a1', '16.dp1.a1', '16.dq1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8701, -1, 6605, -1, 8701, -1, 6609, -1], 'generators': [28, 226, 8], 'label': '256.5742.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bw1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594177
    {'ambient': '256.5742', 'aut_centralizer_order': 16, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 32, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.l1.a1', '4.y1.a1'], 'contains': ['16.h1.a1', '16.bk1.a1', '16.bl1.a1', '16.dl1.a1', '16.dn1.a1', '16.dr1.a1', '16.dt1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3618, -1, 4230, -1, 3617, -1, 4232, -1], 'generators': [18, 226, 8], 'label': '256.5742.8.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bx1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594178
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.m1.a1', '4.x1.a1'], 'contains': ['16.i1.a1', '16.bk1.a1', '16.bl1.a1', '16.dm1.a1', '16.do1.a1', '16.ds1.a1', '16.du1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5956, -1, 6358, -1, 5955, -1, 6362, -1], 'generators': [30, 226, 8], 'label': '256.5742.8.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.by1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.by1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594179
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.j1.a1', '16.bm1.a1', '16.bo1.a1', '16.bq1.a1', '16.bt1.a1', '16.cg1.a1', '16.cz1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3542, -1, 6044, -1, 3542, -1, 6048, -1], 'generators': [64, 2, 164], 'label': '256.5742.8.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bz1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
  • id: 64594180
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.j1.a1', '16.bn1.a1', '16.bp1.a1', '16.bs1.a1', '16.bu1.a1', '16.cy1.a1', '16.da1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4289, -1, 5347, -1, 4289, -1, 5351, -1], 'generators': [16, 2, 164], 'label': '256.5742.8.ca1.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.ca1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 64594181
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.j1.a1', '16.bw1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1150, -1, 1514, -1, 1150, -1, 1515, -1], 'generators': [1, 164], 'label': '256.5742.8.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.cb1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594182
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.j1.a1', '16.dc1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1374, -1, 1441, -1, 1374, -1, 1442, -1], 'generators': [81, 164], 'label': '256.5742.8.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.cc1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 64594183
    {'ambient': '256.5742', 'aut_centralizer_order': 8, 'aut_label': '8.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.p1.a1', '4.bb1.a1'], 'contains': ['16.k1.a1', '16.bm1.a1', '16.bp1.a1', '16.ce1.a1', '16.cf1.a1', '16.cr1.a1', '16.cs1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8977, -1, 9259, -1, 8976, -1, 9264, -1], 'generators': [18, 64, 164], 'label': '256.5742.8.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cd1.a1', 'projective_image': '128.522', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}