Abstract group data - 512.60809

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 16, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8, 64], [1, 34, 8, 64], [1, 34, 8, 96], [5, 6, 424, 224], [33, 34, 40, 352], [305, 182, 8, 456], [33, 230, 56, 120], [29, 286, 152, 352]], 'aut_group': '4096.brd', 'aut_hash': 5830821769979981028, 'aut_nilpotency_class': 6, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 48, 'aut_perms': [1783695150402495069294310932636883913049412181984824819938371, 1783094320606454130075446691322640360335694161432706524328529, 5357992358992059921476714661111567210702372017934917776760, 3846642698600853553456182128479492607973304506144693712712, 5837149538456654733880306131955503407384486594606488779689364, 4063816081365005558226645640473410027397918129834380293866977, 8303704181275948731262704876027745672110166722044616431520343], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 4, 1], [2, 16, 1, 1], [2, 16, 2, 1], [2, 32, 1, 1], [4, 4, 1, 3], [4, 16, 1, 1], [4, 16, 2, 1], [4, 64, 2, 1], [8, 4, 2, 1], [8, 4, 4, 1], [8, 8, 1, 1], [8, 8, 2, 1], [8, 16, 4, 1], [8, 32, 1, 1], [16, 32, 2, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_4\\times \\OD_{16}).D_4^2', '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': 8, 'autcentquo_group': '512.420058', 'autcentquo_hash': 4262671825627166463, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4^2.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 8, 4], [2, 16, 3], [2, 32, 1], [4, 4, 3], [4, 16, 3], [4, 64, 2], [8, 4, 6], [8, 8, 3], [8, 16, 4], [8, 32, 1], [16, 32, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '256.6661', 'commutator_count': 1, 'commutator_label': '64.174', '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', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 60809, '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, 1], [2, 8, 1, 4], [2, 16, 1, 3], [2, 32, 1, 1], [4, 4, 1, 3], [4, 16, 1, 3], [4, 64, 1, 2], [8, 4, 2, 3], [8, 8, 1, 1], [8, 8, 2, 1], [8, 16, 2, 2], [8, 32, 1, 1], [16, 32, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 10752, 'exponent': 16, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[4, 1, 8], [8, 1, 2]], 'familial': False, 'frattini_label': '64.174', 'frattini_quotient': '8.5', 'hash': 60809, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 4, 4, 8], 'inner_gens': [[1, 6, 8, 456], [5, 2, 184, 120], [1, 402, 8, 64], [185, 10, 8, 64]], 'inner_hash': 6661, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': False, 'inner_tex': 'D_4^2:C_2^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 6], [4, 18], [8, 3]], 'label': '512.60809', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D8wrC2', 'ngens': 3, 'nilpotency_class': 6, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 35, 'number_divisions': 28, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 201, 'number_subgroup_classes': 357, 'number_subgroups': 2598, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 115], [4, 188], [8, 144], [16, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 2, 8, 96], [153, 94, 8, 456], [33, 2, 40, 320], [33, 2, 8, 64]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [126, 55, 289, 288], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 6], [8, 7], [16, 1]], 'representations': {'PC': {'code': '202050378031308156279437029341143090179702581064918285869530', 'gens': [1, 2, 4, 7], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 109, 46, 3324, 525, 102, 6853, 562, 130, 28734, 3795, 7080, 186, 28807, 6352, 6937, 214, 23336, 11681]}, 'Perm': {'d': 16, 'gens': [11212821043200, 1313941697263, 1307761464367, 5606234750016, 6354391823, 2796059347200, 4097467152142, 5167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_8\\wr C_2', 'transitive_degree': 16, 'wreath_data': ['D_8', 'C_2', '2T1'], 'wreath_product': True}
• 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: 110537427
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 60809, 'group_order': 512, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 110537438
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 60809, 'group_order': 512, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 110537449
    {'aut_label': '2B', 'centralizer': '2.c1.a1', 'counter': 3, 'group_counter': 60809, 'group_order': 512, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 256, 'size': 2}
  • id: 110537456
    {'aut_label': '2C', 'centralizer': '8.p1.b1', 'counter': 4, 'group_counter': 60809, 'group_order': 512, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 3, 'size': 8}
  • id: 110537457
    {'aut_label': '2C', 'centralizer': '8.p1.b1', 'counter': 5, 'group_counter': 60809, 'group_order': 512, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 259, 'size': 8}
  • id: 110537458
    {'aut_label': '2C', 'centralizer': '8.p1.a1', 'counter': 6, 'group_counter': 60809, 'group_order': 512, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 71, 'size': 8}
  • id: 110537459
    {'aut_label': '2C', 'centralizer': '8.p1.a1', 'counter': 7, 'group_counter': 60809, 'group_order': 512, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 203, 'size': 8}
  • id: 110537460
    {'aut_label': '2G', 'centralizer': '16.bn1.a1', 'counter': 8, 'group_counter': 60809, 'group_order': 512, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 1, 'size': 16}
  • id: 110537461
    {'aut_label': '2H', 'centralizer': '16.g1.a1', 'counter': 9, 'group_counter': 60809, 'group_order': 512, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 308, 'size': 16}
  • id: 110537428
    {'aut_label': '2H', 'centralizer': '16.g1.b1', 'counter': 10, 'group_counter': 60809, 'group_order': 512, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 140, 'size': 16}
  • id: 110537429
    {'aut_label': '2J', 'centralizer': '32.g1.a1', 'counter': 11, 'group_counter': 60809, 'group_order': 512, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 68, 'size': 32}
  • id: 110537430
    {'aut_label': '4A', 'centralizer': '4.i1.a1', 'counter': 12, 'group_counter': 60809, 'group_order': 512, 'label': '4A', 'order': 4, 'powers': [3], 'representative': 128, 'size': 4}
  • id: 110537431
    {'aut_label': '4B', 'centralizer': '4.m1.a1', 'counter': 13, 'group_counter': 60809, 'group_order': 512, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 16, 'size': 4}
  • id: 110537432
    {'aut_label': '4C', 'centralizer': '4.i1.a1', 'counter': 14, 'group_counter': 60809, 'group_order': 512, 'label': '4C', 'order': 4, 'powers': [3], 'representative': 160, 'size': 4}
  • id: 110537433
    {'aut_label': '4D', 'centralizer': '16.bk1.a1', 'counter': 15, 'group_counter': 60809, 'group_order': 512, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 257, 'size': 16}
  • id: 110537434
    {'aut_label': '4E', 'centralizer': '16.e1.a1', 'counter': 16, 'group_counter': 60809, 'group_order': 512, 'label': '4E', 'order': 4, 'powers': [3], 'representative': 131, 'size': 16}
  • id: 110537435
    {'aut_label': '4E', 'centralizer': '16.e1.b1', 'counter': 17, 'group_counter': 60809, 'group_order': 512, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 75, 'size': 16}
  • id: 110537436
    {'aut_label': '4G', 'centralizer': '64.o1.a1', 'counter': 18, 'group_counter': 60809, 'group_order': 512, 'label': '4G', 'order': 4, 'powers': [9], 'representative': 182, 'size': 64}
  • id: 110537437
    {'aut_label': '4G', 'centralizer': '64.o1.b1', 'counter': 19, 'group_counter': 60809, 'group_order': 512, 'label': '4H', 'order': 4, 'powers': [10], 'representative': 254, 'size': 64}
  • id: 110537439
    {'aut_label': '8A1', 'centralizer': '4.i1.a1', 'counter': 20, 'group_counter': 60809, 'group_order': 512, 'label': '8A1', 'order': 8, 'powers': [12], 'representative': 64, 'size': 4}
  • id: 110537440
    {'aut_label': '8A1', 'centralizer': '4.i1.a1', 'counter': 21, 'group_counter': 60809, 'group_order': 512, 'label': '8A3', 'order': 8, 'powers': [12], 'representative': 320, 'size': 4}
  • id: 110537441
    {'aut_label': '8A1', 'centralizer': '4.i1.a1', 'counter': 22, 'group_counter': 60809, 'group_order': 512, 'label': '8B1', 'order': 8, 'powers': [12], 'representative': 96, 'size': 4}
  • id: 110537442
    {'aut_label': '8A1', 'centralizer': '4.i1.a1', 'counter': 23, 'group_counter': 60809, 'group_order': 512, 'label': '8B3', 'order': 8, 'powers': [12], 'representative': 352, 'size': 4}
  • id: 110537443
    {'aut_label': '8C1', 'centralizer': '4.m1.a1', 'counter': 24, 'group_counter': 60809, 'group_order': 512, 'label': '8C1', 'order': 8, 'powers': [13], 'representative': 392, 'size': 4}
  • id: 110537444
    {'aut_label': '8C1', 'centralizer': '4.m1.a1', 'counter': 25, 'group_counter': 60809, 'group_order': 512, 'label': '8C3', 'order': 8, 'powers': [13], 'representative': 152, 'size': 4}
  • id: 110537445
    {'aut_label': '8D', 'centralizer': '8.e1.a1', 'counter': 26, 'group_counter': 60809, 'group_order': 512, 'label': '8D', 'order': 8, 'powers': [13], 'representative': 264, 'size': 8}
  • id: 110537446
    {'aut_label': '8E1', 'centralizer': '8.e1.a1', 'counter': 27, 'group_counter': 60809, 'group_order': 512, 'label': '8E1', 'order': 8, 'powers': [14], 'representative': 80, 'size': 8}
  • id: 110537447
    {'aut_label': '8E1', 'centralizer': '8.e1.a1', 'counter': 28, 'group_counter': 60809, 'group_order': 512, 'label': '8E3', 'order': 8, 'powers': [14], 'representative': 72, 'size': 8}
  • id: 110537448
    {'aut_label': '8F1', 'centralizer': '16.e1.a1', 'counter': 29, 'group_counter': 60809, 'group_order': 512, 'label': '8F1', 'order': 8, 'powers': [12], 'representative': 67, 'size': 16}
  • id: 110537450
    {'aut_label': '8F1', 'centralizer': '16.e1.a1', 'counter': 30, 'group_counter': 60809, 'group_order': 512, 'label': '8F3', 'order': 8, 'powers': [12], 'representative': 323, 'size': 16}
  • id: 110537451
    {'aut_label': '8F1', 'centralizer': '16.e1.b1', 'counter': 31, 'group_counter': 60809, 'group_order': 512, 'label': '8G1', 'order': 8, 'powers': [12], 'representative': 11, 'size': 16}
  • id: 110537452
    {'aut_label': '8F1', 'centralizer': '16.e1.b1', 'counter': 32, 'group_counter': 60809, 'group_order': 512, 'label': '8G3', 'order': 8, 'powers': [12], 'representative': 267, 'size': 16}
  • id: 110537453
    {'aut_label': '8H', 'centralizer': '32.ba1.a1', 'counter': 33, 'group_counter': 60809, 'group_order': 512, 'label': '8H', 'order': 8, 'powers': [13], 'representative': 57, 'size': 32}
  • id: 110537454
    {'aut_label': '16A1', 'centralizer': '32.bm1.a1', 'counter': 34, 'group_counter': 60809, 'group_order': 512, 'label': '16A1', 'order': 16, 'powers': [24], 'representative': 453, 'size': 32}
  • id: 110537455
    {'aut_label': '16A1', 'centralizer': '32.bm1.a1', 'counter': 35, 'group_counter': 60809, 'group_order': 512, 'label': '16A3', 'order': 16, 'powers': [25], 'representative': 333, 'size': 32}
• 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: 4653151
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4653162
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4653172
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 4653173
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 4653174
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4653175
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4653176
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 4653177
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 4653178
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 0, 0, -2, 0, 2, 0, 2, 2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653152
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, -2, -2, 2, 0, -2, 0, 2, 2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0], 'schur_index': 1}
  • id: 4653153
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 0, -2, 0, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653154
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 0, 0, -2, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653155
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, 2, 0, -2, 0, 2, 2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0], 'schur_index': 1}
  • id: 4653156
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, -2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653157
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4a', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 0, 0, -2, 0, 0, -4, 4, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 4653158
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4b', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, 0, 0, 2, 0, 0, -4, 4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 4653159
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4c', 'multiplicity': 1, 'nt': [8, 35], 'qdim': 4, 'qvalues': [4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653160
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4d', 'multiplicity': 1, 'nt': [8, 35], 'qdim': 4, 'qvalues': [4, 4, 4, -2, -2, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 2, -2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653161
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4e', 'multiplicity': 1, 'nt': [8, 35], 'qdim': 4, 'qvalues': [4, 4, 4, 2, 2, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, -2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653163
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4f', 'multiplicity': 1, 'nt': [8, 35], 'qdim': 4, 'qvalues': [4, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653164
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4g', 'multiplicity': 2, 'nt': [16, 665], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653165
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4h', 'multiplicity': 2, 'nt': [16, 665], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653166
    {'cdim': 4, 'counter': 23, 'faithful': True, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4i', 'multiplicity': 2, 'nt': [16, 972], 'qdim': 8, 'qvalues': [8, -8, 0, -4, 4, -4, 4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653167
    {'cdim': 4, 'counter': 24, 'faithful': True, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4j', 'multiplicity': 2, 'nt': [16, 972], 'qdim': 8, 'qvalues': [8, -8, 0, -4, 4, 4, -4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653168
    {'cdim': 4, 'counter': 25, 'faithful': True, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4k', 'multiplicity': 2, 'nt': [16, 972], 'qdim': 8, 'qvalues': [8, -8, 0, 4, -4, -4, 4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653169
    {'cdim': 4, 'counter': 26, 'faithful': True, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.4l', 'multiplicity': 2, 'nt': [16, 972], 'qdim': 8, 'qvalues': [8, -8, 0, 4, -4, 4, -4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653170
    {'cdim': 8, 'counter': 27, 'faithful': False, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.8a', 'multiplicity': 1, 'nt': [16, 659], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4653171
    {'cdim': 8, 'counter': 28, 'faithful': True, 'group': '512.60809', 'group_order': 512, 'image': None, 'label': '512.60809.8b', 'multiplicity': 2, 'nt': [32, 21596], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 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: 7444886
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 512, 'label': '512.60809.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7444897
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 256, 'label': '512.60809.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7444908
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 256, 'label': '512.60809.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7444915
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 256, 'label': '512.60809.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7444916
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 256, 'label': '512.60809.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7444917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 256, 'label': '512.60809.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7444918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 256, 'label': '512.60809.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7444919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 512, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 256, 'label': '512.60809.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7444920
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 64, 'label': '512.60809.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444887
    {'center': '4.a1.b1', 'center_index': 4, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 64, 'label': '512.60809.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444888
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 64, 'label': '512.60809.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444889
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 64, 'label': '512.60809.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444890
    {'center': '4.a1.b1', 'center_index': 4, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.b1', 'kernel_order': 64, 'label': '512.60809.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444891
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 64, 'label': '512.60809.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444892
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 8, 'label': '512.60809.4a', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444893
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 8, 'label': '512.60809.4b', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444894
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '128.928', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 4, 'label': '512.60809.4c', 'nt': [8, 35], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444895
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '128.928', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 4, 'label': '512.60809.4d', 'nt': [8, 35], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444896
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '128.928', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 4, 'label': '512.60809.4e', 'nt': [8, 35], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444898
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '128.928', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 4, 'label': '512.60809.4f', 'nt': [8, 35], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444899
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '256.6661', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1.a1', 'kernel_order': 2, 'label': '512.60809.4g1', 'nt': [16, 665], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 7444900
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '256.6661', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1.a1', 'kernel_order': 2, 'label': '512.60809.4g2', 'nt': [16, 665], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 7444901
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '256.6661', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1.a1', 'kernel_order': 2, 'label': '512.60809.4h1', 'nt': [16, 665], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 7444902
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '256.6661', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1.a1', 'kernel_order': 2, 'label': '512.60809.4h2', 'nt': [16, 665], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 7444903
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4i1', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 1], [2, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444904
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4i2', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[-2, 1], [-2, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444905
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4j1', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [1, 1], [-1, 3]], [[2, 1], [2, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444906
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4j2', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 1], [-2, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444907
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4k1', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [1, 1], [-1, 3]], [[2, 1], [2, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444909
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4k2', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 1], [-2, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444910
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4l1', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 1], [2, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444911
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 8, 'dim': 4, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.4l2', 'nt': [16, 972], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 0], [-1, 1], [1, 3]], [[-2, 0], [-1, 1], [1, 3]], [[2, 0], [1, 1], [-1, 3]], [[-2, 0], [1, 1], [-1, 3]], [[-2, 1], [-2, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444912
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '256.6661', 'image_order': 256, 'indicator': 1, 'kernel': '256.a1.a1', 'kernel_order': 2, 'label': '512.60809.8a', 'nt': [16, 659], 'q_character': None, 'values': [[[8, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7444913
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 8, 'dim': 8, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.8b1', 'nt': [32, 21596], '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]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[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]]]}
  • id: 7444914
    {'center': '256.a1.a1', 'center_index': 256, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 8, 'dim': 8, 'faithful': True, 'field': [-2, 0, 1], 'group': '512.60809', 'group_counter': 60809, 'group_order': 512, 'image': None, 'image_isoclass': '512.60809', 'image_order': 512, 'indicator': 1, 'kernel': '512.a1.a1', 'kernel_order': 1, 'label': '512.60809.8b2', 'nt': [32, 21596], '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]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[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]]]}
• 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: 67267731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 512, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '512.60809.1.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': '512.60809', 'subgroup_hash': 4561790705136276924, 'subgroup_order': 512, 'subgroup_tex': 'D_8\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 67267842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.6661', 'subgroup_hash': 6661, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67267953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.6661', 'subgroup_hash': 6661, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': '256.503', 'subgroup_hash': 503, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 256, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.503', 'subgroup_hash': 503, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.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': '256.12955', 'subgroup_hash': 12955, 'subgroup_order': 256, 'subgroup_tex': 'D_8^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.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': '256.5298', 'subgroup_hash': 5298, 'subgroup_order': 256, 'subgroup_tex': 'D_8:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.517', 'subgroup_hash': 517, 'subgroup_order': 256, 'subgroup_tex': 'C_8^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.351', 'subgroup_hash': 351, 'subgroup_order': 128, 'subgroup_tex': 'D_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.351', 'subgroup_hash': 351, 'subgroup_order': 128, 'subgroup_tex': 'D_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2024', 'subgroup_hash': 2024, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.444', 'subgroup_hash': 444, 'subgroup_order': 128, 'subgroup_tex': 'C_8:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.140', 'subgroup_hash': 140, 'subgroup_order': 128, 'subgroup_tex': '(C_4\\times C_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.140', 'subgroup_hash': 140, 'subgroup_order': 128, 'subgroup_tex': '(C_4\\times C_8):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.89', 'subgroup_hash': 89, 'subgroup_order': 128, 'subgroup_tex': 'C_8.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '128.399', 'subgroup_hash': 399, 'subgroup_order': 128, 'subgroup_tex': 'C_8:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.399', 'subgroup_hash': 399, 'subgroup_order': 128, 'subgroup_tex': 'C_8:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.351', 'subgroup_hash': 351, 'subgroup_order': 128, 'subgroup_tex': 'D_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.307', 'subgroup_hash': 307, 'subgroup_order': 128, 'subgroup_tex': 'C_8\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2011', 'subgroup_hash': 2011, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2011', 'subgroup_hash': 2011, 'subgroup_order': 128, 'subgroup_tex': 'D_4\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.134', 'subgroup_hash': 134, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.134', 'subgroup_hash': 134, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.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': '128.945', 'subgroup_hash': 945, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.4.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': '128.67', 'subgroup_hash': 67, 'subgroup_order': 128, 'subgroup_tex': 'C_8\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 67267942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 67267954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'U1', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267998
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.2', 'subgroup_hash': 2, 'subgroup_order': 64, 'subgroup_tex': 'C_8^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.147', 'subgroup_hash': 147, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.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': '64.147', 'subgroup_hash': 147, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.115', 'subgroup_hash': 115, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.6', 'subgroup_hash': 6, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.6', 'subgroup_hash': 6, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m2.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.m2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m2.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': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.118', 'subgroup_hash': 118, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.250', 'subgroup_hash': 250, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.250', 'subgroup_hash': 250, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.190', 'subgroup_hash': 190, 'subgroup_order': 64, 'subgroup_tex': 'D_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.124', 'subgroup_hash': 124, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.257', 'subgroup_hash': 257, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67268048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.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': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.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': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.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': '64.42', 'subgroup_hash': 42, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '64.16', 'subgroup_hash': 16, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.16.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.16.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.b1', '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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.c1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67268078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67268079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67268087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67267740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 67267741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 67267766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.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': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.18', 'subgroup_hash': 18, 'subgroup_order': 32, 'subgroup_tex': 'D_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 67267772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.e1', 'outer_equivalence': False, 'perfect': False, '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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.f1', 'outer_equivalence': False, 'perfect': False, '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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.g1', 'outer_equivalence': False, 'perfect': False, '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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.16.bp1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.h1', 'outer_equivalence': False, 'perfect': False, '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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', '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', 'L2', 'C5'], '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: 67267782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67267792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67267793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 67267794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67267828
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 67267847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bo1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bo1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bp1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bp1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bq1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bq1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bs1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bs1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bu1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bu1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bv1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bv1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.32.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 237, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.64.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': '64.138', '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': ['U3', 'L3', 'D2', 'C6'], '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: 67267885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267894
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267914
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267915
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267916
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.v1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.w1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.w1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.z1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.z1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.ba1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.ba1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67267939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bf1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bf1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267957
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bh1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267958
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi1.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267960
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.64.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 67267961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bk1.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.64.bk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67267966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.60809.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.928', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 928, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr D_4', 'simple': False, 'solvable': True, 'special_labels': ['U4', 'L4', 'C7'], '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: 67267967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.d1.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': 128, 'quotient_simple': 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: 67267972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 317, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 318, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267978
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h2.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 67267981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.h2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h2.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': 128, 'quotient_simple': 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: 67267982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 67267985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.j1.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': 128, 'quotient_simple': 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: 67267986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67267988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67267989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67267990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67267992
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n2.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 67267994
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n2.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': 128, 'quotient_simple': 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: 67267995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.n2.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n2.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67267997
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67267999
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67268000
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67268001
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67268002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67268003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '512.60809.128.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67268004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 67268005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.128.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': 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: 67268006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 2, 'counter': 347, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '512.60809.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '256.6661', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6661, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U5', 'L5', 'C8'], '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: 67268007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.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': 256, '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: 67268008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.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': 256, '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: 67268010
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.c1.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': 256, '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: 67268011
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, '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: 67268012
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, '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: 67268013
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.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': 256, '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: 67268014
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.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': 256, '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: 67268015
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, '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: 67268016
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '512.60809.256.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.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': 256, '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: 67268017
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '512.60809', 'ambient_counter': 60809, 'ambient_order': 512, 'ambient_tex': 'D_8\\wr C_2', 'central': True, 'central_factor': False, 'centralizer_order': 512, 'characteristic': True, 'core_order': 1, 'counter': 357, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '512.60809.512.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '512.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '512.60809', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4561790705136276924, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 512, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U6', 'L6', 'D3', 'C9'], '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: 67267846
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 512, 'centralizer': '32.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.bm1.a1', '16.bo1.a1'], 'contains': ['64.s1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9949, -1, 9974, -1, 9934, -1, 9966, -1], 'generators': [65], 'label': '512.60809.32.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '32.bm1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267960
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '64.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.t1.a1', '32.bw1.a1', '32.bw1.b1'], 'contains': ['128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2644, -1, 3609, -1, 2640, -1, 3606, -1], 'generators': [368], 'label': '512.60809.64.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '64.bj1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267731
    {'ambient': '512.60809', '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': '256.a1.a1', 'complements': ['512.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6343, 5028, 6856, 5118, 6334, 4916, 6850, 5167], 'generators': [1, 2, 64], 'label': '512.60809.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '256.6661', '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': '256.6661'}
  • id: 67267732
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '512.7530050', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.b1', '8.b1.b1', '8.c1.a1', '8.i1.b1', '8.l1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5267, 8762, 6354, 2444, 5260, 8568, 6347, 2467], 'generators': [67, 4, 392], 'label': '512.60809.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.b1', '8.b1.b1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267733
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.i1.a1', '32.k1.a1', '32.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6013, -1, 6814, -1, 6004, -1, 6808, -1], 'generators': [305, 2], 'label': '512.60809.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '16.q1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 67267734
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1'], 'contains': ['32.i1.b1', '32.k1.b1', '32.l1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6013, -1, 7319, -1, 6004, -1, 7312, -1], 'generators': [393, 66], 'label': '512.60809.16.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '16.q1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 67267735
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.r1.a1', '8.u1.a1'], 'contains': ['32.j1.a1', '32.n1.a1', '32.w1.a1', '32.bc1.a1', '32.bg1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7523, -1, 8196, -1, 7512, -1, 8188, -1], 'generators': [1, 132, 256], 'label': '512.60809.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.r1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67267736
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.r1.b1', '8.u1.a1'], 'contains': ['32.j1.a1', '32.n1.b1', '32.w1.a1', '32.bc1.b1', '32.bg1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7523, -1, 8442, -1, 7512, -1, 8434, -1], 'generators': [1, 396, 256], 'label': '512.60809.16.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.r1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67267737
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.r1.b1', '8.t1.a1'], 'contains': ['32.a1.a1', '32.j1.a1', '32.w1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6803, -1, 7843, -1, 6794, -1, 7837, -1], 'generators': [1, 128], 'label': '512.60809.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.s1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267738
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.t1.a1', '8.u1.a1'], 'contains': ['32.j1.a1', '32.v1.a1', '32.w1.a1', '32.ba1.a1', '32.bb1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8183, -1, 8652, -1, 8172, -1, 8645, -1], 'generators': [1, 8, 256], 'label': '512.60809.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.t1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267739
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.r1.a1', '8.u1.a1'], 'contains': ['32.i1.a1', '32.j1.a1', '32.n1.a1', '32.z1.a1', '32.be1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7053, -1, 7974, -1, 7043, -1, 7967, -1], 'generators': [1, 4, 304, 256], 'label': '512.60809.16.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': '16.u1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267740
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.r1.b1', '8.u1.a1'], 'contains': ['32.i1.b1', '32.j1.a1', '32.n1.b1', '32.z1.b1', '32.be1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7053, -1, 8085, -1, 7043, -1, 8078, -1], 'generators': [1, 12, 304, 256], 'label': '512.60809.16.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '16.u1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267741
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.t1.a1', '8.u1.a1'], 'contains': ['32.j1.a1', '32.v1.a1', '32.bd1.a1', '32.bf1.a1', '32.bl1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9296, -1, 9217, -1, 9282, -1, 9208, -1], 'generators': [1, 392, 256], 'label': '512.60809.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.v1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67267742
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.p1.b1', '8.v1.a1'], 'contains': ['32.m1.a1', '32.p1.a1', '32.s1.a1', '32.bv1.a1', '32.bv1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1437, -1, 1499, -1, 1434, -1, 1496, -1], 'generators': [64, 4, 32], 'label': '512.60809.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.w1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267743
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dgh', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['128.o1.a1', '128.o1.d1', '128.o1.b1', '128.o1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'contains': ['8.c1.a1', '8.q1.a1', '8.r1.a1', '8.r1.b1', '8.t1.a1', '8.u1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7202, 3331, 7703, 7332, 7191, 3257, 7696, 7401], 'generators': [1, 4, 392, 128], 'label': '512.60809.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.d1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '256.6661', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267744
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.p1.a1', '8.v1.b1'], 'contains': ['32.m1.b1', '32.p1.a2', '32.s1.a1', '32.bv1.c1', '32.bv1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1437, -1, 2729, -1, 1434, -1, 2726, -1], 'generators': [64, 396, 32], 'label': '512.60809.16.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.w1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267745
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.m2.a1', '8.v1.a1'], 'contains': ['32.m1.a1', '32.p1.a1', '32.t1.a1', '32.bw1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2685, -1, 2864, -1, 2681, -1, 2860, -1], 'generators': [368, 4, 32], 'label': '512.60809.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.x1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67267746
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '8.m2.b1', '8.v1.b1'], 'contains': ['32.m1.b1', '32.p1.a2', '32.t1.a1', '32.bw1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2685, -1, 4408, -1, 2681, -1, 4403, -1], 'generators': [368, 396, 32], 'label': '512.60809.16.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.x1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67267747
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.i1.b1', '8.m2.a1'], 'contains': ['32.m1.a1', '32.r1.b1', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2901, -1, 3602, -1, 2897, -1, 3598, -1], 'generators': [371, 4], 'label': '512.60809.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.y1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67267748
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.i1.a1', '8.m2.b1'], 'contains': ['32.m1.b1', '32.r1.a1', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2901, -1, 4833, -1, 2897, -1, 4829, -1], 'generators': [307, 396], 'label': '512.60809.16.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.y1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67267749
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.h1.a1', '8.w1.a1'], 'contains': ['32.l1.a1', '32.n1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5801, -1, 7097, -1, 5792, -1, 7091, -1], 'generators': [2, 304], 'label': '512.60809.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.z1.a1', 'projective_image': '256.6661', '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': '64.138'}
  • id: 67267750
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.h1.b1', '8.w1.b1'], 'contains': ['32.l1.b1', '32.n1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5801, -1, 7207, -1, 5792, -1, 7201, -1], 'generators': [66, 304], 'label': '512.60809.16.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '16.z1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 67267751
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.n1.a1', '32.w1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6553, -1, 7601, -1, 6544, -1, 7595, -1], 'generators': [129, 4], 'label': '512.60809.16.ba1.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': '16.ba1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267752
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '8.q1.a1', '8.r1.b1'], 'contains': ['32.n1.b1', '32.w1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6553, -1, 7713, -1, 6544, -1, 7706, -1], 'generators': [129, 12], 'label': '512.60809.16.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '16.ba1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267753
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.q1.a1', '8.u1.a1'], 'contains': ['32.n1.a1', '32.n1.b1', '32.v1.a1', '32.bh1.a1', '32.bi1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7758, -1, 8318, -1, 7746, -1, 8311, -1], 'generators': [4, 392, 256], 'label': '512.60809.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.bb1.a1', 'projective_image': '256.6661', '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': '32.49'}
  • id: 67267754
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1024.djj', 'aut_weyl_index': 4, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '8.v1.a1', '8.v1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6360, 1635, 6099, 1279, 6344, 1599, 6093, 1290], 'generators': [64, 4, 392], 'label': '512.60809.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267755
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.j1.a1', '8.m1.a1'], 'contains': ['32.p1.a1', '32.r1.a1', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2085, -1, 3357, -1, 2081, -1, 3353, -1], 'generators': [311, 452], 'label': '512.60809.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.bc1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67267756
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.j1.b1', '8.m1.b1'], 'contains': ['32.p1.a2', '32.r1.b1', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2085, -1, 4631, -1, 2081, -1, 4627, -1], 'generators': [191, 452], 'label': '512.60809.16.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bc1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67267757
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.j1.a1', '8.j1.b1', '8.n1.a1', '8.v1.a1', '8.v1.b1', '8.x1.a1'], 'contains': ['32.a1.a1', '32.p1.a1', '32.p1.a2', '32.q1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5108, -1, 5796, -1, 5100, -1, 5790, -1], 'generators': [452, 128, 304], 'label': '512.60809.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bd1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67267758
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.s1.a1', '8.y1.a1'], 'contains': ['32.q1.a1', '32.v1.a1', '32.bj1.a1', '32.bk1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9079, -1, 9330, -1, 9066, -1, 9321, -1], 'generators': [452, 392, 256], 'label': '512.60809.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.be1.a1', 'projective_image': '256.6661', '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': '32.43'}
  • id: 67267759
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.f1.b1', '8.o1.a1'], 'contains': ['32.r1.a1', '32.r1.b1', '32.s1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1653, -1, 4028, -1, 1650, -1, 4024, -1], 'generators': [311, 64], 'label': '512.60809.16.bf1.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': '16.bf1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267760
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.k1.a1', '8.k1.b1', '8.o1.a1', '8.v1.a1', '8.v1.b1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.s1.a1', '32.t1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3923, -1, 5058, -1, 3917, -1, 5053, -1], 'generators': [64, 304], 'label': '512.60809.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bg1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267761
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.i1.b1', '8.j1.a1', '8.k1.a1', '8.l1.b1', '8.x1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.u1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4608, -1, 5706, -1, 4602, -1, 5700, -1], 'generators': [67, 304], 'label': '512.60809.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bh1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267762
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.i1.a1', '8.j1.b1', '8.k1.b1', '8.l1.a1', '8.x1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.u1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4608, -1, 5886, -1, 4602, -1, 5881, -1], 'generators': [395, 304], 'label': '512.60809.16.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bh1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267763
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.t1.a1', '8.y1.a1'], 'contains': ['32.v1.a1', '32.w1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7974, -1, 8543, -1, 7962, -1, 8535, -1], 'generators': [129, 392], 'label': '512.60809.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bi1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67267764
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.48', 'aut_weyl_index': 128, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.y1.a1', '8.ba1.a1'], 'contains': ['32.v1.a1', '32.bm1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9476, -1, 9447, -1, 9462, -1, 9438, -1], 'generators': [65, 256], 'label': '512.60809.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.bj1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267765
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '512.420058', 'aut_weyl_index': 8, 'centralizer': '256.a1.a1', 'complements': ['128.o1.a1', '128.o1.d1', '128.o1.b1', '128.o1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.c1.a1', '8.w1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6621, 6929, 6636, 3654, 6604, 6776, 6630, 3689], 'generators': [2, 392], 'label': '512.60809.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '256.6661', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267766
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '128.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.z1.a1', '32.z1.b1', '32.ba1.a1', '32.bg1.a1', '32.bg1.b1', '32.bh1.a1', '32.bl1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8606, -1, 8984, -1, 8594, -1, 8977, -1], 'generators': [257, 4, 392], 'label': '512.60809.16.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bk1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267767
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.z1.b1', '32.bb1.a1', '32.bc1.b1', '32.bd1.a1', '32.be1.a1', '32.bg1.a1', '32.bi1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8413, -1, 8773, -1, 8401, -1, 8765, -1], 'generators': [1, 4, 136], 'label': '512.60809.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bl1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67267768
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.z1.a1', '32.bb1.a1', '32.bc1.a1', '32.bd1.a1', '32.be1.b1', '32.bg1.b1', '32.bi1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8413, -1, 8883, -1, 8401, -1, 8875, -1], 'generators': [257, 4, 136], 'label': '512.60809.16.bl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bl1.a2', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a2', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67267769
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.123', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1'], 'contains': ['32.bf1.a1', '32.bj1.a1', '32.bm1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9838, -1, 9862, -1, 9824, -1, 9855, -1], 'generators': [1, 452], 'label': '512.60809.16.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '16.bm1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67267770
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '128.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.ba1.a1', '32.bc1.a1', '32.bc1.b1', '32.be1.a1', '32.be1.b1', '32.bf1.a1', '32.bh1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8822, -1, 9103, -1, 8809, -1, 9092, -1], 'generators': [1, 4, 392], 'label': '512.60809.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bn1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267771
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.123', 'aut_weyl_index': 64, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1'], 'contains': ['32.bj1.a1', '32.bl1.a1', '32.bm1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9661, -1, 9706, -1, 9647, -1, 9699, -1], 'generators': [257, 452], 'label': '512.60809.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '16.bo1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67267772
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1'], 'contains': ['32.bn1.b1', '32.bo1.c1', '32.bp1.b1', '32.bq1.a1', '32.bs1.a1', '32.bu1.c1', '32.bv1.b1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 407, -1, 369, -1, 406, -1], 'generators': [35, 96, 4], 'label': '512.60809.16.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '16.bp1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267773
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1'], 'contains': ['32.bn1.a1', '32.bo1.d1', '32.bp1.b1', '32.bq1.a1', '32.bs1.b1', '32.bu1.d1', '32.bv1.a1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 1003, -1, 369, -1, 980, -1], 'generators': [35, 64, 4], 'label': '512.60809.16.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '16.bp1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267774
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.bn1.d1', '32.bo1.a1', '32.bp1.d1', '32.bq1.c1', '32.bs1.c1', '32.bu1.b1', '32.bv1.d1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 1903, -1, 369, -1, 1900, -1], 'generators': [395, 96, 396], 'label': '512.60809.16.bp1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.bp1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267775
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.bn1.c1', '32.bo1.a1', '32.bp1.c1', '32.bq1.d1', '32.bs1.c1', '32.bu1.a1', '32.bv1.c1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 2036, -1, 369, -1, 2034, -1], 'generators': [395, 64, 396], 'label': '512.60809.16.bp1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.bp1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267776
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '512.420058', 'aut_weyl_index': 8, 'centralizer': '256.a1.a1', 'complements': ['128.o1.a1', '128.o1.d1', '128.o1.c1', '128.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.c1.a1', '8.w1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6621, 6929, 6778, 4955, 6604, 6776, 6772, 5002], 'generators': [66, 392], 'label': '512.60809.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '256.6661', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267777
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1'], 'contains': ['32.bn1.a1', '32.bo1.c1', '32.bp1.a1', '32.bq1.b1', '32.bs1.a1', '32.bu1.a1', '32.bv1.a1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 824, -1, 369, -1, 823, -1], 'generators': [3, 64, 4], 'label': '512.60809.16.bp1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '16.bp1.e1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.e1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267778
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1'], 'contains': ['32.bn1.b1', '32.bo1.d1', '32.bp1.a1', '32.bq1.b1', '32.bs1.b1', '32.bu1.b1', '32.bv1.b1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 599, -1, 369, -1, 599, -1], 'generators': [3, 96, 4], 'label': '512.60809.16.bp1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '16.bp1.f1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.f1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267779
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.bn1.c1', '32.bo1.b1', '32.bp1.d1', '32.bq1.c1', '32.bs1.d1', '32.bu1.d1', '32.bv1.c1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 2171, -1, 369, -1, 2169, -1], 'generators': [427, 64, 396], 'label': '512.60809.16.bp1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.bp1.g1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.g1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267780
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.bn1.d1', '32.bo1.b1', '32.bp1.c1', '32.bq1.d1', '32.bs1.d1', '32.bu1.c1', '32.bv1.d1'], 'core': '512.a1.a1', 'coset_action_label': '16T972', 'count': 8, 'diagramx': [370, -1, 1768, -1, 369, -1, 1765, -1], 'generators': [427, 96, 396], 'label': '512.60809.16.bp1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.bp1.h1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.h1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267781
    {'ambient': '512.60809', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.m1.a1', '16.m1.b1', '16.s1.a1', '16.bd1.a1', '16.bg1.a1', '16.bh1.a1', '16.bh1.b1'], 'contains': ['64.a1.a1', '64.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5283, 5493, 5885, 3637, 5275, 5278, 5881, 3671], 'generators': [128, 304], 'label': '512.60809.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.b1', '16.a1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267782
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a1', '16.n1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.g1.a1', '64.v1.a1', '64.v1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4495, -1, 5532, -1, 4489, -1, 5527, -1], 'generators': [3, 308, 32], 'label': '512.60809.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267783
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.i1.b1', '16.n1.b1'], 'contains': ['64.b1.b1', '64.d1.b1', '64.g1.b1', '64.v1.c1', '64.v1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4495, -1, 6296, -1, 4489, -1, 6291, -1], 'generators': [459, 188, 32], 'label': '512.60809.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '32.b1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267784
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.k1.a1', '16.o1.b1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.g1.b1', '64.w1.a1', '64.w1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4083, -1, 5316, -1, 4076, -1, 5312, -1], 'generators': [3, 244, 32], 'label': '512.60809.32.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '32.c1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267785
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.k1.a1', '16.o1.a1'], 'contains': ['64.b1.b1', '64.e1.a1', '64.g1.a1', '64.w1.c1', '64.w1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4083, -1, 5181, -1, 4076, -1, 5177, -1], 'generators': [307, 244, 32], 'label': '512.60809.32.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '32.c1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267786
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.m1.a1', '16.n1.a1', '16.o1.a1'], 'contains': ['64.b1.a1', '64.f1.a1', '64.g1.a1', '64.x1.a1', '64.y1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3806, -1, 4028, -1, 3801, -1, 4025, -1], 'generators': [3, 128, 32], 'label': '512.60809.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.d1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267806
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.i1.a1', '16.r1.a1', '16.u1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.p1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6640, -1, 7336, -1, 6630, -1, 7330, -1], 'generators': [4, 304, 256], 'label': '512.60809.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.n1.a1', 'projective_image': '256.6661', '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': '64.138'}
  • id: 67267787
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dgh', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['128.o1.a1', '128.o1.d1', '128.o1.c1', '128.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'contains': ['8.c1.a1', '8.ba1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7434, 5028, 7418, 6211, 7424, 4916, 7411, 6270], 'generators': [65, 4], 'label': '512.60809.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.b1', '2.b1.a1', '2.d1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '256.6661', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267788
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.d1.b1', '16.e1.b1', '16.f1.b1', '16.m1.b1', '16.n1.b1', '16.o1.b1'], 'contains': ['64.b1.b1', '64.f1.a1', '64.g1.b1', '64.x1.b1', '64.y1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3806, -1, 4902, -1, 3801, -1, 4898, -1], 'generators': [455, 432, 32], 'label': '512.60809.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.d1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267789
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.k1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5098, -1, 6062, -1, 5091, -1, 6057, -1], 'generators': [3, 304], 'label': '512.60809.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.e1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267790
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.k1.a1', '16.m1.b1'], 'contains': ['64.a1.a1', '64.b1.b1', '64.g1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5098, -1, 6419, -1, 5091, -1, 6414, -1], 'generators': [455, 304], 'label': '512.60809.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.e1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267791
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.i1.a1', '16.n1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.h1.a1', '64.z1.a1', '64.z1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4914, -1, 5966, -1, 4907, -1, 5961, -1], 'generators': [3, 4, 256, 32], 'label': '512.60809.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '32.f1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267792
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '16.i1.b1', '16.n1.b1'], 'contains': ['64.b1.b1', '64.d1.b1', '64.h1.b1', '64.z1.c1', '64.z1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4914, -1, 6625, -1, 4907, -1, 6621, -1], 'generators': [459, 396, 256, 32], 'label': '512.60809.32.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '32.f1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267793
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.o1.a1', '16.o1.b1'], 'contains': ['64.b1.a1', '64.b1.b1', '64.e1.a1', '64.i1.a1', '64.ba1.a1', '64.ba1.b1', '64.ba1.c1', '64.ba1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4289, -1, 5423, -1, 4283, -1, 5420, -1], 'generators': [3, 452, 256, 32], 'label': '512.60809.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '32.g1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267794
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.j1.a1', '16.l1.a1', '16.m1.a1', '16.n1.a1', '16.o1.b1', '16.p1.a1'], 'contains': ['64.b1.a1', '64.f1.a1', '64.bb1.a1', '64.bb1.b1', '64.bc1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1934, -1, 3142, -1, 1931, -1, 3139, -1], 'generators': [3, 432, 32], 'label': '512.60809.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.h1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267795
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.j1.b1', '16.l1.b1', '16.m1.b1', '16.n1.b1', '16.o1.a1', '16.p1.a1'], 'contains': ['64.b1.b1', '64.f1.a1', '64.bb1.c1', '64.bb1.d1', '64.bc1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1934, -1, 3545, -1, 1931, -1, 3542, -1], 'generators': [455, 128, 32], 'label': '512.60809.32.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.h1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267796
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.q1.a1', '16.u1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.j1.a1', '64.l1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6897, -1, 7850, -1, 6887, -1, 7844, -1], 'generators': [1, 4, 256], 'label': '512.60809.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '32.i1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267797
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '16.q1.b1', '16.u1.b1'], 'contains': ['64.c1.a1', '64.d1.b1', '64.j1.b1', '64.l1.b1', '64.n1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6897, -1, 7985, -1, 6887, -1, 7979, -1], 'generators': [1, 12, 256], 'label': '512.60809.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '32.i1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267798
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493114', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.b1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.v1.b1', '8.x1.a1', '8.z1.a1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4310, -1, 5487, -1, 4375, -1, 5482, -1], 'generators': [3, 64, 396], 'label': '512.60809.4.f1.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.f1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67267799
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.r1.b1', '16.s1.a1', '16.t1.a1', '16.u1.a1', '16.u1.b1', '16.v1.a1'], 'contains': ['64.a1.a1', '64.c1.a1', '64.k1.a1', '64.m1.a1', '64.r1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7301, -1, 8196, -1, 7290, -1, 8190, -1], 'generators': [1, 304, 256], 'label': '512.60809.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.j1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267800
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a1', '16.q1.a1'], 'contains': ['64.d1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5466, -1, 6173, -1, 5459, -1, 6168, -1], 'generators': [307, 4], 'label': '512.60809.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '32.k1.a1', 'projective_image': '256.6661', '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': '32.27'}
  • id: 67267801
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.i1.b1', '16.q1.b1'], 'contains': ['64.d1.b1', '64.g1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5466, -1, 6529, -1, 5459, -1, 6524, -1], 'generators': [251, 396], 'label': '512.60809.32.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '32.k1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 67267802
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.q1.a1', '16.z1.a1'], 'contains': ['64.d1.a1', '64.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5936, -1, 6721, -1, 5927, -1, 6717, -1], 'generators': [2, 256], 'label': '512.60809.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '32.l1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267803
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '16.q1.b1', '16.z1.b1'], 'contains': ['64.d1.b1', '64.o1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5936, -1, 7212, -1, 5927, -1, 7207, -1], 'generators': [66, 256], 'label': '512.60809.32.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '32.l1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267804
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.h1.b1', '16.n1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1'], 'contains': ['64.d1.a1', '64.f1.a1', '64.bd1.a1', '64.be1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2841, -1, 3007, -1, 2837, -1, 3005, -1], 'generators': [4, 128, 32], 'label': '512.60809.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.m1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267805
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '16.c1.b1', '16.h1.a1', '16.n1.b1', '16.w1.b1', '16.x1.b1', '16.y1.b1'], 'contains': ['64.d1.b1', '64.f1.a1', '64.bd1.b1', '64.be1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2841, -1, 5047, -1, 2837, -1, 5043, -1], 'generators': [396, 128, 32], 'label': '512.60809.32.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.m1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267807
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '16.i1.b1', '16.r1.b1', '16.u1.b1', '16.z1.b1', '16.ba1.b1', '16.bb1.a1'], 'contains': ['64.a1.a1', '64.d1.b1', '64.p1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6640, -1, 7470, -1, 6630, -1, 7464, -1], 'generators': [396, 304, 256], 'label': '512.60809.32.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '32.n1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 67267808
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.d1.b1', '16.k1.a1'], 'contains': ['64.e1.a1', '64.g1.a1', '64.g1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4731, -1, 5654, -1, 4723, -1, 5650, -1], 'generators': [307, 452], 'label': '512.60809.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '32.o1.a1', 'projective_image': '256.6661', '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': '16.14'}
  • id: 67267809
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493114', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.a1', '8.i1.b1', '8.j1.b1', '8.k1.b1', '8.v1.a1', '8.x1.a1', '8.z1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4310, -1, 5731, -1, 4375, -1, 5726, -1], 'generators': [395, 64, 4], 'label': '512.60809.4.f1.b1', '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.f1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67267810
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.j1.a1', '16.o1.a1', '16.w1.a1', '16.x1.a1', '16.bc1.a1', '16.bd1.a1'], 'contains': ['64.e1.a1', '64.f1.a1', '64.bf1.a1', '64.bg1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2191, -1, 2873, -1, 2188, -1, 2870, -1], 'generators': [452, 128, 32], 'label': '512.60809.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.p1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267811
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.j1.b1', '16.o1.b1', '16.w1.b1', '16.x1.b1', '16.bc1.b1', '16.bd1.a1'], 'contains': ['64.e1.a1', '64.f1.a1', '64.bf1.a2', '64.bg1.a2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2191, -1, 4173, -1, 2188, -1, 4169, -1], 'generators': [452, 432, 32], 'label': '512.60809.32.p1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.p1.a2', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a2', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267812
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.138', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.bd1.a1', '16.be1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.q1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5701, -1, 7090, -1, 5693, -1, 7085, -1], 'generators': [452, 304, 256], 'label': '512.60809.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.q1.a1', 'projective_image': '256.6661', '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': '32.27'}
  • id: 67267813
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.b1', '16.l1.b1', '16.m1.a1', '16.y1.b1', '16.bc1.a1', '16.bf1.a1'], 'contains': ['64.f1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3058, -1, 4689, -1, 3053, -1, 4686, -1], 'generators': [307, 432], 'label': '512.60809.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.r1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267814
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.d1.a1', '16.l1.a1', '16.m1.b1', '16.y1.a1', '16.bc1.b1', '16.bf1.a1'], 'contains': ['64.f1.a1', '64.g1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3058, -1, 4779, -1, 3053, -1, 4776, -1], 'generators': [247, 128], 'label': '512.60809.32.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.r1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267815
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.e1.b1', '16.p1.a1', '16.w1.a1', '16.w1.b1', '16.bf1.a1', '16.bg1.a1'], 'contains': ['64.f1.a1', '64.bh1.a1', '64.bh1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [907, -1, 1706, -1, 906, -1, 1704, -1], 'generators': [64, 32], 'label': '512.60809.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.s1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267816
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.f1.b1', '16.l1.a1', '16.l1.b1', '16.x1.a1', '16.x1.b1', '16.bg1.a1'], 'contains': ['64.f1.a1', '64.bj1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2448, -1, 3680, -1, 2445, -1, 3677, -1], 'generators': [368, 32], 'label': '512.60809.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.t1.a1', 'projective_image': '256.6661', '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: 67267817
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.f1.a1', '16.h1.b1', '16.j1.a1', '16.y1.a1', '16.bc1.a1', '16.bh1.a1'], 'contains': ['64.f1.a1', '64.bi1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1162, -1, 2738, -1, 1161, -1, 2736, -1], 'generators': [67, 32], 'label': '512.60809.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.u1.a1', 'projective_image': '256.6661', '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: 67267818
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.f1.b1', '16.h1.a1', '16.j1.b1', '16.y1.b1', '16.bc1.b1', '16.bh1.b1'], 'contains': ['64.f1.a1', '64.bi1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1162, -1, 3813, -1, 1161, -1, 3810, -1], 'generators': [395, 32], 'label': '512.60809.32.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.u1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267819
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.t1.a1', '16.v1.a1', '16.bb1.a1', '16.be1.a1', '16.bi1.a1', '16.bj1.a1'], 'contains': ['64.a1.a1', '64.s1.a1', '64.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8724, -1, 9333, -1, 8712, -1, 9326, -1], 'generators': [392, 256], 'label': '512.60809.32.v1.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.v1.a1', 'projective_image': '256.6661', '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: 67267820
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.h1.a1', '8.r1.a1', '8.w1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5891, -1, 7030, -1, 5882, -1, 7024, -1], 'generators': [1, 2, 128], 'label': '512.60809.4.g1.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.g1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267821
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.r1.b1', '16.s1.a1', '16.t1.a1', '16.ba1.a1', '16.ba1.b1', '16.bi1.a1'], 'contains': ['64.a1.a1', '64.u1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7121, -1, 8101, -1, 7111, -1, 8095, -1], 'generators': [129, 256], 'label': '512.60809.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.w1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267822
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1'], 'contains': ['64.h1.a1', '64.l1.a1', '64.o1.a1', '64.bk1.a1', '64.bk1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6382, -1, 6845, -1, 6374, -1, 6839, -1], 'generators': [1, 2, 32], 'label': '512.60809.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '32.x1.a1', 'projective_image': '256.6661', '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': '8.5'}
  • id: 67267823
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1'], 'contains': ['64.h1.b1', '64.l1.b1', '64.o1.b1', '64.bk1.c1', '64.bk1.d1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6382, -1, 7605, -1, 6374, -1, 7599, -1], 'generators': [185, 66, 32], 'label': '512.60809.32.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '32.x1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267824
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1'], 'contains': ['64.h1.a1', '64.n1.a1', '64.o1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6148, -1, 6967, -1, 6139, -1, 6962, -1], 'generators': [257, 2], 'label': '512.60809.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '32.y1.a1', 'projective_image': '256.6661', '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': '8.5'}
  • id: 67267825
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1'], 'contains': ['64.h1.b1', '64.n1.b1', '64.o1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6148, -1, 7727, -1, 6139, -1, 7721, -1], 'generators': [441, 66], 'label': '512.60809.32.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '32.y1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67267826
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.bk1.a1', '16.bl1.a2'], 'contains': ['64.j1.a1', '64.k1.a1', '64.n1.a1', '64.p1.a1', '64.r1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7474, -1, 8286, -1, 7463, -1, 8280, -1], 'generators': [257, 4, 304], 'label': '512.60809.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.z1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267827
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.b1', '16.bk1.a1', '16.bl1.a1'], 'contains': ['64.j1.b1', '64.k1.a1', '64.n1.b1', '64.p1.b1', '64.r1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7474, -1, 8513, -1, 7463, -1, 8506, -1], 'generators': [257, 12, 304], 'label': '512.60809.32.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.z1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267828
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.bk1.a1', '16.bn1.a1'], 'contains': ['64.k1.a1', '64.s1.a1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8980, -1, 9466, -1, 8967, -1, 9460, -1], 'generators': [1, 8], 'label': '512.60809.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.ba1.a1', 'projective_image': '256.6661', '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: 67267829
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.bl1.a1', '16.bl1.a2'], 'contains': ['64.k1.a1', '64.t1.a1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8368, -1, 9005, -1, 8356, -1, 8998, -1], 'generators': [1, 264], 'label': '512.60809.32.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bb1.a1', 'projective_image': '256.6661', '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': '8.5'}
  • id: 67267830
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.bl1.a2', '16.bn1.a1'], 'contains': ['64.m1.a1', '64.p1.a1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8071, -1, 9090, -1, 8059, -1, 9083, -1], 'generators': [1, 132], 'label': '512.60809.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bc1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267831
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.b1', '8.g1.b1', '8.h1.b1', '8.r1.b1', '8.w1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5891, -1, 7282, -1, 5882, -1, 7275, -1], 'generators': [393, 66, 128], 'label': '512.60809.4.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.g1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267832
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.b1', '16.bl1.a1', '16.bn1.a1'], 'contains': ['64.m1.a1', '64.p1.b1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8071, -1, 9231, -1, 8059, -1, 9224, -1], 'generators': [1, 396], 'label': '512.60809.32.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bc1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267833
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bl1.a1', '16.bl1.a2'], 'contains': ['64.m1.a1', '64.r1.a1', '64.t1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9199, -1, 9581, -1, 9186, -1, 9574, -1], 'generators': [1, 136], 'label': '512.60809.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bd1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267834
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.bl1.a1', '16.bn1.a1'], 'contains': ['64.j1.a1', '64.k1.a1', '64.l1.a1', '64.m1.a1', '64.p1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7690, -1, 8399, -1, 7679, -1, 8393, -1], 'generators': [1, 4, 304], 'label': '512.60809.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.be1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267835
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.b1', '16.bl1.a2', '16.bn1.a1'], 'contains': ['64.j1.b1', '64.k1.a1', '64.l1.b1', '64.m1.a1', '64.p1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7690, -1, 8625, -1, 7679, -1, 8619, -1], 'generators': [1, 12, 304], 'label': '512.60809.32.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.be1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267836
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '32.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bm1.a1', '16.bn1.a1'], 'contains': ['64.m1.a1', '64.s1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9663, -1, 9753, -1, 9649, -1, 9746, -1], 'generators': [1, 392], 'label': '512.60809.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.bf1.a1', 'projective_image': '256.6661', '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': '16.7'}
  • id: 67267837
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.bk1.a1', '16.bl1.a1'], 'contains': ['64.p1.a1', '64.r1.a1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7911, -1, 8811, -1, 7900, -1, 8805, -1], 'generators': [257, 132], 'label': '512.60809.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bg1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267838
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.b1', '16.bk1.a1', '16.bl1.a2'], 'contains': ['64.p1.b1', '64.r1.a1', '64.u1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7911, -1, 8908, -1, 7900, -1, 8901, -1], 'generators': [257, 396], 'label': '512.60809.32.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bg1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267839
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bk1.a1', '16.bn1.a1'], 'contains': ['64.p1.a1', '64.p1.b1', '64.s1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8529, -1, 9161, -1, 8517, -1, 9154, -1], 'generators': [4, 392], 'label': '512.60809.32.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bh1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267840
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bl1.a1', '16.bl1.a2'], 'contains': ['64.p1.a1', '64.p1.b1', '64.t1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8206, -1, 8728, -1, 8194, -1, 8721, -1], 'generators': [4, 136], 'label': '512.60809.32.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.bi1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67267841
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.bm1.a1', '16.bo1.a1'], 'contains': ['64.q1.a1', '64.s1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9798, -1, 9895, -1, 9784, -1, 9887, -1], 'generators': [452, 392], 'label': '512.60809.32.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '32.bj1.a1', 'projective_image': '256.6661', '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': '16.7'}
  • id: 67267842
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.djj', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['256.f1.a1', '256.c1.c1', '256.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.g1.a1', '4.k1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5925, 6929, 7014, 7728, 5916, 6776, 7008, 7802], 'generators': [1, 2, 392], 'label': '512.60809.2.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.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267843
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1024.diu', 'aut_weyl_index': 4, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.j1.b1', '8.l1.a1', '8.l1.b1', '8.n1.a1', '8.x1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4978, -1, 5858, -1, 4971, -1, 5852, -1], 'generators': [3, 452, 392], 'label': '512.60809.4.h1.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.h1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67267844
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1'], 'contains': ['64.q1.a1', '64.t1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9359, -1, 9824, -1, 9346, -1, 9816, -1], 'generators': [452, 136], 'label': '512.60809.32.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.y1.a1', 'old_label': '32.bk1.a1', 'projective_image': '256.6661', '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': '16.8'}
  • id: 67267845
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '32.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bk1.a1', '16.bo1.a1'], 'contains': ['64.r1.a1', '64.s1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9512, -1, 9674, -1, 9497, -1, 9667, -1], 'generators': [257, 392], 'label': '512.60809.32.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.bl1.a1', 'projective_image': '256.6661', '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': '16.7'}
  • id: 67267847
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.bp1.b1', '16.bp1.e1'], 'contains': ['64.x1.a1', '64.bh1.a1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10871', 'count': 8, 'diagramx': [246, -1, 474, -1, 246, -1, 474, -1], 'generators': [3, 64], 'label': '512.60809.32.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bn1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267848
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.bp1.a1', '16.bp1.f1'], 'contains': ['64.x1.a1', '64.bh1.b1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10871', 'count': 8, 'diagramx': [246, -1, 129, -1, 246, -1, 129, -1], 'generators': [3, 96], 'label': '512.60809.32.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bn1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267849
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.bp1.d1', '16.bp1.g1'], 'contains': ['64.x1.b1', '64.bh1.a1', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10871', 'count': 8, 'diagramx': [246, -1, 2193, -1, 246, -1, 2191, -1], 'generators': [395, 64], 'label': '512.60809.32.bn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bn1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267850
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.bp1.c1', '16.bp1.h1'], 'contains': ['64.x1.b1', '64.bh1.b1', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10871', 'count': 8, 'diagramx': [246, -1, 1572, -1, 246, -1, 1571, -1], 'generators': [395, 96], 'label': '512.60809.32.bn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bn1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267851
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.bp1.c1', '16.bp1.d1'], 'contains': ['64.bb1.a1', '64.bd1.b1', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10872', 'count': 8, 'diagramx': [712, -1, 2020, -1, 711, -1, 2018, -1], 'generators': [3, 396], 'label': '512.60809.32.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bo1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267852
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.bp1.g1', '16.bp1.h1'], 'contains': ['64.bb1.b1', '64.bd1.b1', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10872', 'count': 8, 'diagramx': [712, -1, 1878, -1, 711, -1, 1877, -1], 'generators': [35, 396], 'label': '512.60809.32.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bo1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267853
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.bp1.a1', '16.bp1.e1'], 'contains': ['64.bb1.c1', '64.bd1.a1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10872', 'count': 8, 'diagramx': [712, -1, 373, -1, 711, -1, 372, -1], 'generators': [67, 4], 'label': '512.60809.32.bo1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bo1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267854
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53342', 'aut_weyl_index': 16, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.e1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.l1.b1', '8.o1.a1', '8.z1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4684, -1, 5610, -1, 4675, -1, 5604, -1], 'generators': [3, 64, 392], 'label': '512.60809.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.i1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67267855
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.bp1.b1', '16.bp1.f1'], 'contains': ['64.bb1.d1', '64.bd1.a1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10872', 'count': 8, 'diagramx': [712, -1, 576, -1, 711, -1, 576, -1], 'generators': [99, 4], 'label': '512.60809.32.bo1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bo1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267856
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.bp1.e1', '16.bp1.f1'], 'contains': ['64.bb1.a1', '64.bf1.a1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10870', 'count': 8, 'diagramx': [441, -1, 302, -1, 441, -1, 301, -1], 'generators': [7, 452], 'label': '512.60809.32.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bp1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267857
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.bp1.a1', '16.bp1.b1'], 'contains': ['64.bb1.b1', '64.bf1.a1', '64.bi1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10870', 'count': 8, 'diagramx': [441, -1, 231, -1, 441, -1, 231, -1], 'generators': [39, 452], 'label': '512.60809.32.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bp1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267858
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.bp1.d1', '16.bp1.h1'], 'contains': ['64.bb1.c1', '64.bf1.a2', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10870', 'count': 8, 'diagramx': [441, -1, 1949, -1, 441, -1, 1948, -1], 'generators': [399, 452], 'label': '512.60809.32.bp1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bp1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267859
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.bp1.c1', '16.bp1.g1'], 'contains': ['64.bb1.d1', '64.bf1.a2', '64.bi1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10870', 'count': 8, 'diagramx': [441, -1, 2091, -1, 441, -1, 2089, -1], 'generators': [431, 452], 'label': '512.60809.32.bp1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bp1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267860
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bp1.a1', '16.bp1.b1'], 'contains': ['64.v1.b1', '64.x1.a1', '64.z1.a1', '64.bb1.b1', '64.bd1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10868', 'count': 8, 'diagramx': [1677, -1, 1026, -1, 1675, -1, 1025, -1], 'generators': [35, 4, 128], 'label': '512.60809.32.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bq1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267861
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bp1.e1', '16.bp1.f1'], 'contains': ['64.v1.a1', '64.x1.a1', '64.z1.b1', '64.bb1.a1', '64.bd1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10868', 'count': 8, 'diagramx': [1677, -1, 1367, -1, 1675, -1, 1366, -1], 'generators': [3, 4, 128], 'label': '512.60809.32.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bq1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267862
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '16.bp1.c1', '16.bp1.g1'], 'contains': ['64.v1.d1', '64.x1.b1', '64.z1.c1', '64.bb1.d1', '64.bd1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10868', 'count': 8, 'diagramx': [1677, -1, 3410, -1, 1675, -1, 3408, -1], 'generators': [491, 396, 128], 'label': '512.60809.32.bq1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bq1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267863
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '16.bp1.d1', '16.bp1.h1'], 'contains': ['64.v1.c1', '64.x1.b1', '64.z1.d1', '64.bb1.c1', '64.bd1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10868', 'count': 8, 'diagramx': [1677, -1, 3276, -1, 1675, -1, 3273, -1], 'generators': [459, 396, 128], 'label': '512.60809.32.bq1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bq1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267864
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1'], 'contains': ['64.v1.a1', '64.v1.b1', '64.y1.a1', '64.z1.a1', '64.z1.b1', '64.bc1.a1', '64.be1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T21635', 'count': 16, 'diagramx': [3531, -1, 4441, -1, 3525, -1, 4438, -1], 'generators': [3, 4, 160], 'label': '512.60809.32.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '32.br1.a1', 'projective_image': '512.60809', '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': '4.2'}
  • id: 67267865
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493114', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.b1', '8.f1.b1', '8.i1.a1', '8.j1.b1', '8.k1.b1', '8.m1.b1', '8.m2.b1', '8.n1.a1', '8.o1.a1', '8.p1.a1', '8.v1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3583, -1, 4910, -1, 3578, -1, 4905, -1], 'generators': [395, 64, 396, 304], 'label': '512.60809.4.j1.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.j1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67267866
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1'], 'contains': ['64.v1.c1', '64.v1.d1', '64.y1.b1', '64.z1.c1', '64.z1.d1', '64.bc1.b1', '64.be1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T21635', 'count': 16, 'diagramx': [3531, -1, 5777, -1, 3525, -1, 5773, -1], 'generators': [459, 396, 160], 'label': '512.60809.32.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '32.br1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267867
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.bp1.a1', '16.bp1.e1'], 'contains': ['64.w1.c1', '64.x1.a1', '64.ba1.a1', '64.bb1.c1', '64.bf1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10869', 'count': 8, 'diagramx': [1419, -1, 892, -1, 1418, -1, 891, -1], 'generators': [3, 452, 128], 'label': '512.60809.32.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bs1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267868
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.bp1.b1', '16.bp1.f1'], 'contains': ['64.w1.d1', '64.x1.a1', '64.ba1.b1', '64.bb1.d1', '64.bf1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10869', 'count': 8, 'diagramx': [1419, -1, 1232, -1, 1418, -1, 1232, -1], 'generators': [35, 452, 128], 'label': '512.60809.32.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bs1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267869
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.bp1.c1', '16.bp1.d1'], 'contains': ['64.w1.a1', '64.x1.b1', '64.ba1.c1', '64.bb1.a1', '64.bf1.a2'], 'core': '512.a1.a1', 'coset_action_label': '32T10869', 'count': 8, 'diagramx': [1419, -1, 2532, -1, 1418, -1, 2531, -1], 'generators': [3, 452, 400], 'label': '512.60809.32.bs1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bs1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267870
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.bp1.g1', '16.bp1.h1'], 'contains': ['64.w1.b1', '64.x1.b1', '64.ba1.d1', '64.bb1.b1', '64.bf1.a2'], 'core': '512.a1.a1', 'coset_action_label': '32T10869', 'count': 8, 'diagramx': [1419, -1, 2398, -1, 1418, -1, 2396, -1], 'generators': [35, 452, 400], 'label': '512.60809.32.bs1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bs1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267871
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1'], 'contains': ['64.w1.c1', '64.w1.d1', '64.y1.a1', '64.ba1.a1', '64.ba1.b1', '64.bc1.b1', '64.bg1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T21959', 'count': 16, 'diagramx': [3273, -1, 4307, -1, 3268, -1, 4304, -1], 'generators': [3, 452, 160], 'label': '512.60809.32.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '32.bt1.a1', 'projective_image': '512.60809', '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': '4.2'}
  • id: 67267872
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1'], 'contains': ['64.w1.a1', '64.w1.b1', '64.y1.b1', '64.ba1.c1', '64.ba1.d1', '64.bc1.a1', '64.bg1.a2'], 'core': '512.a1.a1', 'coset_action_label': '32T21959', 'count': 16, 'diagramx': [3273, -1, 4576, -1, 3268, -1, 4573, -1], 'generators': [3, 452, 432], 'label': '512.60809.32.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '32.bt1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267873
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bp1.d1', '16.bp1.e1'], 'contains': ['64.bb1.a1', '64.bb1.c1', '64.bh1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10866', 'count': 2, 'diagramx': [51, -1, 1129, -1, 51, -1, 1128, -1], 'generators': [7, 64], 'label': '512.60809.32.bu1.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': '32.bu1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267874
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bp1.c1', '16.bp1.f1'], 'contains': ['64.bb1.a1', '64.bb1.d1', '64.bh1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10866', 'count': 2, 'diagramx': [51, -1, 789, -1, 51, -1, 788, -1], 'generators': [7, 96], 'label': '512.60809.32.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bu1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267875
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bp1.a1', '16.bp1.h1'], 'contains': ['64.bb1.b1', '64.bb1.c1', '64.bh1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10866', 'count': 2, 'diagramx': [51, -1, 718, -1, 51, -1, 717, -1], 'generators': [39, 96], 'label': '512.60809.32.bu1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bu1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267876
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.10493114', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.i1.b1', '8.j1.a1', '8.k1.a1', '8.m1.a1', '8.m2.a1', '8.n1.a1', '8.o1.a1', '8.p1.b1', '8.v1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3583, -1, 4589, -1, 3578, -1, 4584, -1], 'generators': [3, 64, 4, 304], 'label': '512.60809.4.j1.b1', '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.j1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67267877
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.43', 'aut_weyl_index': 128, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bp1.b1', '16.bp1.g1'], 'contains': ['64.bb1.b1', '64.bb1.d1', '64.bh1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10866', 'count': 2, 'diagramx': [51, -1, 1470, -1, 51, -1, 1469, -1], 'generators': [39, 64], 'label': '512.60809.32.bu1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bu1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267878
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.bp1.b1', '16.bp1.e1'], 'contains': ['64.bd1.a1', '64.bf1.a1', '64.bh1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10867', 'count': 8, 'diagramx': [576, -1, 647, -1, 576, -1, 647, -1], 'generators': [64, 4], 'label': '512.60809.32.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bv1.a1', 'projective_image': '512.60809', '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: 67267879
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.bp1.a1', '16.bp1.f1'], 'contains': ['64.bd1.a1', '64.bf1.a1', '64.bh1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10867', 'count': 8, 'diagramx': [576, -1, 26, -1, 576, -1, 26, -1], 'generators': [96, 4], 'label': '512.60809.32.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '32.bv1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267880
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.b1', '16.bp1.d1', '16.bp1.g1'], 'contains': ['64.bd1.b1', '64.bf1.a2', '64.bh1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T10867', 'count': 8, 'diagramx': [576, -1, 2294, -1, 576, -1, 2293, -1], 'generators': [64, 396], 'label': '512.60809.32.bv1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bv1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267881
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.b1', '16.bp1.c1', '16.bp1.h1'], 'contains': ['64.bd1.b1', '64.bf1.a2', '64.bh1.b1'], 'core': '512.a1.a1', 'coset_action_label': '32T10867', 'count': 8, 'diagramx': [576, -1, 1807, -1, 576, -1, 1806, -1], 'generators': [96, 396], 'label': '512.60809.32.bv1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.bv1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267882
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1'], 'contains': ['64.be1.a1', '64.bg1.a1', '64.bj1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T21596', 'count': 16, 'diagramx': [2644, -1, 2636, -1, 2640, -1, 2634, -1], 'generators': [368, 4], 'label': '512.60809.32.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.x1.a1', 'old_label': '32.bw1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267883
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.b1'], 'contains': ['64.be1.b1', '64.bg1.a2', '64.bj1.a1'], 'core': '512.a1.a1', 'coset_action_label': '32T21596', 'count': 16, 'diagramx': [2644, -1, 3916, -1, 2640, -1, 3912, -1], 'generators': [368, 396], 'label': '512.60809.32.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.x1.b1', 'old_label': '32.bw1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267884
    {'ambient': '512.60809', 'aut_centralizer_order': 512, 'aut_label': '64.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.e1.a1', '32.e1.b1', '32.j1.a1', '32.n1.a1', '32.n1.b1', '32.q1.a1', '32.v1.a1', '32.w1.a1'], 'contains': ['128.a1.a1', '128.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6382, 5493, 6979, 3637, 6374, 5278, 6973, 3671], 'generators': [304, 256], 'label': '512.60809.64.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': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267885
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.h1.a1', '128.h1.b1', '128.h2.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4191, -1, 5497, -1, 4183, -1, 5493, -1], 'generators': [3, 256, 32], 'label': '512.60809.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '64.b1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267886
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.c1.b1', '32.d1.b1', '32.e1.b1', '32.f1.b1', '32.g1.a1', '32.h1.b1'], 'contains': ['128.a1.a1', '128.b1.b1', '128.h1.c1', '128.h1.d1', '128.h2.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4191, -1, 5986, -1, 4183, -1, 5982, -1], 'generators': [455, 256, 32], 'label': '512.60809.64.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.b1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267887
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.r1.a1', '8.w1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5641, -1, 6905, -1, 5573, -1, 6898, -1], 'generators': [393, 2], 'label': '512.60809.4.k1.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.k1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267888
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.i1.b1', '32.j1.a1'], 'contains': ['128.a1.a1', '128.c1.a1', '128.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6988, -1, 7850, -1, 6977, -1, 7844, -1], 'generators': [1, 256], 'label': '512.60809.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.c1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267889
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.f1.a1', '32.i1.a1', '32.k1.a1', '32.l1.a1', '32.m1.a1', '32.n1.a1'], 'contains': ['128.a1.a1', '128.d1.a1', '128.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4914, -1, 6308, -1, 4907, -1, 6304, -1], 'generators': [4, 256, 32], 'label': '512.60809.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '64.d1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267890
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.f1.b1', '32.i1.b1', '32.k1.b1', '32.l1.b1', '32.m1.b1', '32.n1.b1'], 'contains': ['128.a1.a1', '128.d1.b1', '128.i1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4914, -1, 6562, -1, 4907, -1, 6558, -1], 'generators': [396, 256, 32], 'label': '512.60809.64.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '64.d1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267891
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.c1.b1', '32.g1.a1', '32.o1.a1', '32.p1.a1', '32.p1.a2', '32.q1.a1'], 'contains': ['128.a1.a1', '128.e1.a1', '128.j1.a1', '128.j1.a2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4346, -1, 5417, -1, 4337, -1, 5413, -1], 'generators': [452, 256, 32], 'label': '512.60809.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '64.e1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267892
    {'ambient': '512.60809', 'aut_centralizer_order': 1024, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '32.h1.a1', '32.h1.b1', '32.m1.a1', '32.m1.b1', '32.p1.a1', '32.p1.a2', '32.r1.a1', '32.r1.b1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.u1.b1'], 'contains': ['128.a1.a1', '128.k1.a1', '128.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2448, -1, 3853, -1, 2445, -1, 3850, -1], 'generators': [128, 32], 'label': '512.60809.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.f1.a1', 'projective_image': '256.6661', '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: 67267893
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.c1.b1', '32.d1.a1', '32.e1.a1', '32.k1.a1', '32.o1.a1', '32.r1.a1'], 'contains': ['128.a1.a1', '128.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4550, -1, 5604, -1, 4542, -1, 5600, -1], 'generators': [307, 32], 'label': '512.60809.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '64.g1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267894
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.c1.a1', '32.d1.b1', '32.e1.b1', '32.k1.b1', '32.o1.a1', '32.r1.b1'], 'contains': ['128.a1.a1', '128.m1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4550, -1, 5879, -1, 4542, -1, 5875, -1], 'generators': [247, 32], 'label': '512.60809.64.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.g1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267895
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.x1.a1', '32.y1.a1'], 'contains': ['128.b1.a1', '128.d1.a1', '128.n1.a1', '128.n2.a1', '128.n2.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5069, -1, 6389, -1, 5061, -1, 6384, -1], 'generators': [3, 4, 32], 'label': '512.60809.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '64.h1.a1', 'projective_image': '256.6661', '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: 67267896
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.x1.b1', '32.y1.b1'], 'contains': ['128.b1.b1', '128.d1.b1', '128.n1.b1', '128.n2.c1', '128.n2.d1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5069, -1, 7085, -1, 5061, -1, 7080, -1], 'generators': [459, 396, 32], 'label': '512.60809.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '64.h1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267897
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1'], 'contains': ['128.b1.a1', '128.b1.b1', '128.e1.a1', '128.o1.a1', '128.o1.b1', '128.o1.c1', '128.o1.d1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4758, -1, 6067, -1, 4750, -1, 6062, -1], 'generators': [3, 452, 32], 'label': '512.60809.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '64.i1.a1', 'projective_image': '256.6661', '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': '1.1'}
  • id: 67267898
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.b1.b1', '8.r1.b1', '8.w1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5641, -1, 7156, -1, 5573, -1, 7149, -1], 'generators': [1, 66], 'label': '512.60809.4.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.k1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267899
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.z1.a1', '32.be1.a1'], 'contains': ['128.c1.a1', '128.d1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7123, -1, 8055, -1, 7112, -1, 8049, -1], 'generators': [1, 260], 'label': '512.60809.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.u1.a1', 'old_label': '64.j1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267900
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.z1.b1', '32.be1.b1'], 'contains': ['128.c1.a1', '128.d1.b1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7123, -1, 8126, -1, 7112, -1, 8119, -1], 'generators': [1, 268], 'label': '512.60809.64.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.u1.b1', 'old_label': '64.j1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267901
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.z1.a1', '32.z1.b1', '32.ba1.a1', '32.bb1.a1', '32.be1.a1', '32.be1.b1'], 'contains': ['128.c1.a1', '128.f1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7690, -1, 8456, -1, 7679, -1, 8448, -1], 'generators': [1, 48], 'label': '512.60809.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.k1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267902
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.x1.a1', '32.be1.a1'], 'contains': ['128.c1.a1', '128.d1.a1', '128.p1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6843, -1, 7530, -1, 6833, -1, 7495, -1], 'generators': [1, 4, 32], 'label': '512.60809.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '64.l1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267903
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.x1.b1', '32.be1.b1'], 'contains': ['128.c1.a1', '128.d1.b1', '128.p1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6843, -1, 7774, -1, 6833, -1, 7769, -1], 'generators': [1, 12, 32], 'label': '512.60809.64.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '64.l1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267904
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.bc1.a1', '32.bc1.b1', '32.bd1.a1', '32.be1.a1', '32.be1.b1', '32.bf1.a1'], 'contains': ['128.c1.a1', '128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8155, -1, 8964, -1, 8144, -1, 8957, -1], 'generators': [1, 304], 'label': '512.60809.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '64.m1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267905
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.y1.a1', '32.z1.a1'], 'contains': ['128.d1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6638, -1, 7667, -1, 6629, -1, 7661, -1], 'generators': [257, 4], 'label': '512.60809.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '64.n1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267906
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.y1.b1', '32.z1.b1'], 'contains': ['128.d1.b1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6638, -1, 7953, -1, 6629, -1, 7946, -1], 'generators': [257, 12], 'label': '512.60809.64.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '64.n1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267907
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.x1.a1', '32.y1.a1'], 'contains': ['128.d1.a1', '128.q1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5964, -1, 6845, -1, 5955, -1, 6839, -1], 'generators': [2, 32], 'label': '512.60809.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '64.o1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267908
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.b1', '32.x1.b1', '32.y1.b1'], 'contains': ['128.d1.b1', '128.q1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5964, -1, 7394, -1, 5955, -1, 7358, -1], 'generators': [66, 32], 'label': '512.60809.64.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '64.o1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267909
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.6270162', 'aut_weyl_index': 8, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.s1.a1', '8.t1.a1', '8.y1.a1', '8.ba1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8129, -1, 8479, -1, 8116, -1, 8413, -1], 'generators': [1, 452, 128], 'label': '512.60809.4.l1.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.l1.a1', 'projective_image': '256.6661', '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': '128.351'}
  • id: 67267910
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '32.z1.a1', '32.bc1.a1', '32.be1.a1', '32.bg1.a1', '32.bh1.a1', '32.bi1.a1'], 'contains': ['128.d1.a1', '128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7494, -1, 8660, -1, 7484, -1, 8654, -1], 'generators': [4, 304], 'label': '512.60809.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.p1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267911
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.b1', '32.z1.b1', '32.bc1.b1', '32.be1.b1', '32.bg1.b1', '32.bh1.a1', '32.bi1.a1'], 'contains': ['128.d1.b1', '128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7494, -1, 8731, -1, 7484, -1, 8725, -1], 'generators': [396, 304], 'label': '512.60809.64.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.p1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267912
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1.a1', '32.bj1.a1', '32.bk1.a1'], 'contains': ['128.e1.a1', '128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8503, -1, 9106, -1, 8491, -1, 9098, -1], 'generators': [452, 304], 'label': '512.60809.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.q1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267913
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.z1.a1', '32.z1.b1', '32.bd1.a1', '32.bg1.a1', '32.bg1.b1', '32.bl1.a1'], 'contains': ['128.f1.a1', '128.g1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8020, -1, 8807, -1, 8009, -1, 8801, -1], 'generators': [257, 304], 'label': '512.60809.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '64.r1.a1', 'projective_image': '256.6661', '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': '8.3'}
  • id: 67267914
    {'ambient': '512.60809', 'aut_centralizer_order': 512, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.v1.a1', '32.ba1.a1', '32.bf1.a1', '32.bh1.a1', '32.bj1.a1', '32.bl1.a1', '32.bm1.a1'], 'contains': ['128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9244, -1, 9570, -1, 9231, -1, 9563, -1], 'generators': [392], 'label': '512.60809.64.s1.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': '64.s1.a1', 'projective_image': '256.6661', '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: 67267915
    {'ambient': '512.60809', 'aut_centralizer_order': 512, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.v1.a1', '32.bb1.a1', '32.bd1.a1', '32.bi1.a1', '32.bk1.a1'], 'contains': ['128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8368, -1, 9035, -1, 8356, -1, 9028, -1], 'generators': [136], 'label': '512.60809.64.t1.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': '64.t1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267916
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.w1.a1', '32.ba1.a1', '32.bb1.a1', '32.bc1.a1', '32.bc1.b1', '32.bg1.a1', '32.bg1.b1'], 'contains': ['128.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7884, -1, 8894, -1, 7874, -1, 8887, -1], 'generators': [129], 'label': '512.60809.64.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.u1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67267917
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.bq1.b1', '32.br1.a1'], 'contains': ['128.h1.a1', '128.i1.a1', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3883, -1, 4441, -1, 3876, -1, 4438, -1], 'generators': [3, 308], 'label': '512.60809.64.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '64.v1.a1', 'projective_image': '512.60809', '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': '4.2'}
  • id: 67267918
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.bq1.a1', '32.br1.a1'], 'contains': ['128.h1.b1', '128.i1.a1', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3883, -1, 4371, -1, 3876, -1, 4368, -1], 'generators': [35, 308], 'label': '512.60809.64.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '64.v1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267919
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.bq1.d1', '32.br1.b1'], 'contains': ['128.h1.c1', '128.i1.b1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3883, -1, 5707, -1, 3876, -1, 5702, -1], 'generators': [459, 188], 'label': '512.60809.64.v1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '64.v1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267920
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2310', 'aut_weyl_index': 32, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.e1.a1', '8.t1.a1', '8.ba1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7746, -1, 8058, -1, 7733, -1, 8114, -1], 'generators': [1, 64], 'label': '512.60809.4.m1.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.m1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67267921
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.bq1.c1', '32.br1.b1'], 'contains': ['128.h1.d1', '128.i1.b1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3883, -1, 5777, -1, 3876, -1, 5773, -1], 'generators': [491, 188], 'label': '512.60809.64.v1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '64.v1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267922
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.bs1.c1', '32.bt1.b1'], 'contains': ['128.h1.a1', '128.j1.a1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3339, -1, 4583, -1, 3332, -1, 4580, -1], 'generators': [3, 244], 'label': '512.60809.64.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '64.w1.a1', 'projective_image': '512.60809', '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': '4.2'}
  • id: 67267923
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.bs1.d1', '32.bt1.b1'], 'contains': ['128.h1.b1', '128.j1.a1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3339, -1, 4512, -1, 3332, -1, 4509, -1], 'generators': [35, 244], 'label': '512.60809.64.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '64.w1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267924
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.bs1.a1', '32.bt1.a1'], 'contains': ['128.h1.c1', '128.j1.a2', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3339, -1, 4159, -1, 3332, -1, 4156, -1], 'generators': [307, 244], 'label': '512.60809.64.w1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '64.w1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267925
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.bs1.b1', '32.bt1.a1'], 'contains': ['128.h1.d1', '128.j1.a2', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3339, -1, 4300, -1, 3332, -1, 4297, -1], 'generators': [275, 244], 'label': '512.60809.64.w1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '64.w1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267926
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.bn1.a1', '32.bn1.b1', '32.bq1.a1', '32.bq1.b1', '32.bs1.a1', '32.bs1.b1'], 'contains': ['128.h2.a1', '128.k1.a1', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1872, -1, 1299, -1, 1869, -1, 1324, -1], 'generators': [3, 128], 'label': '512.60809.64.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '64.x1.a1', 'projective_image': '512.60809', '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: 67267927
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.bn1.c1', '32.bn1.d1', '32.bq1.c1', '32.bq1.d1', '32.bs1.c1', '32.bs1.d1'], 'contains': ['128.h2.b1', '128.k1.a1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1872, -1, 2904, -1, 1869, -1, 2902, -1], 'generators': [455, 400], 'label': '512.60809.64.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '64.x1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267928
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.br1.a1', '32.bt1.a1'], 'contains': ['128.h2.a1', '128.l1.a1', '128.m1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3534, -1, 4056, -1, 3527, -1, 4054, -1], 'generators': [3, 160], 'label': '512.60809.64.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '64.y1.a1', 'projective_image': '512.60809', '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: 67267929
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.br1.b1', '32.bt1.b1'], 'contains': ['128.h2.b1', '128.l1.a1', '128.m1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3534, -1, 5078, -1, 3527, -1, 5074, -1], 'generators': [455, 432], 'label': '512.60809.64.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '64.y1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267930
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.bq1.a1', '32.br1.a1'], 'contains': ['128.h1.b1', '128.h2.a1', '128.i1.a1', '128.n1.a1', '128.n2.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 5255, -1, 4020, -1, 5252, -1], 'generators': [35, 4, 256], 'label': '512.60809.64.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '64.z1.a1', 'projective_image': '512.60809', '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: 67267931
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': ['64.bk1.c1', '64.bk1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.g1.a1', '4.j1.b1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.i1.a1', '16.m1.a1', '16.n1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4813, 8735, 5744, 6581, 4806, 8542, 5738, 6981], 'generators': [3, 4, 128, 304], 'label': '512.60809.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267932
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.bq1.b1', '32.br1.a1'], 'contains': ['128.h1.a1', '128.h2.a1', '128.i1.a1', '128.n1.a1', '128.n2.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 5336, -1, 4020, -1, 5332, -1], 'generators': [3, 4, 256], 'label': '512.60809.64.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '64.z1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267933
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.bq1.c1', '32.br1.b1'], 'contains': ['128.h1.d1', '128.h2.b1', '128.i1.b1', '128.n1.b1', '128.n2.d1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 6228, -1, 4020, -1, 6223, -1], 'generators': [491, 396, 256], 'label': '512.60809.64.z1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '64.z1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267934
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.bq1.d1', '32.br1.b1'], 'contains': ['128.h1.c1', '128.h2.b1', '128.i1.b1', '128.n1.b1', '128.n2.c1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 6147, -1, 4020, -1, 6143, -1], 'generators': [459, 396, 256], 'label': '512.60809.64.z1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '64.z1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267935
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.bs1.a1', '32.bt1.a1'], 'contains': ['128.h1.c1', '128.h2.a1', '128.j1.a2', '128.o1.a1', '128.o1.c1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3738, -1, 4730, -1, 3732, -1, 4726, -1], 'generators': [3, 452, 256], 'label': '512.60809.64.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '64.ba1.a1', 'projective_image': '512.60809', '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: 67267936
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.bs1.b1', '32.bt1.a1'], 'contains': ['128.h1.d1', '128.h2.a1', '128.j1.a2', '128.o1.b1', '128.o1.d1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3738, -1, 4810, -1, 3732, -1, 4806, -1], 'generators': [35, 452, 256], 'label': '512.60809.64.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '64.ba1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267937
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.bs1.c1', '32.bt1.b1'], 'contains': ['128.h1.a1', '128.h2.b1', '128.j1.a1', '128.o1.a1', '128.o1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3738, -1, 4971, -1, 3732, -1, 4967, -1], 'generators': [3, 452, 288], 'label': '512.60809.64.ba1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '64.ba1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267938
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.bs1.d1', '32.bt1.b1'], 'contains': ['128.h1.b1', '128.h2.b1', '128.j1.a1', '128.o1.c1', '128.o1.d1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3738, -1, 4891, -1, 3732, -1, 4887, -1], 'generators': [35, 452, 288], 'label': '512.60809.64.ba1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '64.ba1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267939
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.bo1.a1', '32.bp1.a1', '32.bq1.b1', '32.bs1.c1', '32.bu1.a1', '32.bu1.b1'], 'contains': ['128.h1.a1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1407, -1, 1732, -1, 1405, -1, 1691, -1], 'generators': [3, 400], 'label': '512.60809.64.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bb1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267940
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.bo1.b1', '32.bp1.b1', '32.bq1.a1', '32.bs1.d1', '32.bu1.c1', '32.bu1.d1'], 'contains': ['128.h1.b1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1407, -1, 1662, -1, 1405, -1, 1620, -1], 'generators': [35, 400], 'label': '512.60809.64.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bb1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267941
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.bo1.c1', '32.bp1.c1', '32.bq1.d1', '32.bs1.a1', '32.bu1.a1', '32.bu1.c1'], 'contains': ['128.h1.c1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1407, -1, 1803, -1, 1405, -1, 1761, -1], 'generators': [455, 128], 'label': '512.60809.64.bb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bb1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267942
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': ['64.bk1.a1', '64.bk1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.g1.b1', '4.j1.a1'], 'contains': ['16.a1.b1', '16.c1.b1', '16.i1.b1', '16.m1.b1', '16.n1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4813, 8735, 6178, 2842, 4806, 8542, 6172, 2868], 'generators': [459, 396, 128, 304], 'label': '512.60809.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.a1.b1'], 'normal_contains': ['16.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267943
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.bo1.d1', '32.bp1.d1', '32.bq1.c1', '32.bs1.b1', '32.bu1.b1', '32.bu1.d1'], 'contains': ['128.h1.d1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1407, -1, 1873, -1, 1405, -1, 1832, -1], 'generators': [487, 128], 'label': '512.60809.64.bb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bb1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267944
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.br1.a1', '32.bt1.b1'], 'contains': ['128.h1.a1', '128.h1.b1', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3069, -1, 4229, -1, 3062, -1, 4226, -1], 'generators': [3, 432], 'label': '512.60809.64.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '64.bc1.a1', 'projective_image': '512.60809', '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': '4.2'}
  • id: 67267945
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.br1.b1', '32.bt1.a1'], 'contains': ['128.h1.c1', '128.h1.d1', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3069, -1, 4654, -1, 3062, -1, 4650, -1], 'generators': [455, 160], 'label': '512.60809.64.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.bc1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267946
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.bo1.c1', '32.bo1.d1', '32.bq1.a1', '32.bq1.b1', '32.bv1.a1', '32.bv1.b1'], 'contains': ['128.i1.a1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1677, -1, 1026, -1, 1675, -1, 1025, -1], 'generators': [4, 128], 'label': '512.60809.64.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '64.bd1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267947
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.b1', '32.bo1.a1', '32.bo1.b1', '32.bq1.c1', '32.bq1.d1', '32.bv1.c1', '32.bv1.d1'], 'contains': ['128.i1.b1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1677, -1, 2330, -1, 1675, -1, 2329, -1], 'generators': [396, 128], 'label': '512.60809.64.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '64.bd1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267948
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.br1.a1', '32.bw1.a1'], 'contains': ['128.i1.a1', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3204, -1, 3751, -1, 3197, -1, 3747, -1], 'generators': [4, 160], 'label': '512.60809.64.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m2.a1', 'old_label': '64.be1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267949
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.b1', '32.br1.b1', '32.bw1.b1'], 'contains': ['128.i1.b1', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3204, -1, 5180, -1, 3197, -1, 5176, -1], 'generators': [396, 160], 'label': '512.60809.64.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m2.b1', 'old_label': '64.be1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267950
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.bp1.a1', '32.bp1.b1', '32.bs1.a1', '32.bs1.b1', '32.bv1.a1', '32.bv1.b1'], 'contains': ['128.j1.a2', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1542, -1, 892, -1, 1540, -1, 891, -1], 'generators': [452, 128], 'label': '512.60809.64.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '64.bf1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267951
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a2', '32.bp1.c1', '32.bp1.d1', '32.bs1.c1', '32.bs1.d1', '32.bv1.c1', '32.bv1.d1'], 'contains': ['128.j1.a1', '128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1542, -1, 2260, -1, 1540, -1, 2258, -1], 'generators': [452, 400], 'label': '512.60809.64.bf1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '64.bf1.a2', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bf1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267952
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.bt1.a1', '32.bw1.a1'], 'contains': ['128.j1.a2', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2933, -1, 3680, -1, 2927, -1, 3677, -1], 'generators': [452, 160], 'label': '512.60809.64.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '64.bg1.a1', 'projective_image': '512.60809', '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': '8.3'}
  • id: 67267953
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.djj', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['256.f1.a1', '256.c1.a1', '256.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.a1', '4.d1.b1', '4.g1.b1', '4.k1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5925, 6929, 7156, 6427, 5916, 6776, 7149, 6489], 'generators': [1, 66, 392], 'label': '512.60809.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.a1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '256.6661', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67267954
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': ['64.bk1.c1', '64.bk1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.b1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.bh1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 7517, 6265, 7719, 5316, 7351, 6259, 8131], 'generators': [395, 4], 'label': '512.60809.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267955
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a2', '32.bt1.b1', '32.bw1.b1'], 'contains': ['128.j1.a1', '128.l1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2933, -1, 3955, -1, 2927, -1, 3952, -1], 'generators': [452, 432], 'label': '512.60809.64.bg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.b1', 'old_label': '64.bg1.a2', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg1.a2', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267956
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.bn1.a1', '32.bn1.c1', '32.bu1.a1', '32.bu1.d1', '32.bv1.a1', '32.bv1.c1'], 'contains': ['128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [576, -1, 1550, -1, 576, -1, 1509, -1], 'generators': [64], 'label': '512.60809.64.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bh1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267957
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.bn1.b1', '32.bn1.d1', '32.bu1.b1', '32.bu1.c1', '32.bv1.b1', '32.bv1.d1'], 'contains': ['128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [576, -1, 1114, -1, 576, -1, 1179, -1], 'generators': [96], 'label': '512.60809.64.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bh1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267958
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.a1', '32.bn1.a1', '32.bn1.b1', '32.bo1.c1', '32.bo1.d1', '32.bp1.a1', '32.bp1.b1'], 'contains': ['128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [712, -1, 423, -1, 711, -1, 423, -1], 'generators': [67], 'label': '512.60809.64.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '64.bi1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267959
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.b1', '32.bn1.c1', '32.bn1.d1', '32.bo1.a1', '32.bo1.b1', '32.bp1.c1', '32.bp1.d1'], 'contains': ['128.k1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [712, -1, 1985, -1, 711, -1, 1983, -1], 'generators': [395], 'label': '512.60809.64.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '64.bi1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267961
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.a1'], 'contains': ['128.n2.a1', '128.p1.a1', '128.q1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 6743, -1, 6150, -1, 6737, -1], 'generators': [1, 2], 'label': '512.60809.64.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.a1', 'old_label': '64.bk1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267962
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.a1'], 'contains': ['128.n2.b1', '128.p1.a1', '128.q1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 6672, -1, 6150, -1, 6667, -1], 'generators': [33, 2], 'label': '512.60809.64.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.a1', 'old_label': '64.bk1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267963
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.b1'], 'contains': ['128.n2.c1', '128.p1.b1', '128.q1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 7161, -1, 6150, -1, 7156, -1], 'generators': [185, 66], 'label': '512.60809.64.bk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.b1', 'old_label': '64.bk1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267964
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.b1'], 'contains': ['128.n2.d1', '128.p1.b1', '128.q1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 7232, -1, 6150, -1, 7226, -1], 'generators': [153, 66], 'label': '512.60809.64.bk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.b1', 'old_label': '64.bk1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67267965
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': ['64.bk1.a1', '64.bk1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.f1.a1', '4.k1.b1'], 'contains': ['16.a1.b1', '16.bh1.a1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 7517, 6355, 3637, 5316, 7351, 6349, 3671], 'generators': [67, 396], 'label': '512.60809.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.b1'], 'normal_contains': ['16.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267966
    {'ambient': '512.60809', 'aut_centralizer_order': 2048, 'aut_label': '128.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.b1.b1', '64.c1.a1', '64.d1.a1', '64.d1.b1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.g1.b1'], 'contains': ['256.a1.a1', '256.b1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4684, 5493, 5878, 3637, 4675, 5278, 5874, 3671], 'generators': [256, 32], 'label': '512.60809.128.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': '2.1', 'quotient_action_kernel': '64.226', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267967
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.h1.a1', '64.i1.a1'], 'contains': ['256.a1.a1', '256.c1.a1', '256.c1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4837, -1, 6039, -1, 4828, -1, 6035, -1], 'generators': [3, 32], 'label': '512.60809.128.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '128.b1.a1', 'projective_image': '256.6661', '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: 67267968
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '64.h1.b1', '64.i1.a1'], 'contains': ['256.a1.a1', '256.c1.c1', '256.c1.d1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4837, -1, 6281, -1, 4828, -1, 6276, -1], 'generators': [455, 32], 'label': '512.60809.128.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '128.b1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267969
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.j1.a1', '64.j1.b1', '64.k1.a1', '64.l1.a1', '64.l1.b1', '64.m1.a1'], 'contains': ['256.a1.a1', '256.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7123, -1, 7850, -1, 7112, -1, 7844, -1], 'generators': [1, 32], 'label': '512.60809.128.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '128.c1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267970
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '64.h1.a1', '64.j1.a1', '64.l1.a1', '64.n1.a1', '64.o1.a1', '64.p1.a1'], 'contains': ['256.a1.a1', '256.e1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5985, -1, 7115, -1, 5976, -1, 7110, -1], 'generators': [4, 32], 'label': '512.60809.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '128.d1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267971
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.b1', '64.h1.b1', '64.j1.b1', '64.l1.b1', '64.n1.b1', '64.o1.b1', '64.p1.b1'], 'contains': ['256.a1.a1', '256.e1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5985, -1, 7394, -1, 5976, -1, 7358, -1], 'generators': [396, 32], 'label': '512.60809.128.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '128.d1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267972
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.i1.a1', '64.q1.a1'], 'contains': ['256.a1.a1', '256.f1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5145, -1, 5959, -1, 5136, -1, 5954, -1], 'generators': [452, 32], 'label': '512.60809.128.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1.a1', 'old_label': '128.e1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267973
    {'ambient': '512.60809', 'aut_centralizer_order': 1024, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.k1.a1', '64.m1.a1', '64.p1.a1', '64.p1.b1', '64.q1.a1', '64.r1.a1', '64.s1.a1', '64.t1.a1', '64.u1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7952, -1, 8807, -1, 7941, -1, 8801, -1], 'generators': [304], 'label': '512.60809.128.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '128.f1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267974
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.j1.a1', '64.j1.b1', '64.k1.a1', '64.n1.a1', '64.n1.b1', '64.r1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6978, -1, 8003, -1, 6968, -1, 7997, -1], 'generators': [257], 'label': '512.60809.128.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '128.g1.a1', 'projective_image': '256.6661', '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': '2.1'}
  • id: 67267975
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.v1.a1', '64.w1.a1', '64.z1.b1', '64.ba1.c1', '64.bb1.a1', '64.bc1.a1'], 'contains': ['256.b1.a1', '256.c1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3585, -1, 4922, -1, 3578, -1, 4918, -1], 'generators': [3, 288], 'label': '512.60809.128.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '128.h1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267976
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '512.420058', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.bb1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7202, 5493, 6693, 4955, 7191, 5371, 6687, 5002], 'generators': [4, 392, 128], 'label': '512.60809.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.b1', '4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1'], 'normal_contains': ['16.a1.b1', '16.a1.a1', '16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67267977
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.v1.b1', '64.w1.b1', '64.z1.a1', '64.ba1.d1', '64.bb1.b1', '64.bc1.a1'], 'contains': ['256.b1.a1', '256.c1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3585, -1, 4761, -1, 3578, -1, 4757, -1], 'generators': [35, 288], 'label': '512.60809.128.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '128.h1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267978
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '64.v1.c1', '64.w1.c1', '64.z1.d1', '64.ba1.a1', '64.bb1.c1', '64.bc1.b1'], 'contains': ['256.b1.a1', '256.c1.c1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3585, -1, 5154, -1, 3578, -1, 5150, -1], 'generators': [455, 256], 'label': '512.60809.128.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '128.h1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267979
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '64.v1.d1', '64.w1.d1', '64.z1.c1', '64.ba1.b1', '64.bb1.d1', '64.bc1.b1'], 'contains': ['256.b1.a1', '256.c1.d1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3585, -1, 5234, -1, 3578, -1, 5230, -1], 'generators': [487, 256], 'label': '512.60809.128.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '128.h1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267980
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.x1.a1', '64.y1.a1', '64.z1.a1', '64.z1.b1', '64.ba1.a1', '64.ba1.b1'], 'contains': ['256.b1.a1', '256.c1.a1', '256.c1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3874, -1, 5002, -1, 3867, -1, 4999, -1], 'generators': [3, 256], 'label': '512.60809.128.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '128.h2.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267981
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.h2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '64.x1.b1', '64.y1.b1', '64.z1.c1', '64.z1.d1', '64.ba1.c1', '64.ba1.d1'], 'contains': ['256.b1.a1', '256.c1.c1', '256.c1.d1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3874, -1, 5637, -1, 3867, -1, 5632, -1], 'generators': [455, 288], 'label': '512.60809.128.h2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '128.h2.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267982
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '64.v1.a1', '64.v1.b1', '64.z1.a1', '64.z1.b1', '64.bd1.a1', '64.be1.a1'], 'contains': ['256.b1.a1', '256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 4841, -1, 4020, -1, 4838, -1], 'generators': [4, 256], 'label': '512.60809.128.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.a1', 'old_label': '128.i1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267983
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.b1', '64.v1.c1', '64.v1.d1', '64.z1.c1', '64.z1.d1', '64.bd1.b1', '64.be1.b1'], 'contains': ['256.b1.a1', '256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4028, -1, 5798, -1, 4020, -1, 5793, -1], 'generators': [396, 256], 'label': '512.60809.128.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.n1.b1', 'old_label': '128.i1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267984
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.w1.a1', '64.w1.b1', '64.ba1.c1', '64.ba1.d1', '64.bf1.a2', '64.bg1.a2'], 'contains': ['256.b1.a1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3430, -1, 4680, -1, 3424, -1, 4677, -1], 'generators': [452, 288], 'label': '512.60809.128.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.b1', 'old_label': '128.j1.a1', 'projective_image': '512.60809', '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': '2.1'}
  • id: 67267985
    {'ambient': '512.60809', 'aut_centralizer_order': 64, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.w1.c1', '64.w1.d1', '64.ba1.a1', '64.ba1.b1', '64.bf1.a1', '64.bg1.a1'], 'contains': ['256.b1.a1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3430, -1, 4600, -1, 3424, -1, 4596, -1], 'generators': [452, 256], 'label': '512.60809.128.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.o1.a1', 'old_label': '128.j1.a2', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.j1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267986
    {'ambient': '512.60809', 'aut_centralizer_order': 1024, 'aut_label': '128.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.f1.a1', '64.x1.a1', '64.x1.b1', '64.bb1.a1', '64.bb1.b1', '64.bb1.c1', '64.bb1.d1', '64.bd1.a1', '64.bd1.b1', '64.bf1.a1', '64.bf1.a2', '64.bh1.a1', '64.bh1.b1', '64.bi1.a1', '64.bi1.b1'], 'contains': ['256.b1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1610, -1, 1768, -1, 1607, -1, 1726, -1], 'generators': [128], 'label': '512.60809.128.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.k1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267987
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '512.420058', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': ['64.bk1.a1', '64.bk1.b1', '64.bk1.c1', '64.bk1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.bd1.a1', '16.be1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6828, 1635, 6498, 817, 6818, 1599, 6492, 825], 'generators': [452, 392, 128], 'label': '512.60809.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67267988
    {'ambient': '512.60809', 'aut_centralizer_order': 1024, 'aut_label': '128.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.f1.a1', '64.y1.a1', '64.y1.b1', '64.bc1.a1', '64.bc1.b1', '64.be1.a1', '64.be1.b1', '64.bg1.a1', '64.bg1.a2', '64.bj1.a1'], 'contains': ['256.b1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3069, -1, 4056, -1, 3062, -1, 4054, -1], 'generators': [160], 'label': '512.60809.128.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.l1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267989
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.g1.a1', '64.v1.a1', '64.v1.b1', '64.w1.c1', '64.w1.d1', '64.x1.a1', '64.y1.a1'], 'contains': ['256.b1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3729, -1, 4336, -1, 3722, -1, 4332, -1], 'generators': [307], 'label': '512.60809.128.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '128.m1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267990
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '128.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.g1.b1', '64.v1.c1', '64.v1.d1', '64.w1.a1', '64.w1.b1', '64.x1.b1', '64.y1.b1'], 'contains': ['256.b1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3729, -1, 5078, -1, 3722, -1, 5074, -1], 'generators': [247], 'label': '512.60809.128.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '128.m1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267991
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.z1.a1', '64.z1.b1'], 'contains': ['256.c1.a1', '256.c1.b1', '256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4529, -1, 5717, -1, 4521, -1, 5713, -1], 'generators': [3, 36], 'label': '512.60809.128.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1.a1', 'old_label': '128.n1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267992
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.z1.c1', '64.z1.d1'], 'contains': ['256.c1.c1', '256.c1.d1', '256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4529, -1, 6362, -1, 4521, -1, 6357, -1], 'generators': [459, 428], 'label': '512.60809.128.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1.b1', 'old_label': '128.n1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267993
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.z1.b1', '64.bk1.a1'], 'contains': ['256.c1.a1', '256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6200, -1, 4982, -1, 6196, -1], 'generators': [3, 4], 'label': '512.60809.128.n2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '128.n2.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267994
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.z1.a1', '64.bk1.b1'], 'contains': ['256.c1.b1', '256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6120, -1, 4982, -1, 6115, -1], 'generators': [35, 4], 'label': '512.60809.128.n2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '128.n2.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267995
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.z1.d1', '64.bk1.c1'], 'contains': ['256.c1.c1', '256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6748, -1, 4982, -1, 6742, -1], 'generators': [459, 396], 'label': '512.60809.128.n2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '128.n2.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n2.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267996
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.n2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.z1.c1', '64.bk1.d1'], 'contains': ['256.c1.d1', '256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6828, -1, 4982, -1, 6823, -1], 'generators': [491, 396], 'label': '512.60809.128.n2.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '128.n2.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n2.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67267997
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.ba1.a1', '64.ba1.c1'], 'contains': ['256.c1.a1', '256.c1.c1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4375, -1, 5395, -1, 4367, -1, 5391, -1], 'generators': [3, 452], 'label': '512.60809.128.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '128.o1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67267998
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '8.e1.a1', 'complements': ['64.bk1.a1', '64.bk1.b1', '64.bk1.c1', '64.bk1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.bg1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6370, 3564, 6097, 2092, 6360, 3485, 6091, 2111], 'generators': [64, 392], 'label': '512.60809.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67267999
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.ba1.b1', '64.ba1.c1'], 'contains': ['256.c1.a1', '256.c1.d1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4375, -1, 5556, -1, 4367, -1, 5552, -1], 'generators': [3, 484], 'label': '512.60809.128.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '128.o1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268000
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.ba1.a1', '64.ba1.d1'], 'contains': ['256.c1.b1', '256.c1.c1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4375, -1, 5315, -1, 4367, -1, 5311, -1], 'generators': [35, 484], 'label': '512.60809.128.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '128.o1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268001
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.ba1.b1', '64.ba1.d1'], 'contains': ['256.c1.b1', '256.c1.d1', '256.f1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4375, -1, 5476, -1, 4367, -1, 5472, -1], 'generators': [35, 452], 'label': '512.60809.128.o1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '128.o1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268002
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.p1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '64.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.l1.a1', '64.bk1.a1', '64.bk1.b1'], 'contains': ['256.d1.a1', '256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 6909, -1, 6150, -1, 6903, -1], 'generators': [1, 4], 'label': '512.60809.128.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.a1', 'old_label': '128.p1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67268003
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.p1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '64.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.l1.b1', '64.bk1.c1', '64.bk1.d1'], 'contains': ['256.d1.a1', '256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [6159, -1, 7196, -1, 6150, -1, 7191, -1], 'generators': [1, 12], 'label': '512.60809.128.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.b1', 'old_label': '128.p1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67268004
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.q1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '64.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.o1.a1', '64.bk1.a1', '64.bk1.b1'], 'contains': ['256.e1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5840, -1, 6672, -1, 5832, -1, 6667, -1], 'generators': [2], 'label': '512.60809.128.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.a1', 'old_label': '128.q1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67268005
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '128.q1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '64.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.o1.b1', '64.bk1.c1', '64.bk1.d1'], 'contains': ['256.e1.b1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5840, -1, 7040, -1, 5832, -1, 7035, -1], 'generators': [66], 'label': '512.60809.128.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.x1.b1', 'old_label': '128.q1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67268006
    {'ambient': '512.60809', 'aut_centralizer_order': 4096, 'aut_label': '256.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.b1.b1', '128.c1.a1', '128.d1.a1', '128.d1.b1', '128.e1.a1', '128.f1.a1', '128.g1.a1'], 'contains': ['512.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5540, 5493, 6863, 3637, 5571, 5278, 6948, 3671], 'generators': [32], 'label': '512.60809.256.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1'], 'normal_contains': ['512.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': '1.1', 'quotient_action_kernel': '256.6661', 'quotient_action_kernel_order': 256, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268007
    {'ambient': '512.60809', 'aut_centralizer_order': 2048, 'aut_label': '256.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.h2.a1', '128.h2.b1', '128.i1.a1', '128.i1.b1', '128.j1.a1', '128.j1.a2', '128.k1.a1', '128.l1.a1', '128.m1.a1', '128.m1.b1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3729, -1, 4963, -1, 3722, -1, 4958, -1], 'generators': [256], 'label': '512.60809.256.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '256.b1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268008
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.a1', '128.h1.a1', '128.h2.a1', '128.n1.a1', '128.n2.a1', '128.o1.a1', '128.o1.b1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4529, -1, 5561, -1, 4521, -1, 5555, -1], 'generators': [3], 'label': '512.60809.256.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '256.c1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268009
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '16.w1.a1', '16.y1.a1', '16.bc1.a1', '16.bf1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2085, -1, 3779, -1, 2081, -1, 3775, -1], 'generators': [307, 64, 4], 'label': '512.60809.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '8.f1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67268010
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.a1', '128.h1.b1', '128.h2.a1', '128.n1.a1', '128.n2.b1', '128.o1.c1', '128.o1.d1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4529, -1, 5485, -1, 4521, -1, 5474, -1], 'generators': [35], 'label': '512.60809.256.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.b1', 'old_label': '256.c1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268011
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.b1', '128.h1.c1', '128.h2.b1', '128.n1.b1', '128.n2.c1', '128.o1.a1', '128.o1.c1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4529, -1, 5634, -1, 4521, -1, 5628, -1], 'generators': [455], 'label': '512.60809.256.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '256.c1.c1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268012
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.b1', '128.h1.d1', '128.h2.b1', '128.n1.b1', '128.n2.d1', '128.o1.b1', '128.o1.d1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4529, -1, 5705, -1, 4521, -1, 5698, -1], 'generators': [487], 'label': '512.60809.256.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '256.c1.d1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268013
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '256.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.c1.a1', '128.p1.a1', '128.p1.b1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6159, -1, 6944, -1, 6150, -1, 7029, -1], 'generators': [1], 'label': '512.60809.256.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.bn1.a1', 'old_label': '256.d1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268014
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.d1.a1', '128.i1.a1', '128.n1.a1', '128.n2.a1', '128.n2.b1', '128.p1.a1', '128.q1.a1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6160, -1, 4982, -1, 6156, -1], 'generators': [4], 'label': '512.60809.256.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '256.e1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268015
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.d1.b1', '128.i1.b1', '128.n1.b1', '128.n2.c1', '128.n2.d1', '128.p1.b1', '128.q1.b1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4991, -1, 6770, -1, 4982, -1, 6783, -1], 'generators': [396], 'label': '512.60809.256.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.b1', 'old_label': '256.e1.b1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268016
    {'ambient': '512.60809', 'aut_centralizer_order': 128, 'aut_label': '256.f1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.e1.a1', '128.j1.a1', '128.j1.a2', '128.o1.a1', '128.o1.b1', '128.o1.c1', '128.o1.d1'], 'contains': ['512.a1.a1'], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [4385, -1, 5405, -1, 4377, -1, 5398, -1], 'generators': [452], 'label': '512.60809.256.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '256.f1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268017
    {'ambient': '512.60809', 'aut_centralizer_order': None, 'aut_label': '512.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': ['256.a1.a1', '256.b1.a1', '256.c1.a1', '256.c1.b1', '256.c1.c1', '256.c1.d1', '256.d1.a1', '256.e1.a1', '256.e1.b1', '256.f1.a1'], 'contains': [], 'core': '512.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4760, 5493, 5669, 3637, 4752, 5278, 5663, 3671], 'generators': [], 'label': '512.60809.512.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '512.a1.a1', 'normal_contained_in': ['256.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '512.a1.a1', 'projective_image': '512.60809', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67268018
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.b1', '16.d1.b1', '16.e1.b1', '16.w1.b1', '16.y1.b1', '16.bc1.b1', '16.bf1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2085, -1, 4235, -1, 2081, -1, 4230, -1], 'generators': [187, 64, 396], 'label': '512.60809.8.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.f1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268019
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.q1.a1', '16.u1.a1', '16.z1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6129, -1, 7099, -1, 6120, -1, 7093, -1], 'generators': [1, 2, 304], 'label': '512.60809.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '8.g1.a1', 'projective_image': '256.6661', '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': '64.138'}
  • id: 67268020
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1'], 'contains': ['16.g1.b1', '16.i1.b1', '16.q1.b1', '16.u1.b1', '16.z1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6129, -1, 7571, -1, 6120, -1, 7565, -1], 'generators': [393, 66, 304], 'label': '512.60809.8.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '8.g1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 67268021
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.i1.a1', '16.z1.a1', '16.ba1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5821, -1, 7260, -1, 5813, -1, 7254, -1], 'generators': [129, 2], 'label': '512.60809.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '8.h1.a1', 'projective_image': '256.6661', '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': '64.138'}
  • id: 67268022
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.djj', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['256.f1.a1', '256.d1.a1', '256.c1.c1', '256.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.b1', '4.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6664, 9131, 6682, 9183, 6655, 8930, 6676, 9270], 'generators': [65, 66], 'label': '512.60809.2.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.b1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '256.6661', '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': '256.6661'}
  • id: 67268023
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1'], 'contains': ['16.i1.b1', '16.z1.b1', '16.ba1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5821, -1, 7411, -1, 5813, -1, 7404, -1], 'generators': [9, 66], 'label': '512.60809.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '8.h1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 67268024
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.j1.a1'], 'contains': ['16.a1.b1', '16.h1.a1', '16.m1.a1', '16.y1.b1', '16.bh1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4238, -1, 5526, -1, 4232, -1, 5521, -1], 'generators': [3, 396, 304], 'label': '512.60809.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.i1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268025
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.f1.b1', '4.j1.b1'], 'contains': ['16.a1.a1', '16.h1.b1', '16.m1.b1', '16.y1.a1', '16.bh1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4238, -1, 5149, -1, 4232, -1, 5144, -1], 'generators': [67, 4, 304], 'label': '512.60809.8.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.i1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67268026
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.h1.a1', '4.j1.b1'], 'contains': ['16.j1.a1', '16.m1.a1', '16.bc1.a1', '16.bd1.a1', '16.bh1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3690, -1, 4646, -1, 3685, -1, 4641, -1], 'generators': [7, 452, 304], 'label': '512.60809.8.j1.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': '8.j1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268027
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.j1.b1', '16.m1.b1', '16.bc1.b1', '16.bd1.a1', '16.bh1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3690, -1, 5435, -1, 3685, -1, 5430, -1], 'generators': [399, 452, 304], 'label': '512.60809.8.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.j1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67268028
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.i1.a1', '4.j1.b1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.m1.a1', '16.bg1.a1', '16.bh1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3474, -1, 4533, -1, 3469, -1, 4529, -1], 'generators': [3, 64, 304], 'label': '512.60809.8.k1.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': '8.k1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268029
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.i1.a1', '4.j1.a1'], 'contains': ['16.e1.b1', '16.f1.b1', '16.m1.b1', '16.bg1.a1', '16.bh1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3474, -1, 4759, -1, 3469, -1, 4754, -1], 'generators': [395, 64, 304], 'label': '512.60809.8.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.k1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268030
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.b1.a1', '16.m1.a1', '16.bh1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5151, -1, 5920, -1, 5143, -1, 5915, -1], 'generators': [3, 392], 'label': '512.60809.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.l1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268031
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.b1.a1', '16.m1.b1', '16.bh1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5151, -1, 6011, -1, 5143, -1, 6005, -1], 'generators': [67, 392], 'label': '512.60809.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.l1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268032
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.h1.b1', '16.l1.b1', '16.o1.a1', '16.x1.a1', '16.bc1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2616, -1, 3408, -1, 2612, -1, 3406, -1], 'generators': [307, 368, 4], 'label': '512.60809.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '8.m1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67268033
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1024.djj', 'aut_weyl_index': 4, 'centralizer': '256.a1.a1', 'complements': ['256.f1.a1', '256.d1.a1', '256.c1.a1', '256.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.d1.a1', '4.e1.a1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6664, 9131, 6856, 3654, 6655, 8930, 6850, 3689], 'generators': [65, 2], 'label': '512.60809.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '256.6661', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '256.6661'}
  • id: 67268034
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.b1', '16.f1.b1', '16.h1.a1', '16.l1.a1', '16.o1.b1', '16.x1.b1', '16.bc1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2616, -1, 4091, -1, 2612, -1, 4087, -1], 'generators': [395, 368, 396], 'label': '512.60809.8.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.m1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268035
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.m2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.j1.a1', '16.l1.a1', '16.n1.a1', '16.x1.a1', '16.y1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2950, -1, 3619, -1, 2946, -1, 3614, -1], 'generators': [3, 368, 4], 'label': '512.60809.8.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '8.m2.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m2.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268036
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.m2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.d1.b1', '16.f1.b1', '16.j1.b1', '16.l1.b1', '16.n1.b1', '16.x1.b1', '16.y1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2950, -1, 4378, -1, 2946, -1, 4374, -1], 'generators': [187, 368, 396], 'label': '512.60809.8.m2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.m2.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m2.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268037
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.418967', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.d1.a1', '16.d1.b1', '16.k1.a1', '16.m1.a1', '16.m1.b1', '16.o1.a1', '16.o1.b1', '16.bd1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4403, -1, 5062, -1, 4397, -1, 5057, -1], 'generators': [3, 452, 128, 304], 'label': '512.60809.8.n1.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': '8.n1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268038
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53342', 'aut_weyl_index': 16, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.l1.a1', '16.l1.b1', '16.m1.a1', '16.m1.b1', '16.p1.a1', '16.bf1.a1', '16.bg1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2319, -1, 3936, -1, 2316, -1, 3932, -1], 'generators': [7, 64, 304], 'label': '512.60809.8.o1.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': '8.o1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268039
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.e1.b1', '16.h1.a1', '16.j1.b1', '16.n1.b1', '16.o1.b1', '16.p1.a1', '16.w1.b1', '16.bp1.c1', '16.bp1.d1', '16.bp1.g1', '16.bp1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1437, -1, 2656, -1, 1434, -1, 2654, -1], 'generators': [395, 64, 396, 32], 'label': '512.60809.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.p1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268040
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1'], 'contains': ['16.e1.a1', '16.h1.b1', '16.j1.a1', '16.n1.a1', '16.o1.a1', '16.p1.a1', '16.w1.a1', '16.bp1.a1', '16.bp1.b1', '16.bp1.e1', '16.bp1.f1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1437, -1, 1566, -1, 1434, -1, 1564, -1], 'generators': [3, 64, 4, 32], 'label': '512.60809.8.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '8.p1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268041
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.54053', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.r1.a1', '16.r1.b1', '16.t1.a1', '16.ba1.a1', '16.ba1.b1', '16.bb1.a1', '16.bi1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7523, -1, 8142, -1, 7512, -1, 8135, -1], 'generators': [129, 4, 392], 'label': '512.60809.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.q1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268042
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.r1.a1', '16.s1.a1', '16.u1.a1', '16.ba1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6553, -1, 7703, -1, 6544, -1, 7696, -1], 'generators': [1, 4, 128], 'label': '512.60809.8.r1.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.r1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67268043
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.g1.b1', '4.k1.b1'], 'contains': ['16.a1.b1', '16.r1.b1', '16.s1.a1', '16.u1.b1', '16.ba1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6553, -1, 7795, -1, 6544, -1, 7787, -1], 'generators': [1, 396, 128], 'label': '512.60809.8.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.r1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67268044
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['256.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.c1.a1', '4.f1.a1', '4.f1.b1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4978, 5028, 5795, 2245, 4971, 4916, 5789, 2266], 'generators': [3, 64, 4, 392], 'label': '512.60809.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67268045
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.v1.a1', '16.be1.a1', '16.bj1.a1', '16.bm1.a1', '16.bo1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9386, -1, 9388, -1, 9372, -1, 9379, -1], 'generators': [1, 452, 256], 'label': '512.60809.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.s1.a1', 'projective_image': '256.6661', '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': '64.140'}
  • id: 67268046
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.s1.a1', '16.t1.a1', '16.v1.a1', '16.bi1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7823, -1, 8299, -1, 7812, -1, 8292, -1], 'generators': [1, 392, 128], 'label': '512.60809.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.t1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67268047
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.54053', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.r1.a1', '16.r1.b1', '16.t1.a1', '16.u1.a1', '16.u1.b1', '16.v1.a1', '16.bb1.a1', '16.bk1.a1', '16.bl1.a1', '16.bl1.a2', '16.bn1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8095, -1, 8442, -1, 8084, -1, 8434, -1], 'generators': [1, 4, 392, 256], 'label': '512.60809.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.u1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268048
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.b1', '4.j1.b1'], 'contains': ['16.a1.a1', '16.w1.a1', '16.x1.a1', '16.bd1.a1', '16.bg1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3964, -1, 4924, -1, 3958, -1, 4919, -1], 'generators': [64, 4, 304], 'label': '512.60809.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.v1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268049
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.a1', '4.j1.a1'], 'contains': ['16.a1.b1', '16.w1.b1', '16.x1.b1', '16.bd1.a1', '16.bg1.a1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3964, -1, 5292, -1, 3958, -1, 5287, -1], 'generators': [64, 396, 304], 'label': '512.60809.8.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.v1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.b1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 67268050
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.g1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.z1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5571, -1, 6847, -1, 5563, -1, 6840, -1], 'generators': [2, 128], 'label': '512.60809.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.w1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67268051
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.g1.b1', '4.k1.b1'], 'contains': ['16.a1.b1', '16.z1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5571, -1, 6957, -1, 5563, -1, 6951, -1], 'generators': [66, 128], 'label': '512.60809.8.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.w1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67268052
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '512.418967', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.f1.b1', '4.h1.a1'], 'contains': ['16.bd1.a1', '16.bh1.a1', '16.bh1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4978, -1, 5830, -1, 4971, -1, 5825, -1], 'generators': [395, 452], 'label': '512.60809.8.x1.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': '8.x1.a1', 'projective_image': '256.6661', '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': '64.226'}
  • id: 67268053
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 16, 'centralizer': '256.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.be1.a1', '16.bi1.a1', '16.bj1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8859, -1, 8979, -1, 8847, -1, 8972, -1], 'generators': [129, 452], 'label': '512.60809.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.y1.a1', 'projective_image': '256.6661', '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': '64.140'}
  • id: 67268054
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53342', 'aut_weyl_index': 16, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.f1.b1', '4.i1.a1'], 'contains': ['16.bg1.a1', '16.bh1.a1', '16.bh1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4608, -1, 5637, -1, 4602, -1, 5631, -1], 'generators': [399, 64], 'label': '512.60809.8.z1.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': '8.z1.a1', 'projective_image': '256.6661', '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: 67268055
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '256.a1.a1', 'complements': ['256.c1.a1', '256.c1.b1', '256.c1.c1', '256.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.l1.a1', '4.m1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7318, 869, 7589, 5118, 7307, 849, 7525, 5167], 'generators': [1, 64, 4], 'label': '512.60809.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '256.6661', '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': '256.6661'}
  • id: 67268056
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 64, 'centralizer': '64.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.bj1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8289, -1, 8543, -1, 8277, -1, 8535, -1], 'generators': [65, 128], 'label': '512.60809.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.ba1.a1', 'projective_image': '256.6661', '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': '32.39'}
  • id: 67268057
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.i1.b1', '8.r1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.a1.a1', '32.m1.a1', '32.n1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5281, 6354, 6147, 5768, 5273, 6214, 6142, 5987], 'generators': [4, 128, 304], 'label': '512.60809.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67268058
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 2, 'aut_weyl_group': '128.928', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.b1.b1', '8.c1.a1', '8.i1.a1', '8.r1.b1', '8.v1.b1', '8.w1.b1'], 'contains': ['32.a1.a1', '32.m1.b1', '32.n1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5281, 6354, 6237, 3637, 5273, 6214, 6232, 3671], 'generators': [396, 128, 304], 'label': '512.60809.16.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': ['8.a1.b1', '8.b1.b1', '8.c1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.b1', 'subgroup_fusion': None, 'weyl_group': '128.928'}
  • id: 67268059
    {'ambient': '512.60809', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '8.l1.a1', '8.l1.b1', '8.t1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.v1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7288, 4617, 6521, 2353, 7277, 4515, 6515, 2376], 'generators': [392, 128], 'label': '512.60809.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.c1.a1', '8.d1.a1', '8.e1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '256.6661', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 67268060
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.m1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.k1.a1', '32.m1.a1', '32.r1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4157, -1, 4733, -1, 4152, -1, 4728, -1], 'generators': [307, 4, 128], 'label': '512.60809.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.c1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268061
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.f1.b1', '8.m1.b1'], 'contains': ['32.b1.b1', '32.d1.b1', '32.k1.b1', '32.m1.b1', '32.r1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4157, -1, 5604, -1, 4152, -1, 5599, -1], 'generators': [251, 396, 128], 'label': '512.60809.16.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.c1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268062
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.m2.a1', '8.n1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.o1.a1', '32.p1.a1', '32.r1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3688, -1, 4530, -1, 3683, -1, 4526, -1], 'generators': [307, 452, 128], 'label': '512.60809.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.d1.a1', 'projective_image': '256.6661', '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': '32.46'}
  • id: 67268063
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.m2.b1', '8.n1.a1'], 'contains': ['32.c1.b1', '32.d1.b1', '32.o1.a1', '32.p1.a2', '32.r1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3688, -1, 4934, -1, 3683, -1, 4930, -1], 'generators': [307, 452, 432], 'label': '512.60809.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.d1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 67268064
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.k1.a1', '8.p1.b1'], 'contains': ['32.d1.a1', '32.s1.a1', '32.u1.a1', '32.bn1.a1', '32.bn1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [903, -1, 1354, -1, 902, -1, 1352, -1], 'generators': [3, 64, 32], 'label': '512.60809.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.e1.a1', 'projective_image': '256.6661', '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': '4.2'}
  • id: 67268065
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.k1.b1', '8.p1.a1'], 'contains': ['32.d1.b1', '32.s1.a1', '32.u1.b1', '32.bn1.c1', '32.bn1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [903, -1, 2585, -1, 902, -1, 2582, -1], 'generators': [395, 64, 32], 'label': '512.60809.16.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.e1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67268066
    {'ambient': '512.60809', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '256.a1.a1', 'complements': ['256.d1.a1', '256.c1.a1', '256.c1.b1', '256.c1.c1', '256.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.d1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6343, 2990, 6514, 899, 6334, 2923, 6508, 907], 'generators': [2, 64], 'label': '512.60809.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '256.6661', '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': '256.6661'}
  • id: 67268067
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.m1.a1', '8.m2.a1'], 'contains': ['32.d1.a1', '32.t1.a1', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2450, -1, 3255, -1, 2447, -1, 3252, -1], 'generators': [3, 368], 'label': '512.60809.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.f1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67268068
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.m1.b1', '8.m2.b1'], 'contains': ['32.d1.b1', '32.t1.a1', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2450, -1, 4284, -1, 2447, -1, 4280, -1], 'generators': [395, 368], 'label': '512.60809.16.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.f1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67268069
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '128.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.f1.a1', '32.i1.a1', '32.l1.a1', '32.x1.a1', '32.y1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6283, -1, 6955, -1, 6274, -1, 6949, -1], 'generators': [1, 2, 256], 'label': '512.60809.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.a1', 'old_label': '16.g1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268070
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '128.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1'], 'contains': ['32.f1.b1', '32.i1.b1', '32.l1.b1', '32.x1.b1', '32.y1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6283, -1, 7461, -1, 6274, -1, 7454, -1], 'generators': [185, 66, 256], 'label': '512.60809.16.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g1.b1', 'old_label': '16.g1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268071
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.m1.b1', '8.p1.a1'], 'contains': ['32.h1.a1', '32.m1.b1', '32.u1.b1', '32.bo1.a1', '32.bo1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1869, -1, 2998, -1, 1866, -1, 2995, -1], 'generators': [3, 396, 32], 'label': '512.60809.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.h1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268072
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.m1.a1', '8.p1.b1'], 'contains': ['32.h1.b1', '32.m1.a1', '32.u1.a1', '32.bo1.c1', '32.bo1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1869, -1, 2440, -1, 1866, -1, 2437, -1], 'generators': [67, 4, 32], 'label': '512.60809.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.h1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268073
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.f1.a1', '32.k1.a1', '32.n1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5530, -1, 6368, -1, 5522, -1, 6363, -1], 'generators': [3, 4, 304], 'label': '512.60809.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.i1.a1', 'projective_image': '256.6661', '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: 67268074
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.202', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.g1.b1', '8.h1.b1'], 'contains': ['32.b1.b1', '32.e1.b1', '32.f1.b1', '32.k1.b1', '32.n1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5530, -1, 6673, -1, 5522, -1, 6667, -1], 'generators': [459, 396, 304], 'label': '512.60809.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.b1', 'old_label': '16.i1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 67268075
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.m2.a1', '8.p1.b1'], 'contains': ['32.h1.a1', '32.p1.a1', '32.u1.a1', '32.bp1.a1', '32.bp1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1180, -1, 2306, -1, 1178, -1, 2303, -1], 'generators': [7, 452, 32], 'label': '512.60809.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.j1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268076
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.m2.b1', '8.p1.a1'], 'contains': ['32.h1.b1', '32.p1.a2', '32.u1.b1', '32.bp1.c1', '32.bp1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1180, -1, 3133, -1, 1178, -1, 3129, -1], 'generators': [399, 452, 32], 'label': '512.60809.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.j1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268077
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '512.7530050', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.i1.a1', '8.l1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5267, 8762, 6230, 8406, 5260, 8568, 6220, 8486], 'generators': [3, 4, 392], 'label': '512.60809.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '256.6661', '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': '128.928'}
  • id: 67268078
    {'ambient': '512.60809', 'aut_centralizer_order': 4, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1'], 'contains': ['32.c1.a1', '32.c1.b1', '32.e1.a1', '32.e1.b1', '32.g1.a1', '32.o1.a1', '32.q1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4858, -1, 6017, -1, 4851, -1, 6011, -1], 'generators': [3, 452, 304], 'label': '512.60809.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.n1.a1', 'old_label': '16.k1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 67268079
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '8.m2.a1', '8.o1.a1'], 'contains': ['32.h1.a1', '32.r1.b1', '32.t1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2257, -1, 3938, -1, 2254, -1, 3934, -1], 'generators': [7, 368], 'label': '512.60809.16.l1.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': '16.l1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268080
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.m2.b1', '8.o1.a1'], 'contains': ['32.h1.b1', '32.r1.a1', '32.t1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2257, -1, 3848, -1, 2254, -1, 3844, -1], 'generators': [311, 368], 'label': '512.60809.16.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.l1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268081
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '32.h1.a1', '32.r1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4392, -1, 5347, -1, 4386, -1, 5342, -1], 'generators': [3, 128, 304], 'label': '512.60809.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.a1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268082
    {'ambient': '512.60809', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.i1.b1', '8.j1.b1', '8.k1.b1', '8.l1.b1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.d1.b1', '32.e1.b1', '32.h1.b1', '32.r1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4392, -1, 5482, -1, 4386, -1, 5476, -1], 'generators': [455, 128, 304], 'label': '512.60809.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268083
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.m2.a1', '8.p1.b1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '32.h1.a1', '32.m1.a1', '32.bq1.a1', '32.bq1.b1', '32.br1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3432, -1, 3725, -1, 3428, -1, 3721, -1], 'generators': [3, 4, 128, 32], 'label': '512.60809.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.n1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268084
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.m2.b1', '8.p1.a1'], 'contains': ['32.b1.b1', '32.d1.b1', '32.f1.b1', '32.h1.b1', '32.m1.b1', '32.bq1.c1', '32.bq1.d1', '32.br1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3432, -1, 5201, -1, 3428, -1, 5197, -1], 'generators': [459, 396, 128, 32], 'label': '512.60809.16.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.n1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268085
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.n1.a1', '8.p1.b1'], 'contains': ['32.c1.b1', '32.d1.a1', '32.g1.a1', '32.h1.b1', '32.p1.a1', '32.bs1.a1', '32.bs1.b1', '32.bt1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3136, -1, 3479, -1, 3131, -1, 3476, -1], 'generators': [3, 452, 128, 32], 'label': '512.60809.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '16.o1.a1', 'projective_image': '256.6661', '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': '16.11'}
  • id: 67268086
    {'ambient': '512.60809', 'aut_centralizer_order': 8, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '8.n1.a1', '8.p1.a1'], 'contains': ['32.c1.a1', '32.d1.b1', '32.g1.a1', '32.h1.a1', '32.p1.a2', '32.bs1.c1', '32.bs1.d1', '32.bt1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3136, -1, 4150, -1, 3131, -1, 4147, -1], 'generators': [3, 452, 432, 32], 'label': '512.60809.16.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.o1.b1', 'projective_image': '256.6661', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 67268087
    {'ambient': '512.60809', 'aut_centralizer_order': 16, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1735', 'aut_weyl_index': 32, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.h1.a1', '32.h1.b1', '32.s1.a1', '32.bu1.a1', '32.bu1.b1', '32.bu1.c1', '32.bu1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [628, -1, 1633, -1, 626, -1, 1631, -1], 'generators': [7, 64, 32], 'label': '512.60809.16.p1.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': '16.p1.a1', 'projective_image': '256.6661', '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': '8.3'}