Abstract group data - 128.925

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 2, 4, 8], 'aut_gens': [[1, 2, 4, 64], [1, 114, 116, 96], [73, 34, 12, 64], [121, 2, 108, 96], [33, 82, 36, 64], [89, 34, 36, 64]], 'aut_group': '512.6291005', 'aut_hash': 3348211604540306308, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 16, 'aut_perms': [1313988485176, 2702570969380, 11543, 1401166771200, 2789792421584], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 8, 1, 1], [2, 16, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 8, 1, 1], [4, 8, 2, 1], [8, 2, 2, 1], [8, 4, 1, 1], [8, 8, 1, 1], [8, 16, 1, 1], [16, 4, 4, 1], [16, 8, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^3.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '64.261', 'autcentquo_hash': 261, 'autcentquo_nilpotent': True, 'autcentquo_order': 64, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4\\times C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 8, 1], [2, 16, 1], [4, 2, 2], [4, 4, 1], [4, 8, 3], [8, 2, 2], [8, 4, 1], [8, 8, 1], [8, 16, 1], [16, 4, 4], [16, 8, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '64.128', 'commutator_count': 1, 'commutator_label': '16.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 925, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 8, 1, 1], [2, 16, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 8, 1, 3], [8, 2, 2, 1], [8, 4, 1, 1], [8, 8, 1, 1], [8, 16, 1, 1], [16, 4, 4, 1], [16, 8, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 16, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[4, 0, 4]], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '8.5', 'hash': 925, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 2, 8, 2], 'inner_gens': [[1, 2, 76, 96], [1, 2, 84, 96], [121, 114, 4, 64], [33, 34, 4, 64]], 'inner_hash': 128, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': True, 'inner_tex': 'D_4:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 5]], 'label': '128.925', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 16, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D4.D8', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 23, 'number_divisions': 18, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 91, 'number_subgroup_classes': 105, 'number_subgroups': 272, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 32], [8, 32], [16, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [112, 0], 'outer_gens': [[1, 82, 4, 64], [1, 2, 52, 64]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, '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, 3], [16, 1]], 'representations': {'PC': {'code': 319437039483503343767654579102, 'gens': [1, 2, 3, 7], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 232, 1598, 891, 58, 675, 570, 80, 1684, 102, 4710, 2365]}, 'Perm': {'d': 32, 'gens': [8864346395417934845818064966399, 135955991562369039230941840932864000, 76209687101520605238967286053591680, 50973977447449949914510425377438038, 16985047389886805017339919827041862, 25199055155429228508132113875036937, 8231691320578226211046411712681647]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4.D_8', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 108644337
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 925, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 108644348
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 925, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 108644353
    {'aut_label': '2B', 'centralizer': '2.f1.a1', 'counter': 3, 'group_counter': 925, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 64, 'size': 2}
  • id: 108644354
    {'aut_label': '2C', 'centralizer': '4.n1.a1', 'counter': 4, 'group_counter': 925, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 66, 'size': 4}
  • id: 108644355
    {'aut_label': '2D', 'centralizer': '8.r1.a1', 'counter': 5, 'group_counter': 925, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 8}
  • id: 108644356
    {'aut_label': '2E', 'centralizer': '16.h1.a1', 'counter': 6, 'group_counter': 925, 'group_order': 128, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 119, 'size': 16}
  • id: 108644357
    {'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 925, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 16, 'size': 2}
  • id: 108644358
    {'aut_label': '4B', 'centralizer': '2.e1.a1', 'counter': 8, 'group_counter': 925, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 112, 'size': 2}
  • id: 108644359
    {'aut_label': '4C', 'centralizer': '4.m1.a1', 'counter': 9, 'group_counter': 925, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 2, 'size': 4}
  • id: 108644338
    {'aut_label': '4D', 'centralizer': '8.p1.a1', 'counter': 10, 'group_counter': 925, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 65, 'size': 8}
  • id: 108644339
    {'aut_label': '4E', 'centralizer': '8.g1.a1', 'counter': 11, 'group_counter': 925, 'group_order': 128, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 3, 'size': 8}
  • id: 108644340
    {'aut_label': '4E', 'centralizer': '8.g1.a2', 'counter': 12, 'group_counter': 925, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 67, 'size': 8}
  • id: 108644341
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 13, 'group_counter': 925, 'group_order': 128, 'label': '8A1', 'order': 8, 'powers': [7], 'representative': 120, 'size': 2}
  • id: 108644342
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 14, 'group_counter': 925, 'group_order': 128, 'label': '8A3', 'order': 8, 'powers': [7], 'representative': 104, 'size': 2}
  • id: 108644343
    {'aut_label': '8B', 'centralizer': '4.f1.a1', 'counter': 15, 'group_counter': 925, 'group_order': 128, 'label': '8B', 'order': 8, 'powers': [7], 'representative': 8, 'size': 4}
  • id: 108644344
    {'aut_label': '8C', 'centralizer': '8.n1.a1', 'counter': 16, 'group_counter': 925, 'group_order': 128, 'label': '8C', 'order': 8, 'powers': [7], 'representative': 10, 'size': 8}
  • id: 108644345
    {'aut_label': '8D', 'centralizer': '16.v1.a1', 'counter': 17, 'group_counter': 925, 'group_order': 128, 'label': '8D', 'order': 8, 'powers': [8], 'representative': 61, 'size': 16}
  • id: 108644346
    {'aut_label': '16A1', 'centralizer': '4.f1.a1', 'counter': 18, 'group_counter': 925, 'group_order': 128, 'label': '16A1', 'order': 16, 'powers': [15], 'representative': 4, 'size': 4}
  • id: 108644347
    {'aut_label': '16A1', 'centralizer': '4.f1.a1', 'counter': 19, 'group_counter': 925, 'group_order': 128, 'label': '16A-1', 'order': 16, 'powers': [15], 'representative': 36, 'size': 4}
  • id: 108644349
    {'aut_label': '16A1', 'centralizer': '4.f1.a1', 'counter': 20, 'group_counter': 925, 'group_order': 128, 'label': '16A3', 'order': 16, 'powers': [15], 'representative': 20, 'size': 4}
  • id: 108644350
    {'aut_label': '16A1', 'centralizer': '4.f1.a1', 'counter': 21, 'group_counter': 925, 'group_order': 128, 'label': '16A-3', 'order': 16, 'powers': [15], 'representative': 68, 'size': 4}
  • id: 108644351
    {'aut_label': '16B1', 'centralizer': '8.z1.a1', 'counter': 22, 'group_counter': 925, 'group_order': 128, 'label': '16B1', 'order': 16, 'powers': [13], 'representative': 6, 'size': 8}
  • id: 108644352
    {'aut_label': '16B1', 'centralizer': '8.z1.a1', 'counter': 23, 'group_counter': 925, 'group_order': 128, 'label': '16B3', 'order': 16, 'powers': [14], 'representative': 70, 'size': 8}
• 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: 3955159
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1a', '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], 'schur_index': 1}
  • id: 3955169
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1b', '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], 'schur_index': 1}
  • id: 3955170
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1c', '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], 'schur_index': 1}
  • id: 3955171
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1d', '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], 'schur_index': 1}
  • id: 3955172
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1e', '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], 'schur_index': 1}
  • id: 3955173
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1f', '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], 'schur_index': 1}
  • id: 3955174
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1g', '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], 'schur_index': 1}
  • id: 3955175
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.1h', '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], 'schur_index': 1}
  • id: 3955176
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -2, 0, 2, -2, 0, 0, 2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955160
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, -2, 0, -2, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955161
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 0, 0, 2, -2, 0, 2, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955162
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 2, 0, 2, -2, 0, 0, -2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955163
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 0, 2, 2, -2, 0, 0, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955164
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955165
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2g', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955166
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.2h', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955167
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3955168
    {'cdim': 4, 'counter': 18, 'faithful': True, 'group': '128.925', 'group_order': 128, 'image': None, 'label': '128.925.4b', 'multiplicity': 4, 'nt': [32, 2029], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 5552034
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.925.1a', '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]]]}
  • id: 5552045
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 64, 'label': '128.925.1b', '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]]]}
  • id: 5552050
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 64, 'label': '128.925.1c', '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]]]}
  • id: 5552051
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 64, 'label': '128.925.1d', '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]]]}
  • id: 5552052
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 64, 'label': '128.925.1e', '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]]]}
  • id: 5552053
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 64, 'label': '128.925.1f', '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]]]}
  • id: 5552054
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.925.1g', '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]]]}
  • id: 5552055
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.925.1h', '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]]]}
  • id: 5552056
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 16, 'label': '128.925.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552035
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 16, 'label': '128.925.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552036
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.b1', 'kernel_order': 16, 'label': '128.925.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552037
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 16, 'label': '128.925.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552038
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.925.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552039
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 16, 'label': '128.925.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552040
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.e1.a1', 'kernel_order': 8, 'label': '128.925.2g1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 5552041
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.e1.a1', 'kernel_order': 8, 'label': '128.925.2g2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 5552042
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.b1.a1', 'kernel_order': 8, 'label': '128.925.2h1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 5552043
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.b1.a1', 'kernel_order': 8, 'label': '128.925.2h2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 5552044
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 4, 'label': '128.925.4a', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5552046
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '128.925', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1.a1', 'kernel_order': 1, 'label': '128.925.4b1', 'nt': [32, 2029], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 5552047
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '128.925', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1.a1', 'kernel_order': 1, 'label': '128.925.4b2', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 5552048
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '128.925', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1.a1', 'kernel_order': 1, 'label': '128.925.4b3', 'nt': [32, 2029], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]]]}
  • id: 5552049
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '128.925', 'group_counter': 925, 'group_order': 128, 'image': None, 'image_isoclass': '128.925', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1.a1', 'kernel_order': 1, 'label': '128.925.4b4', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[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: 61520859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.925.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.925', 'subgroup_hash': 925, 'subgroup_order': 128, 'subgroup_tex': 'D_4.D_8', 'supersolvable': True, 'sylow': 2}
  • id: 61520876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.259', 'subgroup_hash': 259, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.153', 'subgroup_hash': 153, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.31', 'subgroup_hash': 31, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.190', 'subgroup_hash': 190, 'subgroup_order': 64, 'subgroup_tex': 'D_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.40', 'subgroup_hash': 40, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.187', 'subgroup_hash': 187, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 61520942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.43', 'subgroup_hash': 43, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, '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: 61520860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 61520872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61520873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.18', 'subgroup_hash': 18, 'subgroup_order': 32, 'subgroup_tex': 'D_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 61520883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 61520884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 61520885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C3'], 'split': False, '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: 61520888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.g1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520919
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520921
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.8.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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 61520922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.16.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': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520924
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.925.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520925
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 64, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.925.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61520930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520947
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520949
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.16.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 61520952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.925.32.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': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61520954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 90, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.925.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', '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': ['L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520955
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.925.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61520957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61520958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61520959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520960
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520961
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520962
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61520963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.925.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61520861
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 100, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.925.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.128', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 128, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U3', 'L3', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520862
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 61520863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 61520864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61520865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.925.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 61520866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.925', 'ambient_counter': 925, 'ambient_order': 128, 'ambient_tex': 'D_4.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 105, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.925.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '128.925', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 925, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4.D_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 61520859
    {'ambient': '128.925', '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': '64.a1.a1', 'complements': ['128.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2581, 5458, 2425, 5410, 2588, 5467, 2403, 5467], 'generators': [1, 2, 4], 'label': '128.925.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '64.128', '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': '64.128'}
  • id: 61520860
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.254', 'aut_weyl_index': 8, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.e1.a1', '8.h1.a1', '8.s1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2559, 9310, 4352, 9229, 2567, 9326, 4312, 9326], 'generators': [1, 72, 80], 'label': '128.925.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.39'}
  • id: 61520861
    {'ambient': '128.925', 'aut_centralizer_order': 512, 'aut_label': '64.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6403, 4387, 7456, 4918, 6422, 4395, 7387, 4970], 'generators': [32], 'label': '128.925.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.128', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.128', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61520862
    {'ambient': '128.925', 'aut_centralizer_order': 256, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '2.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.j1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7409, -1, 7023, -1, 7431, -1, 6959, -1], 'generators': [64], 'label': '128.925.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.925', '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': '1.1'}
  • id: 61520863
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6663, -1, 7246, -1, 6684, -1, 7180, -1], 'generators': [50], 'label': '128.925.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '64.c1.a1', 'projective_image': '128.925', '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': '1.1'}
  • id: 61520864
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '8.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5876, -1, 8027, -1, 5894, -1, 7954, -1], 'generators': [1], 'label': '128.925.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.925', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61520865
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 512, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.j1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8839, -1, 1526, -1, 8866, -1, 1610, -1], 'generators': [7], 'label': '128.925.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.925', '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': '1.1'}
  • id: 61520866
    {'ambient': '128.925', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1'], 'contains': [], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6663, 4387, 7246, 4918, 6684, 4395, 7180, 4970], 'generators': [], 'label': '128.925.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.925', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61520867
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.v1.a1', '8.w1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2153, 4111, 1015, 4075, 2159, 4118, 1006, 4118], 'generators': [7, 72, 80], 'label': '128.925.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.43'}
  • id: 61520868
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.f1.b1', '8.j1.a1', '8.y1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3011, 7897, 3981, 7828, 3020, 7911, 3944, 7911], 'generators': [3, 72, 80], 'label': '128.925.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.43'}
  • id: 61520869
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.254', 'aut_weyl_index': 8, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.k1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4834, 5381, 1349, 5334, 4849, 5390, 1337, 5390], 'generators': [5, 72], 'label': '128.925.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.39'}
  • id: 61520870
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 32, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.ba1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1274, 2456, 2289, 2434, 1277, 2460, 2268, 2460], 'generators': [4, 80], 'label': '128.925.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '64.128', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520871
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.48', 'aut_weyl_index': 16, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.z1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [807, 6441, 2671, 6384, 810, 6451, 2647, 6451], 'generators': [6, 80], 'label': '128.925.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520872
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.226', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.g1.a2', '8.h1.a1', '8.j1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1', '8.p1.a1', '8.r1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6653, -1, 7778, -1, 6673, -1, 7706, -1], 'generators': [1, 2, 80, 48], 'label': '128.925.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '64.128', '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': '32.46'}
  • id: 61520873
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.226', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.k1.a1', '8.q1.a1', '8.u1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8889, -1, 325, -1, 8916, -1, 322, -1], 'generators': [5, 2, 48], 'label': '128.925.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '64.128', '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': '32.28'}
  • id: 61520874
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.226', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.j1.a1', '8.t1.a1', '8.t1.b1', '8.x1.a1', '8.x1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5826, -1, 5642, -1, 5844, -1, 5591, -1], 'generators': [1, 74, 80], 'label': '128.925.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '64.128', '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': '32.46'}
  • id: 61520875
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.226', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7875, -1, 652, -1, 7899, -1, 647, -1], 'generators': [5, 74], 'label': '128.925.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '64.128', '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': '32.28'}
  • id: 61520876
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.54053', 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['64.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.l1.b1', '4.m1.a1', '4.n1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3916, 7908, 5053, 7839, 3927, 7922, 5007, 7922], 'generators': [1, 2, 72, 80], 'label': '128.925.2.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': '64.128', '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': '64.128'}
  • id: 61520877
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1', '8.o1.a1', '8.s1.a1', '8.t1.a1', '8.x1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5226, -1, 5268, -1, 5242, -1, 5220, -1], 'generators': [1, 2, 24], 'label': '128.925.4.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '64.128', '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': '32.46'}
  • id: 61520878
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.f1.b1', '8.l1.b1', '8.m1.b1', '8.o1.a1', '8.s1.a1', '8.t1.b1', '8.x1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5226, -1, 6017, -1, 5242, -1, 5962, -1], 'generators': [81, 2, 24], 'label': '128.925.4.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.l1.b1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 61520879
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 8, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.l1.a1', '8.l1.b1', '8.n1.a1', '8.t1.a1', '8.t1.b1', '8.y1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3463, -1, 6338, -1, 3474, -1, 6281, -1], 'generators': [1, 2, 72], 'label': '128.925.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520880
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 8, 'centralizer': '32.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.x1.a1', '8.x1.b1', '8.y1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3916, -1, 4842, -1, 3927, -1, 4797, -1], 'generators': [81, 2, 72], 'label': '128.925.4.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520881
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.123', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.v1.a1', '8.z1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [126, -1, 3231, -1, 126, -1, 3202, -1], 'generators': [1, 6], 'label': '128.925.4.o1.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.o1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.39'}
  • id: 61520882
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.123', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.e1.a1', '8.v1.a1', '8.z1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [457, -1, 2959, -1, 459, -1, 2932, -1], 'generators': [81, 6], 'label': '128.925.4.p1.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.p1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.39'}
  • id: 61520883
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.f1.a1', '8.w1.a1', '8.ba1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1736, -1, 1625, -1, 1741, -1, 1610, -1], 'generators': [3, 4], 'label': '128.925.4.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.q1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520884
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.f1.b1', '8.w1.a1', '8.ba1.a1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1736, -1, 1908, -1, 1741, -1, 1891, -1], 'generators': [83, 4], 'label': '128.925.4.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.q1.b1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520885
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.e1.a1', '16.f1.a1', '16.k1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8274, 2809, 3423, 2993, 8300, 2814, 3392, 3024], 'generators': [2, 80, 48], 'label': '128.925.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520886
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 64, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2284, 5436, 2027, 5334, 2291, 5445, 2009, 5390], 'generators': [72, 80], 'label': '128.925.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '64.128', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520887
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.54053', 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.k1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4636, 690, 1056, 684, 4650, 691, 1046, 691], 'generators': [5, 2, 72], 'label': '128.925.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '64.128', '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': '64.128'}
  • id: 61520888
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.t1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6314, 4046, 2626, 4043, 6333, 4052, 2601, 4085], 'generators': [74, 80], 'label': '128.925.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520889
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '16.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.m1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.o1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1598, 8912, 4212, 8430, 1603, 9271, 4174, 8519], 'generators': [1, 72], 'label': '128.925.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520890
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.n1.a1', '4.p1.a1'], 'contains': ['16.c1.a1', '16.r1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1885, 7919, 3688, 9316, 1890, 8276, 3653, 9414], 'generators': [81, 72], 'label': '128.925.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520891
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.l1.a1', '4.q1.a1'], 'contains': ['16.d1.a1', '16.s1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2683, 6739, 2901, 7544, 2691, 7093, 2874, 7623], 'generators': [3, 24], 'label': '128.925.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '64.128', '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': '32.43'}
  • id: 61520892
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.l1.b1', '4.q1.b1'], 'contains': ['16.d1.a1', '16.s1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2683, 6739, 3159, 6570, 2691, 7093, 3130, 6639], 'generators': [83, 24], 'label': '128.925.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '64.128', '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': '32.43'}
  • id: 61520893
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 64, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.f1.a1', '16.g1.a1', '16.i1.a1', '16.j1.b1', '16.l1.a1', '16.n1.a1', '16.w1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6653, -1, 9414, -1, 6673, -1, 9327, -1], 'generators': [1, 2, 64], 'label': '128.925.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.128', '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': '8.5'}
  • id: 61520894
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 64, 'centralizer': '32.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.f1.a1', '16.g1.a1', '16.i1.a1', '16.j1.a1', '16.l1.b1', '16.n1.b1', '16.w1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6653, -1, 9147, -1, 6673, -1, 9063, -1], 'generators': [1, 50, 64], 'label': '128.925.8.g1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.g1.a2', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61520895
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.m1.a1', '16.o1.a1', '16.r1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5974, -1, 7279, -1, 5993, -1, 7212, -1], 'generators': [1, 80, 48], 'label': '128.925.8.h1.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.h1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520896
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.p1.a1', '16.q1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8681, -1, 667, -1, 8707, -1, 661, -1], 'generators': [7, 80, 48], 'label': '128.925.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.i1.a1', 'projective_image': '64.128', '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': '16.13'}
  • id: 61520897
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.s1.a1', '16.s1.b1', '16.u1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7059, -1, 6260, -1, 7081, -1, 6203, -1], 'generators': [3, 80, 48], 'label': '128.925.8.j1.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.j1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520898
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.196', 'aut_weyl_index': 8, 'centralizer': '16.c1.a1', 'complements': ['64.d1.a1', '64.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1393, 1992, 2692, 1975, 1398, 1996, 2667, 1996], 'generators': [2, 4], 'label': '128.925.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520899
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.v1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9101, -1, 1012, -1, 9129, -1, 1003, -1], 'generators': [5, 48], 'label': '128.925.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.k1.a1', 'projective_image': '64.128', '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: 61520900
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.j1.a1', '16.k1.a1', '16.n1.a1', '16.o1.a1', '16.s1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5162, -1, 7946, -1, 5178, -1, 7873, -1], 'generators': [1, 2, 48], 'label': '128.925.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '64.128', '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: 61520901
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.b1', '4.m1.a1'], 'contains': ['16.j1.b1', '16.k1.a1', '16.n1.b1', '16.o1.a1', '16.s1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5162, -1, 8212, -1, 5178, -1, 8137, -1], 'generators': [73, 2, 48], 'label': '128.925.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.b1', 'projective_image': '64.128', '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: 61520902
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.k1.a1', '16.l1.a1', '16.r1.a1', '16.s1.a1', '16.w1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5569, -1, 6945, -1, 5586, -1, 6881, -1], 'generators': [25, 2, 48], 'label': '128.925.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520903
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.b1', '4.n1.a1'], 'contains': ['16.k1.a1', '16.l1.b1', '16.r1.a1', '16.s1.b1', '16.w1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5569, -1, 7612, -1, 5586, -1, 7542, -1], 'generators': [81, 2, 48], 'label': '128.925.8.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.b1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520904
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 64, 'centralizer': '8.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.m1.a1', '4.n1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.t1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3742, -1, 4514, -1, 3754, -1, 4473, -1], 'generators': [2, 72], 'label': '128.925.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520905
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.l1.b1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.t1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4159, -1, 3963, -1, 4172, -1, 3926, -1], 'generators': [2, 24], 'label': '128.925.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61520906
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.j1.b1', '16.l1.a1', '16.l1.b1', '16.m1.a1', '16.u1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7949, -1, 8479, -1, 7974, -1, 8402, -1], 'generators': [1, 50, 80], 'label': '128.925.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.p1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61520907
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.b1.a1', '16.q1.a1', '16.v1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9751, -1, 78, -1, 9780, -1, 78, -1], 'generators': [5, 50], 'label': '128.925.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '8.q1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520908
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.e1.a1', '16.m1.a1', '16.n1.a1', '16.n1.b1', '16.u1.a1', '16.w1.a1', '16.w1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7543, -1, 8813, -1, 7566, -1, 8732, -1], 'generators': [1, 2, 80], 'label': '128.925.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.r1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61520909
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['64.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.g1.a1', '4.o1.a1', '4.p1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [829, 9310, 3029, 9229, 831, 9326, 3001, 9326], 'generators': [1, 6, 80], 'label': '128.925.2.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.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '64.128', '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': '64.128'}
  • id: 61520910
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.l1.b1'], 'contains': ['16.d1.a1', '16.o1.a1', '16.r1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3330, -1, 5373, -1, 3339, -1, 5323, -1], 'generators': [1, 24], 'label': '128.925.8.s1.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.s1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520911
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.o1.a1', '16.s1.a1', '16.t1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4509, -1, 5918, -1, 4523, -1, 5864, -1], 'generators': [73, 74], 'label': '128.925.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.t1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520912
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.b1', '4.m1.a1'], 'contains': ['16.o1.a1', '16.s1.b1', '16.t1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4509, -1, 6603, -1, 4523, -1, 6542, -1], 'generators': [1, 74], 'label': '128.925.8.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.t1.b1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520913
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.e1.a1', '16.q1.a1', '16.v1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9450, -1, 325, -1, 9479, -1, 322, -1], 'generators': [5, 2], 'label': '128.925.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '8.u1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520914
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.o1.a1', '4.p1.a1'], 'contains': ['16.c1.a1', '16.p1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [779, -1, 1726, -1, 781, -1, 1710, -1], 'generators': [7, 72], 'label': '128.925.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.v1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520915
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.d1.a1', '16.p1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1344, -1, 1262, -1, 1348, -1, 1250, -1], 'generators': [7, 24], 'label': '128.925.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.w1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 61520916
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.r1.a1', '16.s1.a1', '16.t1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4841, -1, 5100, -1, 4856, -1, 5053, -1], 'generators': [81, 74], 'label': '128.925.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.x1.a1', 'projective_image': '64.128', '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': '16.11'}
  • id: 61520917
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 32, 'centralizer': '32.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.b1', '4.n1.a1'], 'contains': ['16.r1.a1', '16.s1.b1', '16.t1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4841, -1, 5645, -1, 4856, -1, 5594, -1], 'generators': [25, 74], 'label': '128.925.8.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.x1.b1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 61520918
    {'ambient': '128.925', 'aut_centralizer_order': 8, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.43', 'aut_weyl_index': 16, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.m1.a1', '4.n1.a1'], 'contains': ['16.c1.a1', '16.s1.a1', '16.s1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2998, -1, 4842, -1, 3006, -1, 4797, -1], 'generators': [3, 72], 'label': '128.925.8.y1.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.y1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520919
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 64, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.o1.a1', '4.p1.a1'], 'contains': ['16.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [472, -1, 2353, -1, 473, -1, 2331, -1], 'generators': [6], 'label': '128.925.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.z1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520920
    {'ambient': '128.925', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1674', 'aut_weyl_index': 4, 'centralizer': '32.c1.a1', 'complements': ['64.c1.a1', '64.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2581, 5458, 2425, 5410, 2588, 5467, 2403, 5467], 'generators': [1, 4], 'label': '128.925.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '64.128', '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': '32.39'}
  • id: 61520921
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 64, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1061, -1, 1494, -1, 1065, -1, 1480, -1], 'generators': [4], 'label': '128.925.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.ba1.a1', 'projective_image': '64.128', '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': '2.1'}
  • id: 61520922
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8200, 4387, 2977, 4918, 8225, 4395, 2952, 4970], 'generators': [80, 48], 'label': '128.925.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '64.128', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520923
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1'], 'contains': ['32.c1.a1', '32.d1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9076, 3239, 3609, 2993, 9104, 3245, 3576, 3024], 'generators': [50, 80], 'label': '128.925.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 61520924
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.e1.a1', '8.n1.a1', '8.v1.a1', '8.y1.a1', '8.z1.a1'], 'contains': ['32.b1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2096, 6981, 4119, 7795, 2103, 6871, 4082, 7844], 'generators': [72], 'label': '128.925.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.e1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520925
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.f1.b1', '8.o1.a1', '8.s1.a1', '8.w1.a1', '8.ba1.a1'], 'contains': ['32.b1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2873, 5535, 3278, 6373, 2882, 5545, 3251, 6374], 'generators': [24], 'label': '128.925.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.f1.a1', '8.f1.b1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '64.128', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520926
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.r1.a1', '8.u1.a1'], 'contains': ['32.c1.a1', '32.g1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8822, 2445, 3818, 3781, 8849, 2449, 3783, 3820], 'generators': [2, 80], 'label': '128.925.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520927
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.g1.a1', '8.g1.a2'], 'contains': ['32.a1.a1', '32.d1.a1', '32.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7833, -1, 7392, -1, 7857, -1, 7324, -1], 'generators': [2, 64], 'label': '128.925.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520928
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.g1.a2', '8.h1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5148, -1, 8808, -1, 5164, -1, 8727, -1], 'generators': [1, 64], 'label': '128.925.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.g1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520929
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9349, -1, 992, -1, 9377, -1, 1081, -1], 'generators': [7, 64, 32], 'label': '128.925.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.h1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 61520930
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.g1.a2', '8.j1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6985, -1, 8088, -1, 7006, -1, 8014, -1], 'generators': [3, 64], 'label': '128.925.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.i1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520931
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53164', 'aut_weyl_index': 2, 'centralizer': '32.a1.a1', 'complements': ['64.c1.a1', '64.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.f1.a1', '4.q1.a1', '4.q1.b1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2026, 3726, 1625, 3693, 2032, 3731, 1610, 3731], 'generators': [3, 4, 80], 'label': '128.925.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.43'}
  • id: 61520932
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.w1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a2', '8.l1.a1', '8.p1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6137, -1, 8390, -1, 6156, -1, 8313, -1], 'generators': [1, 50], 'label': '128.925.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520933
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.l1.b1', '8.p1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6137, -1, 9620, -1, 6156, -1, 9532, -1], 'generators': [73, 50], 'label': '128.925.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.j1.b1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520934
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '8.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.g1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4781, -1, 5883, -1, 4796, -1, 5829, -1], 'generators': [2, 48], 'label': '128.925.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520935
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.m1.a1', '8.p1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6505, -1, 6696, -1, 6524, -1, 6634, -1], 'generators': [25, 50], 'label': '128.925.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.l1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520936
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.l1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a2', '8.m1.b1', '8.p1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6505, -1, 7693, -1, 6524, -1, 7623, -1], 'generators': [81, 50], 'label': '128.925.16.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.l1.b1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520937
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.p1.a1', '8.r1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.h1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7465, -1, 7090, -1, 7488, -1, 7025, -1], 'generators': [1, 80], 'label': '128.925.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520938
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.l1.a1', '8.r1.a1'], 'contains': ['32.e1.a1', '32.g1.a1', '32.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5516, -1, 9318, -1, 5533, -1, 9233, -1], 'generators': [1, 2], 'label': '128.925.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.n1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520939
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a2', '8.l1.b1', '8.r1.a1'], 'contains': ['32.e1.a1', '32.g1.a1', '32.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5516, -1, 9922, -1, 5533, -1, 9831, -1], 'generators': [73, 2], 'label': '128.925.16.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.n1.b1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520940
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.h1.a1', '8.l1.a1', '8.l1.b1', '8.s1.a1', '8.t1.a1', '8.t1.b1'], 'contains': ['32.b1.a1', '32.e1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3651, -1, 6185, -1, 3662, -1, 6128, -1], 'generators': [1, 48], 'label': '128.925.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.o1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520941
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.b1.a1', '32.f1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2619, -1, 1526, -1, 2627, -1, 1610, -1], 'generators': [7, 48], 'label': '128.925.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.p1.a1', 'projective_image': '64.128', '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'}
  • id: 61520942
    {'ambient': '128.925', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['64.d1.a1', '64.c1.a1', '64.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2993, 6628, 2118, 6570, 3003, 6639, 2098, 6639], 'generators': [5, 6], 'label': '128.925.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.128'}
  • id: 61520943
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.q1.a1', '8.u1.a1'], 'contains': ['32.c1.a1', '32.f1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9620, -1, 667, -1, 9649, -1, 661, -1], 'generators': [7, 80], 'label': '128.925.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.q1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520944
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.h1.a1', '8.m1.a1', '8.m1.b1', '8.s1.a1', '8.x1.a1', '8.x1.b1'], 'contains': ['32.b1.a1', '32.h1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3905, -1, 5373, -1, 3917, -1, 5323, -1], 'generators': [81, 48], 'label': '128.925.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.r1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520945
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.j1.a1', '8.l1.a1', '8.m1.a1', '8.t1.a1', '8.x1.a1', '8.y1.a1'], 'contains': ['32.b1.a1', '32.i1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4413, -1, 5164, -1, 4427, -1, 5116, -1], 'generators': [3, 48], 'label': '128.925.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.s1.a1', 'projective_image': '64.128', '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': '8.3'}
  • id: 61520946
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.j1.a1', '8.l1.b1', '8.m1.b1', '8.t1.b1', '8.x1.b1', '8.y1.a1'], 'contains': ['32.b1.a1', '32.i1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4413, -1, 5582, -1, 4427, -1, 5530, -1], 'generators': [75, 48], 'label': '128.925.16.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.s1.b1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 61520947
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '8.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.n1.a1', '8.o1.a1', '8.t1.a1', '8.t1.b1', '8.x1.a1', '8.x1.b1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4159, -1, 4955, -1, 4172, -1, 4909, -1], 'generators': [74], 'label': '128.925.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.t1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520948
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 64, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.p1.a1', '8.r1.a1'], 'contains': ['32.c1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8568, -1, 6394, -1, 8594, -1, 6335, -1], 'generators': [3, 80], 'label': '128.925.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.u1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520949
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.q1.a1', '8.u1.a1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9874, -1, 1215, -1, 9904, -1, 1302, -1], 'generators': [5], 'label': '128.925.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.v1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61520950
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a2', '8.m1.a1', '8.r1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5883, -1, 8599, -1, 5901, -1, 8520, -1], 'generators': [25, 2], 'label': '128.925.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.w1.a1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520951
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 128, 'centralizer': '16.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.m1.b1', '8.r1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5883, -1, 9016, -1, 5901, -1, 8934, -1], 'generators': [81, 2], 'label': '128.925.16.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.w1.b1', 'projective_image': '64.128', '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': '4.2'}
  • id: 61520952
    {'ambient': '128.925', 'aut_centralizer_order': 256, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '64.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7409, 4387, 7023, 4918, 7431, 4395, 6959, 4970], 'generators': [64, 32], 'label': '128.925.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520953
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 16, 'centralizer': '16.c1.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.n1.a1', '8.o1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4438, 833, 3551, 826, 4452, 835, 3518, 835], 'generators': [2, 72, 80], 'label': '128.925.4.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': '64.128', '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': '16.11'}
  • id: 61520954
    {'ambient': '128.925', 'aut_centralizer_order': 256, 'aut_label': '32.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.k1.a1', '16.o1.a1', '16.p1.a1', '16.r1.a1', '16.s1.a1', '16.s1.b1', '16.t1.a1'], 'contains': ['64.a1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4032, 5392, 5164, 5968, 4044, 5390, 5116, 5965], 'generators': [48], 'label': '128.925.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.d1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520955
    {'ambient': '128.925', 'aut_centralizer_order': 256, 'aut_label': '32.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.e1.a1', '16.m1.a1', '16.q1.a1', '16.u1.a1', '16.v1.a1'], 'contains': ['64.a1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8568, 3394, 3714, 3933, 8594, 3400, 3679, 3975], 'generators': [80], 'label': '128.925.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.e1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.128', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520956
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '4.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.f1.a1', '16.j1.a1', '16.j1.b1', '16.k1.a1', '16.l1.a1', '16.l1.b1'], 'contains': ['64.a1.a1', '64.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6663, -1, 7261, -1, 6684, -1, 7195, -1], 'generators': [50, 32], 'label': '128.925.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.128', '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': '2.1'}
  • id: 61520957
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '8.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.j1.a1', '16.j1.b1', '16.m1.a1', '16.n1.a1', '16.n1.b1', '16.o1.a1'], 'contains': ['64.a1.a1', '64.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5610, -1, 8390, -1, 5628, -1, 8313, -1], 'generators': [1, 32], 'label': '128.925.32.e1.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.e1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520958
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.p1.a1', '16.q1.a1'], 'contains': ['64.a1.a1', '64.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8839, -1, 1526, -1, 8866, -1, 1610, -1], 'generators': [7, 32], 'label': '128.925.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.128', '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': '2.1'}
  • id: 61520959
    {'ambient': '128.925', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.f1.a1', '16.k1.a1', '16.n1.a1', '16.n1.b1', '16.w1.a1', '16.w1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6391, -1, 7902, -1, 6411, -1, 7830, -1], 'generators': [2], 'label': '128.925.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520960
    {'ambient': '128.925', 'aut_centralizer_order': 64, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.l1.a1', '16.l1.b1', '16.m1.a1', '16.r1.a1', '16.w1.a1', '16.w1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5883, -1, 7693, -1, 5901, -1, 7623, -1], 'generators': [81], 'label': '128.925.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.128', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61520961
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '8.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.a1', '16.l1.a1', '16.n1.a1', '16.s1.a1', '16.u1.a1', '16.w1.a1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6137, -1, 7485, -1, 6156, -1, 7416, -1], 'generators': [3], 'label': '128.925.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.128', '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': '2.1'}
  • id: 61520962
    {'ambient': '128.925', 'aut_centralizer_order': 32, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '8.g1.a2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.b1', '16.l1.b1', '16.n1.b1', '16.s1.b1', '16.u1.a1', '16.w1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6137, -1, 8111, -1, 6156, -1, 8037, -1], 'generators': [75], 'label': '128.925.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.i1.b1', 'projective_image': '64.128', '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': '2.1'}
  • id: 61520963
    {'ambient': '128.925', 'aut_centralizer_order': 16, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1'], 'contains': ['64.b1.a1', '64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T2029', 'count': 16, 'diagramx': [9129, -1, 1288, -1, 9157, -1, 1374, -1], 'generators': [7, 64], 'label': '128.925.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1.a1', 'old_label': '32.j1.a1', 'projective_image': '128.925', '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': '1.1'}