Abstract group data - 128.56

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 4, 2, 4, 4, 2], 'aut_gens': [[1, 8, 32], [17, 8, 48], [21, 8, 52], [25, 8, 32], [23, 88, 96], [1, 72, 40], [37, 8, 32], [21, 8, 32]], 'aut_group': '1024.dmp', 'aut_hash': 6590592888782812429, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 20, 'aut_perms': [38792297419960320, 372049579608824903, 657153749148352680, 1662343506887984040, 1639177843826448120, 137055202348459806, 404418486604821127], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 4, 1, 2], [4, 4, 4, 2], [4, 8, 2, 1], [8, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '64.138', 'autcentquo_hash': 138, 'autcentquo_nilpotent': True, 'autcentquo_order': 64, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\wr C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 4, 10], [4, 8, 2], [8, 8, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '32.6', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 56, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 4, 1, 2], [4, 4, 2, 4], [4, 8, 2, 1], [8, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '32.23', 'frattini_quotient': '4.2', 'hash': 56, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 4], 'inner_gens': [[1, 88, 120], [81, 8, 32], [73, 8, 32]], 'inner_hash': 6, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^3:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 6]], 'label': '128.56', 'linC_count': 32, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 6, 'linR_count': 8, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:C8', 'ngens': 2, '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': 12, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 26, 'number_divisions': 15, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 59, 'number_subgroups': 144, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 64], 'outer_gens': [[7, 72, 32], [3, 72, 48], [3, 72, 52], [39, 72, 36]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [7, 16, 1560, 5903], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 5], [8, 2]], 'representations': {'PC': {'code': 48661685555083033998044459, 'gens': [1, 4, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 14, 36, 2467, 346, 80, 5045, 2364, 124, 3926]}, 'Perm': {'d': 24, 'gens': [28263537000448541534463, 4566826096255048965916, 57500065530312782227200, 84665895578973748547830, 7921663911634639178880, 111704289647710435978396, 111704289647710435966080]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:C_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: 43443294
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 56, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 43443305
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 56, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 43443313
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 56, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 20, 'size': 1}
  • id: 43443314
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 56, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 4, 'size': 1}
  • id: 43443315
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 56, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 68, 'size': 2}
  • id: 43443316
    {'aut_label': '2E', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 56, 'group_order': 128, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 64, 'size': 2}
  • id: 43443317
    {'aut_label': '4A', 'centralizer': '4.a1.a1', 'counter': 7, 'group_counter': 56, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 8, 'size': 4}
  • id: 43443318
    {'aut_label': '4B', 'centralizer': '4.a1.a1', 'counter': 8, 'group_counter': 56, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 12, 'size': 4}
  • id: 43443319
    {'aut_label': '4C1', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 56, 'group_order': 128, 'label': '4C1', 'order': 4, 'powers': [6], 'representative': 32, 'size': 4}
  • id: 43443295
    {'aut_label': '4C1', 'centralizer': '4.a1.a1', 'counter': 10, 'group_counter': 56, 'group_order': 128, 'label': '4C-1', 'order': 4, 'powers': [6], 'representative': 96, 'size': 4}
  • id: 43443296
    {'aut_label': '4C1', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 56, 'group_order': 128, 'label': '4D1', 'order': 4, 'powers': [6], 'representative': 36, 'size': 4}
  • id: 43443297
    {'aut_label': '4C1', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 56, 'group_order': 128, 'label': '4D-1', 'order': 4, 'powers': [6], 'representative': 100, 'size': 4}
  • id: 43443298
    {'aut_label': '4E1', 'centralizer': '4.e1.a1', 'counter': 13, 'group_counter': 56, 'group_order': 128, 'label': '4E1', 'order': 4, 'powers': [4], 'representative': 2, 'size': 4}
  • id: 43443299
    {'aut_label': '4E1', 'centralizer': '4.e1.a1', 'counter': 14, 'group_counter': 56, 'group_order': 128, 'label': '4E-1', 'order': 4, 'powers': [4], 'representative': 6, 'size': 4}
  • id: 43443300
    {'aut_label': '4E1', 'centralizer': '4.e1.b1', 'counter': 15, 'group_counter': 56, 'group_order': 128, 'label': '4F1', 'order': 4, 'powers': [4], 'representative': 26, 'size': 4}
  • id: 43443301
    {'aut_label': '4E1', 'centralizer': '4.e1.b1', 'counter': 16, 'group_counter': 56, 'group_order': 128, 'label': '4F-1', 'order': 4, 'powers': [4], 'representative': 30, 'size': 4}
  • id: 43443302
    {'aut_label': '4G1', 'centralizer': '8.e1.a1', 'counter': 17, 'group_counter': 56, 'group_order': 128, 'label': '4G1', 'order': 4, 'powers': [3], 'representative': 34, 'size': 8}
  • id: 43443303
    {'aut_label': '4G1', 'centralizer': '8.e1.a1', 'counter': 18, 'group_counter': 56, 'group_order': 128, 'label': '4G-1', 'order': 4, 'powers': [3], 'representative': 38, 'size': 8}
  • id: 43443304
    {'aut_label': '8A1', 'centralizer': '8.h1.a1', 'counter': 19, 'group_counter': 56, 'group_order': 128, 'label': '8A1', 'order': 8, 'powers': [13], 'representative': 1, 'size': 8}
  • id: 43443306
    {'aut_label': '8A1', 'centralizer': '8.h1.a1', 'counter': 20, 'group_counter': 56, 'group_order': 128, 'label': '8A-1', 'order': 8, 'powers': [14], 'representative': 7, 'size': 8}
  • id: 43443307
    {'aut_label': '8A1', 'centralizer': '8.h1.a1', 'counter': 21, 'group_counter': 56, 'group_order': 128, 'label': '8A3', 'order': 8, 'powers': [14], 'representative': 3, 'size': 8}
  • id: 43443308
    {'aut_label': '8A1', 'centralizer': '8.h1.a1', 'counter': 22, 'group_counter': 56, 'group_order': 128, 'label': '8A-3', 'order': 8, 'powers': [13], 'representative': 5, 'size': 8}
  • id: 43443309
    {'aut_label': '8A1', 'centralizer': '8.h1.b1', 'counter': 23, 'group_counter': 56, 'group_order': 128, 'label': '8B1', 'order': 8, 'powers': [15], 'representative': 33, 'size': 8}
  • id: 43443310
    {'aut_label': '8A1', 'centralizer': '8.h1.b1', 'counter': 24, 'group_counter': 56, 'group_order': 128, 'label': '8B-1', 'order': 8, 'powers': [16], 'representative': 39, 'size': 8}
  • id: 43443311
    {'aut_label': '8A1', 'centralizer': '8.h1.b1', 'counter': 25, 'group_counter': 56, 'group_order': 128, 'label': '8B3', 'order': 8, 'powers': [16], 'representative': 35, 'size': 8}
  • id: 43443312
    {'aut_label': '8A1', 'centralizer': '8.h1.b1', 'counter': 26, 'group_counter': 56, 'group_order': 128, 'label': '8B-3', 'order': 8, 'powers': [15], 'representative': 37, '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: 103912
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 103919
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 103920
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 103921
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 103922
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103923
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103926
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103913
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103924
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1g', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103925
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.1h', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103914
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.2c', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103915
    {'cdim': 4, 'counter': 12, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.4a', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103916
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.4b', 'multiplicity': 1, 'nt': [16, 40], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 103917
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.4c', 'multiplicity': 2, 'nt': [16, 131], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 103918
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '128.56', 'group_order': 128, 'image': None, 'label': '128.56.4d', 'multiplicity': 2, 'nt': [16, 154], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 99252
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.56.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 99263
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 64, 'label': '128.56.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 99271
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.56.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 99272
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.56.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 99273
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 32, 'label': '128.56.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 99274
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 32, 'label': '128.56.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 99275
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 32, 'label': '128.56.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 99276
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 32, 'label': '128.56.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 99277
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.b1', 'kernel_order': 16, 'label': '128.56.1g1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]]]}
  • id: 99253
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.b1', 'kernel_order': 16, 'label': '128.56.1g2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]]]}
  • id: 99254
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.b1', 'kernel_order': 16, 'label': '128.56.1g3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]]]}
  • id: 99255
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.b1', 'kernel_order': 16, 'label': '128.56.1g4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]]]}
  • id: 99256
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.56.1h1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]]]}
  • id: 99257
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.56.1h2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 3]]]}
  • id: 99258
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.56.1h3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 1]]]}
  • id: 99259
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.56.1h4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]]]}
  • id: 99260
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 16, 'label': '128.56.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99261
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 16, 'label': '128.56.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99262
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 8, 'label': '128.56.2c1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99264
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 8, 'label': '128.56.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99265
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 4, 'label': '128.56.4a', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99266
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '32.8', 'image_order': 32, 'indicator': -1, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.56.4b', 'nt': [16, 40], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99267
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '64.36', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.56.4c1', 'nt': [16, 131], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99268
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '64.36', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.56.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99269
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '64.35', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 2, 'label': '128.56.4d1', 'nt': [16, 154], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 99270
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '128.56', 'group_counter': 56, 'group_order': 128, 'image': None, 'image_isoclass': '64.35', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 2, 'label': '128.56.4d2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 8192531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.56.1.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': '128.56', 'subgroup_hash': 56, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_8', 'supersolvable': True, 'sylow': 2}
  • id: 8192542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.63', 'subgroup_hash': 63, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.5', 'subgroup_hash': 5, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8192564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.5', 'subgroup_hash': 5, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8192575
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.4.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': ['Phi', 'U1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192534
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.8.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': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192538
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192539
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192540
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8192548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.16.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': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], '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: 8192549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.16.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': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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: 8192559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8192561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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: 8192562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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: 8192563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.16.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: 8192565
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.16.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192566
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8192567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.32.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': '32.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U3'], '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: 8192568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.32.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': '32.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_4', 'simple': 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: 8192569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.56.32.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': '32.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_8', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], '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: 8192570
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192571
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.32.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: 8192573
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.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: 8192574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.56.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8192576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.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: 8192577
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.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: 8192578
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8192580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.56.64.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': '64.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.\\OD_{16}', 'simple': True, 'solvable': True, 'special_labels': ['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: 8192581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.56.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8192582
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.56.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.35', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8192583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.64.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: 8192584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.56.64.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: 8192585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.56', 'ambient_counter': 56, 'ambient_order': 128, 'ambient_tex': 'C_4^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.56.128.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': '128.56', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 56, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_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: 8192531
    {'ambient': '128.56', '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': '32.a1.a1', 'complements': ['128.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2926, 3801, 6513, 6475, 2861, 3488, 6606, 5995], 'generators': [1, 32], 'label': '128.56.1.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.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.6', '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': '32.6'}
  • id: 8192532
    {'ambient': '128.56', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '16.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.h1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1594, -1, 7127, -1, 1562, -1, 7229, -1], 'generators': [1, 80], 'label': '128.56.4.e1.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.e1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8192533
    {'ambient': '128.56', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '16.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.b1.b1', '8.h1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1594, -1, 7623, -1, 1562, -1, 7731, -1], 'generators': [33, 80], 'label': '128.56.4.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '4.e1.b1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8192534
    {'ambient': '128.56', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5007, 5724, 4035, 3946, 4908, 5222, 4093, 3653], 'generators': [88, 4, 80], 'label': '128.56.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.b1.a1', '4.a1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192535
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.l1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2425, 2059, 6517, 9240, 2377, 1878, 6610, 8556], 'generators': [2, 80, 16], 'label': '128.56.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.6', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8192536
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.b1', '4.e1.b1'], 'contains': ['16.a1.a1', '16.e1.b1', '16.l1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2425, 2059, 7272, 6593, 2377, 1878, 7376, 6105], 'generators': [90, 80, 16], 'label': '128.56.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '32.6', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8192537
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6750, 9095, 2908, 540, 6624, 8297, 2949, 500], 'generators': [32, 88], 'label': '128.56.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '64.5', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192538
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.h1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6750, 9095, 3267, 1922, 6624, 8297, 3314, 1780], 'generators': [36, 88], 'label': '128.56.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '64.5', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192539
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.h1.b1', '16.i1.a1', '16.k1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6000, -1, 2022, -1, 5888, -1, 2051, -1], 'generators': [32, 4, 16], 'label': '128.56.8.d1.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.d1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192540
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.j1.a1', '16.j1.a2'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3407, -1, 5399, -1, 3339, -1, 5476, -1], 'generators': [114, 80, 16], 'label': '128.56.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '32.6', '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': '4.2'}
  • id: 8192541
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.e1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1643, -1, 7856, -1, 1612, -1, 7967, -1], 'generators': [2, 88], 'label': '128.56.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '32.6', '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': '4.2'}
  • id: 8192542
    {'ambient': '128.56', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 4, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3394, 5543, 5631, 3946, 3321, 5119, 5712, 3653], 'generators': [32, 2, 88], 'label': '128.56.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.a1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8192543
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.d1.a1', '16.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4219, -1, 4785, -1, 4136, -1, 4853, -1], 'generators': [114, 88], 'label': '128.56.8.g1.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': '8.g1.a1', 'projective_image': '32.6', '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': '4.2'}
  • id: 8192544
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.e1.a1', '16.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [818, -1, 8373, -1, 803, -1, 8492, -1], 'generators': [1, 16], 'label': '128.56.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '8.h1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8192545
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '8.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1'], 'contains': ['16.e1.b1', '16.m1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [818, -1, 8969, -1, 803, -1, 9097, -1], 'generators': [33, 16], 'label': '128.56.8.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.b1', 'old_label': '8.h1.b1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192546
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.h1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7282, -1, 2548, -1, 7139, -1, 2585, -1], 'generators': [32, 92], 'label': '128.56.8.i1.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.i1.a1', 'projective_image': '64.5', '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': '2.1'}
  • id: 8192547
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.d1.a1', '8.e1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.f1.a1', '32.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4900, 3258, 4912, 6324, 4804, 2972, 4982, 5855], 'generators': [4, 80, 16], 'label': '128.56.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192548
    {'ambient': '128.56', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'contains': ['32.c1.a1', '32.d1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6432, 8801, 3241, 1922, 6305, 8029, 3287, 1780], 'generators': [88, 80], 'label': '128.56.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '64.5', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192549
    {'ambient': '128.56', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.i1.a1'], 'contains': ['32.c1.a1', '32.e1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7282, 5724, 2645, 4215, 7139, 5222, 2682, 3903], 'generators': [92, 80], 'label': '128.56.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '64.5', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192550
    {'ambient': '128.56', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4219, -1, 4434, -1, 4136, -1, 4497, -1], 'generators': [88, 4], 'label': '128.56.16.d1.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.d1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192551
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.h1.a1'], 'contains': ['32.a1.a1', '32.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [818, -1, 8373, -1, 803, -1, 8492, -1], 'generators': [2, 16], 'label': '128.56.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8192552
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.f1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '32.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [818, -1, 8969, -1, 803, -1, 9097, -1], 'generators': [90, 16], 'label': '128.56.16.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '16.e1.b1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192553
    {'ambient': '128.56', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2456, 2059, 6513, 6475, 2402, 1940, 6606, 5995], 'generators': [1, 88], 'label': '128.56.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8192554
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3369, -1, 6583, -1, 3303, -1, 6677, -1], 'generators': [114, 16], 'label': '128.56.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8192555
    {'ambient': '128.56', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5582, -1, 3838, -1, 5472, -1, 3892, -1], 'generators': [88, 84], 'label': '128.56.16.g1.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.g1.a1', 'projective_image': '64.5', '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': '2.1'}
  • id: 8192556
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.i1.a1'], 'contains': ['32.c1.a1', '32.j1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9831, -1, 1451, -1, 9638, -1, 1472, -1], 'generators': [32, 16], 'label': '128.56.16.h1.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.h1.a1', 'projective_image': '64.5', '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': '2.1'}
  • id: 8192557
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.d1.a1', '8.i1.a1'], 'contains': ['32.c1.a1', '32.j1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9831, -1, 2048, -1, 9638, -1, 2077, -1], 'generators': [36, 16], 'label': '128.56.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.b1', 'projective_image': '64.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192558
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.f1.a1', '32.j1.a1', '32.j1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8981, -1, 259, -1, 8805, -1, 262, -1], 'generators': [32, 20], 'label': '128.56.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '64.36', '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': '1.1'}
  • id: 8192559
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.f1.a1', '32.g1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2519, -1, 5390, -1, 2469, -1, 5467, -1], 'generators': [114, 80], 'label': '128.56.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192560
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.f1.a1', '32.g1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2519, -1, 5987, -1, 2469, -1, 6072, -1], 'generators': [114, 64], 'label': '128.56.16.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '16.j1.a2', 'projective_image': '64.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192561
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.h1.a1', '32.j1.a1', '32.j1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8131, -1, 856, -1, 7972, -1, 867, -1], 'generators': [32, 4], 'label': '128.56.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.35', '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': '1.1'}
  • id: 8192562
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.h1.a1', '32.i1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1668, -1, 7180, -1, 1636, -1, 7282, -1], 'generators': [2, 80], 'label': '128.56.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.l1.a1', 'projective_image': '64.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192563
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1'], 'contains': ['32.h1.a1', '32.i1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1668, -1, 7776, -1, 1636, -1, 7887, -1], 'generators': [90, 80], 'label': '128.56.16.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.b1', 'old_label': '16.l1.b1', 'projective_image': '64.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192564
    {'ambient': '128.56', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2456, 2059, 7289, 9460, 2402, 1940, 7393, 8759], 'generators': [33, 88], 'label': '128.56.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8192565
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1'], 'contains': ['32.i1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [169, -1, 9425, -1, 165, -1, 9560, -1], 'generators': [1], 'label': '128.56.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.35', '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': '1.1'}
  • id: 8192566
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1'], 'contains': ['32.i1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [169, -1, 9741, -1, 165, -1, 9880, -1], 'generators': [33], 'label': '128.56.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.b1', 'old_label': '16.m1.b1', 'projective_image': '64.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192567
    {'ambient': '128.56', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3706, 2013, 5934, 6981, 3634, 1837, 6027, 6464], 'generators': [4, 16], 'label': '128.56.32.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.c1.a1', '64.a1.a1', '64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.6', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192568
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '64.d1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5244, 3869, 4530, 5599, 5141, 3529, 4604, 5183], 'generators': [84, 16], 'label': '128.56.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.12', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192569
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.h1.a1', '16.h1.b1'], 'contains': ['64.a1.a1', '64.e1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6656, 5724, 3241, 4215, 6526, 5222, 3287, 3903], 'generators': [80, 16], 'label': '128.56.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8192570
    {'ambient': '128.56', 'aut_centralizer_order': 256, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.g1.a1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5725, -1, 4188, -1, 5613, -1, 4248, -1], 'generators': [88], 'label': '128.56.32.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': '64.5', '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: 8192571
    {'ambient': '128.56', 'aut_centralizer_order': 256, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.g1.a1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6175, -1, 3842, -1, 6054, -1, 3897, -1], 'generators': [92], 'label': '128.56.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.5', '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: 8192572
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.i1.a1', '16.j1.a1', '16.j1.a2'], 'contains': ['64.b1.a1', '64.d1.a1', '64.e1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4732, -1, 4899, -1, 4638, -1, 4978, -1], 'generators': [20, 80], 'label': '128.56.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192573
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.j1.a1', '16.j1.a2'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3225, -1, 5596, -1, 3162, -1, 5685, -1], 'generators': [114], 'label': '128.56.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.36', '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': '1.1'}
  • id: 8192574
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.k1.a1', '16.l1.a1', '16.l1.b1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.e1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4219, -1, 5258, -1, 4136, -1, 5343, -1], 'generators': [4, 80], 'label': '128.56.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.35', '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': '1.1'}
  • id: 8192575
    {'ambient': '128.56', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 32, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.d1.a1', '8.i1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6000, 9390, 3088, 1214, 5888, 8566, 3132, 1124], 'generators': [32, 88, 4], 'label': '128.56.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8192576
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1244, -1, 7618, -1, 1219, -1, 7958, -1], 'generators': [2], 'label': '128.56.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192577
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.l1.b1', '16.m1.b1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1244, -1, 8373, -1, 1219, -1, 8421, -1], 'generators': [90], 'label': '128.56.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.b1', 'old_label': '32.i1.b1', 'projective_image': '64.35', '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': '1.1'}
  • id: 8192578
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.i1.a1', '16.k1.a1'], 'contains': ['64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1579', 'count': 4, 'diagramx': [8556, -1, 1153, -1, 8388, -1, 1170, -1], 'generators': [32], 'label': '128.56.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.j1.a1', 'projective_image': '128.56', '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'}
  • id: 8192579
    {'ambient': '128.56', 'aut_centralizer_order': 64, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.i1.a1', '16.k1.a1'], 'contains': ['64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1579', 'count': 4, 'diagramx': [8556, -1, 1610, -1, 8388, -1, 1633, -1], 'generators': [36], 'label': '128.56.32.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.j1.b1', 'projective_image': '128.56', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192580
    {'ambient': '128.56', 'aut_centralizer_order': 1024, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, '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'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5244, 3869, 4360, 5599, 5141, 3529, 4426, 5183], 'generators': [16], 'label': '128.56.64.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': '64.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.5', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192581
    {'ambient': '128.56', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4250, 610, 5408, 8026, 4167, 557, 5494, 7432], 'generators': [20], 'label': '128.56.64.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.36', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192582
    {'ambient': '128.56', 'aut_centralizer_order': 1024, 'aut_label': '64.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.h1.a1', '32.i1.a1', '32.i1.b1'], 'contains': ['128.a1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3737, 2241, 5934, 6813, 3664, 2043, 6027, 6308], 'generators': [4], 'label': '128.56.64.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '64.35', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.35', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8192583
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.f1.a1', '32.h1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4732, -1, 4899, -1, 4638, -1, 4978, -1], 'generators': [84], 'label': '128.56.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.56', '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: 8192584
    {'ambient': '128.56', 'aut_centralizer_order': 512, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.f1.a1', '32.h1.a1', '32.j1.a1', '32.j1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5694, -1, 3548, -1, 5582, -1, 3603, -1], 'generators': [80], 'label': '128.56.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.56', '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: 8192585
    {'ambient': '128.56', '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': [4732, 2241, 4899, 6813, 4638, 2043, 4978, 6308], 'generators': [], 'label': '128.56.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.c1.a1', '64.a1.a1', '64.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.56', '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: 8192586
    {'ambient': '128.56', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.f1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2468, 1946, 6513, 6762, 2420, 1775, 6606, 6261], 'generators': [2, 88, 80], 'label': '128.56.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8192587
    {'ambient': '128.56', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4250, 5724, 4785, 3946, 4167, 5222, 4853, 3653], 'generators': [114, 88, 80], 'label': '128.56.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8192588
    {'ambient': '128.56', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3375, -1, 5399, -1, 3309, -1, 5476, -1], 'generators': [32, 2], 'label': '128.56.4.d1.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.d1.a1', 'projective_image': '32.6', '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': '8.5'}
  • id: 8192589
    {'ambient': '128.56', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.d1.a1', '8.e1.a1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3375, -1, 5895, -1, 3309, -1, 5979, -1], 'generators': [32, 90], 'label': '128.56.4.d1.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.d1.b1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}