Abstract group data - 128.734

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 4, 2, 4, 2, 2, 2, 4], 'aut_gens': [[13485, 4455, 48323, 56453], [13485, 4455, 56389, 56453], [13485, 4455, 13387, 21645], [13485, 20843, 48323, 56453], [13485, 4455, 30919, 56453], [61473, 20963, 48323, 56453], [13485, 4455, 13515, 56453], [13485, 32673, 13387, 21645], [21611, 4455, 30919, 56453], [48165, 53739, 48323, 56453]], 'aut_group': None, 'aut_hash': 1969822349860123513, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 40, 'aut_perms': [670133381802392074356705057145363591391970435664, 732486157433238425487085569061992167711096513524, 418446495558843215148740322471238700710688602920, 104689544639787197571408603032417378878992530070, 2631130187942707189740971091974242579789169931, 418700856322987460676327928399762803632210768404, 732486457400032849919621180284034830752172737000, 121965968971197275514009201971499993035604165561, 7865355689016556955349915239823725256074607915], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 8, 1, 1], [2, 8, 2, 2], [4, 2, 1, 4], [4, 4, 4, 1], [4, 8, 1, 1], [4, 8, 2, 1], [8, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3.C_2^6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 32, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 8, 5], [4, 2, 4], [4, 4, 4], [4, 8, 3], [8, 8, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '32.27', 'commutator_count': 1, 'commutator_label': '16.10', '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': 734, '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], [2, 8, 1, 5], [4, 2, 1, 4], [4, 4, 1, 4], [4, 8, 1, 3], [8, 8, 1, 2], [8, 8, 2, 1]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 336, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '8.5', 'hash': 734, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 2], 'inner_gens': [[13485, 32673, 13387, 21645], [21611, 4455, 30919, 56453], [48165, 53739, 48323, 56453], [48293, 4455, 48323, 56453]], 'inner_hash': 27, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': None, 'inner_tex': 'C_2^2\\wr C_2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [4, 4]], 'label': '128.734', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 24, 'linQ_dim': 6, 'linQ_dim_count': 24, 'linR_count': 24, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:D4', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 26, 'number_divisions': 25, 'number_normal_subgroups': 46, 'number_subgroup_autclasses': 139, 'number_subgroup_classes': 239, 'number_subgroups': 656, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 47], [4, 48], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 2, 4], 'outer_gen_pows': [56453, 4097, 39049, 4097, 4097, 4097], 'outer_gens': [[61473, 37351, 13515, 56453], [13485, 4455, 21709, 21645], [13485, 20843, 61647, 56453], [61473, 37351, 21709, 21645], [61473, 20963, 13387, 21645], [61473, 37351, 4289, 21645]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 32, 'outer_perms': [196162835435764981665662870785606822, 8348204302821459038416821492019701, 187660892854463646960044104980798094, 228196900270941822509039869105384465, 66990084564814550180466325318835161, 263041787167960847292089916291039577], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 5]], 'representations': {'PC': {'code': 79104398895142578185578, 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 85, 36, 675, 794, 80, 1411, 4037, 124]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101729081201910, 58301495106334124, 25038645869518594]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [111169, 111487, 829447, 111745, 113483, 2821273, 4176589]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4225, 21709, 48259, 4419, 4161, 37163, 39049]}, 'Perm': {'d': 12, 'gens': [40764967, 12783016, 1865642, 95242440, 23, 18558023, 139725360]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:D_4', 'transitive_degree': 16, '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: 171566222
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 734, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 4097, 'size': 1}
  • id: 171566233
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 734, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 38921, 'size': 1}
  • id: 171566241
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 734, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 30727, 'size': 1}
  • id: 171566242
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 734, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 61455, 'size': 1}
  • id: 171566243
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 734, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 61583, 'size': 2}
  • id: 171566244
    {'aut_label': '2E', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 734, 'group_order': 128, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 39049, 'size': 2}
  • id: 171566245
    {'aut_label': '2F', 'centralizer': '8.a1.a1', 'counter': 7, 'group_counter': 734, 'group_order': 128, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 13485, 'size': 8}
  • id: 171566246
    {'aut_label': '2F', 'centralizer': '8.a1.b1', 'counter': 8, 'group_counter': 734, 'group_order': 128, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 30889, 'size': 8}
  • id: 171566247
    {'aut_label': '2H', 'centralizer': '8.i1.a1', 'counter': 9, 'group_counter': 734, 'group_order': 128, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 4271, 'size': 8}
  • id: 171566223
    {'aut_label': '2I', 'centralizer': '8.s1.a1', 'counter': 10, 'group_counter': 734, 'group_order': 128, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 49029, 'size': 8}
  • id: 171566224
    {'aut_label': '2H', 'centralizer': '8.i1.a1', 'counter': 11, 'group_counter': 734, 'group_order': 128, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 56483, 'size': 8}
  • id: 171566225
    {'aut_label': '4A', 'centralizer': '2.g1.a1', 'counter': 12, 'group_counter': 734, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 56453, 'size': 2}
  • id: 171566226
    {'aut_label': '4B', 'centralizer': '2.f1.a1', 'counter': 13, 'group_counter': 734, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 13323, 'size': 2}
  • id: 171566227
    {'aut_label': '4C', 'centralizer': '2.g1.a1', 'counter': 14, 'group_counter': 734, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 48259, 'size': 2}
  • id: 171566228
    {'aut_label': '4D', 'centralizer': '2.f1.a1', 'counter': 15, 'group_counter': 734, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 56325, 'size': 2}
  • id: 171566229
    {'aut_label': '4E', 'centralizer': '4.d1.a1', 'counter': 16, 'group_counter': 734, 'group_order': 128, 'label': '4E', 'order': 4, 'powers': [6], 'representative': 48323, 'size': 4}
  • id: 171566230
    {'aut_label': '4E', 'centralizer': '4.d1.a1', 'counter': 17, 'group_counter': 734, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [6], 'representative': 13515, 'size': 4}
  • id: 171566231
    {'aut_label': '4E', 'centralizer': '4.d1.a1', 'counter': 18, 'group_counter': 734, 'group_order': 128, 'label': '4G', 'order': 4, 'powers': [6], 'representative': 56389, 'size': 4}
  • id: 171566232
    {'aut_label': '4E', 'centralizer': '4.d1.a1', 'counter': 19, 'group_counter': 734, 'group_order': 128, 'label': '4H', 'order': 4, 'powers': [6], 'representative': 21581, 'size': 4}
  • id: 171566234
    {'aut_label': '4I', 'centralizer': '8.t1.a1', 'counter': 20, 'group_counter': 734, 'group_order': 128, 'label': '4I', 'order': 4, 'powers': [3], 'representative': 4455, 'size': 8}
  • id: 171566235
    {'aut_label': '4I', 'centralizer': '8.t1.a1', 'counter': 21, 'group_counter': 734, 'group_order': 128, 'label': '4J', 'order': 4, 'powers': [4], 'representative': 20843, 'size': 8}
  • id: 171566236
    {'aut_label': '4K', 'centralizer': '8.s1.a1', 'counter': 22, 'group_counter': 734, 'group_order': 128, 'label': '4K', 'order': 4, 'powers': [2], 'representative': 48909, 'size': 8}
  • id: 171566237
    {'aut_label': '8A', 'centralizer': '8.u1.a1', 'counter': 23, 'group_counter': 734, 'group_order': 128, 'label': '8A', 'order': 8, 'powers': [14], 'representative': 32621, 'size': 8}
  • id: 171566238
    {'aut_label': '8A', 'centralizer': '8.u1.a1', 'counter': 24, 'group_counter': 734, 'group_order': 128, 'label': '8B', 'order': 8, 'powers': [14], 'representative': 16233, 'size': 8}
  • id: 171566239
    {'aut_label': '8C1', 'centralizer': '8.v1.a1', 'counter': 25, 'group_counter': 734, 'group_order': 128, 'label': '8C1', 'order': 8, 'powers': [15], 'representative': 53583, 'size': 8}
  • id: 171566240
    {'aut_label': '8C1', 'centralizer': '8.v1.a1', 'counter': 26, 'group_counter': 734, 'group_order': 128, 'label': '8C-1', 'order': 8, 'powers': [15], 'representative': 53703, '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: 17307893
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1a', '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: 17307904
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1b', '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: 17307911
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1c', '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: 17307912
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1d', '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: 17307913
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 17307914
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17307915
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17307916
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 17307917
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, -2, 0, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307894
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307895
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307896
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, 2, 0, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307897
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2], 'schur_index': 1}
  • id: 17307898
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], 'schur_index': 1}
  • id: 17307899
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, -2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307900
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307901
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307902
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 0, 2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307903
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307905
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307906
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.2m', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307907
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.4a', 'multiplicity': 1, 'nt': [8, 26], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307908
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.4b', 'multiplicity': 1, 'nt': [8, 26], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307909
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.4c', 'multiplicity': 1, 'nt': [8, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 17307910
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '128.734', 'group_order': 128, 'image': None, 'label': '128.734.4d', 'multiplicity': 1, 'nt': [8, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 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: 37928088
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.734.1a', '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: 37928099
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 64, 'label': '128.734.1b', '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: 37928107
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 64, 'label': '128.734.1c', '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: 37928108
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 64, 'label': '128.734.1d', '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: 37928109
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 64, 'label': '128.734.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 37928110
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 64, 'label': '128.734.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 37928111
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.734.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37928112
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.734.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37928113
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.g1.b1', 'kernel_order': 16, 'label': '128.734.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928089
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1.b1', 'kernel_order': 16, 'label': '128.734.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928090
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1.a1', 'kernel_order': 16, 'label': '128.734.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928091
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.g1.a1', 'kernel_order': 16, 'label': '128.734.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928092
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.b1', 'kernel_order': 16, 'label': '128.734.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]]]}
  • id: 37928093
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 16, 'label': '128.734.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 37928094
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 16, 'label': '128.734.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928095
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.b1', 'kernel_order': 16, 'label': '128.734.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928096
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 16, 'label': '128.734.2i', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928097
    {'center': '4.c1.a1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.734.2j', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928098
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.b1', 'kernel_order': 16, 'label': '128.734.2k', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928100
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 16, 'label': '128.734.2l', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928101
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 8, 'label': '128.734.2m1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]]]}
  • id: 37928102
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 8, 'label': '128.734.2m2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]]]}
  • id: 37928103
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '64.134', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.734.4a', 'nt': [8, 26], 'q_character': None, 'values': [[[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]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928104
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '64.134', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1.a1', 'kernel_order': 2, 'label': '128.734.4b', 'nt': [8, 26], 'q_character': None, 'values': [[[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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928105
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '64.134', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1.b1', 'kernel_order': 2, 'label': '128.734.4c', 'nt': [8, 26], 'q_character': None, 'values': [[[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]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37928106
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.734', 'group_counter': 734, 'group_order': 128, 'image': None, 'image_isoclass': '64.134', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1.b1', 'kernel_order': 2, 'label': '128.734.4d', 'nt': [8, 26], 'q_character': None, 'values': [[[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]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 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: 262799316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.734.1.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': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 262799427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.4.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 262799491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 262799492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'U1', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 262799505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bd1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 262799322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.8.bo1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 262799333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799336
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799342
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.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: 262799344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.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: 262799346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799376
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799377
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.16.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799378
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 262799379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bk1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799386
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bk1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 262799388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.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: 262799390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.16.bn1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 188, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.32.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': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, '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: 262799417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.734.32.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': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799418
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 191, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, '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': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 192, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799420
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 193, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799421
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 194, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799422
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.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: 262799423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799424
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799425
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799429
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799441
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799442
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 212, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.r1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.s1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799449
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799451
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.s1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.b2', 'outer_equivalence': False, 'perfect': False, '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: 262799452
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.t1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 262799454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.734.32.t1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.b2', 'outer_equivalence': False, 'perfect': False, '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: 262799456
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799457
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799458
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799459
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.32.u1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 262799460
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 229, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.64.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': '64.73', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 73, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799462
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.64.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': '64.134', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 134, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': True, 'solvable': True, 'special_labels': [], '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: 262799463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.734.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.134', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 134, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': True, 'solvable': True, 'special_labels': [], '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: 262799464
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 262799465
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.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: 262799466
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.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: 262799467
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 262799468
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 262799469
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 262799470
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.734.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 262799471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.734', 'ambient_counter': 734, 'ambient_order': 128, 'ambient_tex': 'C_4^2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 239, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.734.128.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': '128.734', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 734, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 262799364
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.r1.a1', '8.y1.a1'], 'contains': ['32.e1.a1', '32.i1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2676, -1, 4665, -1, 2676, -1, 4659, -1], 'generators': [4271, 13323], 'label': '128.734.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.y1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799316
    {'ambient': '128.734', '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.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4956, 4733, 5410, 4658, 5015, 4731, 5419, 4672], 'generators': [13485, 4455, 48323], 'label': '128.734.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.27', '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': '32.27'}
  • id: 262799317
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2326', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.g1.b1', '8.i1.a1', '8.q1.a1', '8.r1.a1', '8.y1.a1', '8.z1.a1', '8.bg1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2419, 2377, 4736, 6097, 2419, 2377, 4743, 6114], 'generators': [4271, 30727, 39049, 56453], 'label': '128.734.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799318
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.q1.a1', '4.t1.a1'], 'contains': ['16.z1.a1', '16.bg1.a1', '16.bh1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3170, -1, 6085, -1, 3169, -1, 6076, -1], 'generators': [38951, 32621], 'label': '128.734.8.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bn1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799319
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.q1.b1', '4.t1.a1'], 'contains': ['16.z1.a1', '16.bg1.a1', '16.bh1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3170, -1, 6484, -1, 3169, -1, 6475, -1], 'generators': [4271, 32741], 'label': '128.734.8.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bn1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799320
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.q1.a1', '4.t1.b1'], 'contains': ['16.z1.b1', '16.bg1.a1', '16.bh1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3170, -1, 6284, -1, 3169, -1, 6276, -1], 'generators': [21547, 32621], 'label': '128.734.8.bn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bn1.c1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799321
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.q1.b1', '4.t1.b1'], 'contains': ['16.z1.b1', '16.bg1.a1', '16.bh1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3170, -1, 6599, -1, 3169, -1, 6590, -1], 'generators': [56483, 32741], 'label': '128.734.8.bn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bn1.d1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799322
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.bj1.a1', '16.bk1.a1', '16.bl1.a1', '16.bn1.a1', '16.bn1.c1', '16.bn1.e1', '16.bn1.g1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 70, -1, 122, -1, 70, -1], 'generators': [13485, 48323, 30727], 'label': '128.734.8.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.bo1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799323
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.bj1.a1', '16.bk1.a1', '16.bl1.b1', '16.bn1.b1', '16.bn1.d1', '16.bn1.f1', '16.bn1.h1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 551, -1, 122, -1, 551, -1], 'generators': [13485, 13515, 30727], 'label': '128.734.8.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.bo1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799324
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1'], 'contains': ['16.bj1.b1', '16.bk1.a2', '16.bl1.a1', '16.bn1.i1', '16.bn1.k1', '16.bn1.m1', '16.bn1.o1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 1700, -1, 122, -1, 1698, -1], 'generators': [30889, 48323, 30727], 'label': '128.734.8.bo1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '8.bo1.c1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799325
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1'], 'contains': ['16.bj1.b1', '16.bk1.a2', '16.bl1.b1', '16.bn1.j1', '16.bn1.l1', '16.bn1.n1', '16.bn1.p1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 2280, -1, 122, -1, 2277, -1], 'generators': [30889, 13515, 30727], 'label': '128.734.8.bo1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '8.bo1.d1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799326
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.bj1.c1', '16.bk1.b1', '16.bl1.c1', '16.bn1.a1', '16.bn1.d1', '16.bn1.e1', '16.bn1.h1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 231, -1, 122, -1, 230, -1], 'generators': [13485, 48323, 61455], 'label': '128.734.8.bo1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.bo1.e1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799327
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.bj1.c1', '16.bk1.b1', '16.bl1.d1', '16.bn1.b1', '16.bn1.c1', '16.bn1.f1', '16.bn1.g1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 391, -1, 122, -1, 391, -1], 'generators': [13485, 13515, 61455], 'label': '128.734.8.bo1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.bo1.f1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799328
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '8.j1.a1', '8.s1.a1', '8.ba1.a1', '8.bb1.a1', '8.bh1.a1', '8.bi1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7105, 9322, 7483, 7257, 7104, 9319, 7473, 7279], 'generators': [49029, 30727, 39049, 56453], 'label': '128.734.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799329
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1'], 'contains': ['16.bj1.d1', '16.bk1.b2', '16.bl1.c1', '16.bn1.i1', '16.bn1.l1', '16.bn1.m1', '16.bn1.p1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 1958, -1, 122, -1, 1956, -1], 'generators': [30889, 48323, 61455], 'label': '128.734.8.bo1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '8.bo1.g1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799330
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1'], 'contains': ['16.bj1.d1', '16.bk1.b2', '16.bl1.d1', '16.bn1.j1', '16.bn1.k1', '16.bn1.n1', '16.bn1.o1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [122, -1, 2119, -1, 122, -1, 2116, -1], 'generators': [30889, 13515, 61455], 'label': '128.734.8.bo1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '8.bo1.h1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799331
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.l1.a1', '32.l1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4294, 7337, 3620, 3482, 4294, 7394, 3615, 3493], 'generators': [30727, 39049, 38921], 'label': '128.734.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.b1', '8.a1.a1', '8.b1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.27', '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: 262799332
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '8.o1.a1', '8.q1.a1', '8.t1.a1', '8.u1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.f1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6842, 8156, 6926, 6196, 6841, 8214, 6916, 6214], 'generators': [30727, 56453], 'label': '128.734.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'normal_contains': ['32.a1.a1', '32.f1.a1', '32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799333
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.e1.b1', '8.p1.a1', '8.r1.a1', '8.s1.a1', '8.v1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.g1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6266, 2423, 6682, 7165, 6265, 2482, 6673, 7186], 'generators': [30727, 21517], 'label': '128.734.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.b1', '8.e1.a1'], 'normal_contains': ['32.a1.a1', '32.g1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799334
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.w1.a1', '8.y1.a1', '8.ba1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5690, 5493, 5032, 4258, 5690, 5551, 5025, 4272], 'generators': [61583, 56453], 'label': '128.734.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799335
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.f1.b1', '8.x1.a1', '8.z1.a1', '8.bb1.a1', '8.bc1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '32.g1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4686, 4470, 5276, 1737, 4686, 4528, 5268, 1743], 'generators': [48259, 21517], 'label': '128.734.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.f1.a1', '8.f1.b1'], 'normal_contains': ['32.b1.a1', '32.f1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799336
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.f1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.h1.a1', '8.h1.b1', '8.be1.a1', '8.bg1.a1', '8.bh1.a1', '8.bj1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5115, 6516, 4037, 2706, 5114, 6574, 4031, 2714], 'generators': [39049, 56453], 'label': '128.734.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.b1.a1', '8.h1.b1', '8.h1.a1'], 'normal_contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799337
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.g1.a1', '8.g1.b1', '8.bf1.a1', '8.bi1.a1', '8.bk1.a1', '8.bl1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.f1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4069, 3446, 4873, 5227, 4070, 3505, 4865, 5243], 'generators': [48259, 39049], 'label': '128.734.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.b1.a1', '8.g1.b1', '8.g1.a1'], 'normal_contains': ['32.c1.a1', '32.f1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799338
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.n1.b1', '8.o1.a1', '8.p1.a1'], 'contains': ['32.a1.a1', '32.h1.a1', '32.m1.a1', '32.m1.c1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7065, -1, 7711, -1, 7065, -1, 7700, -1], 'generators': [13485, 30727, 38921], 'label': '128.734.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.h1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799339
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.h1.b1', '8.k1.a1', '8.bk1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2094, 6907, 3131, 2265, 2094, 6905, 3127, 2271], 'generators': [48323, 30727, 56453], 'label': '128.734.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.h1.b1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799340
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.m1.c1', '8.m1.d1', '8.n1.c1', '8.n1.d1', '8.o1.a1', '8.p1.a1'], 'contains': ['32.a1.a1', '32.h1.b1', '32.m1.b1', '32.m1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7065, -1, 8232, -1, 7065, -1, 8220, -1], 'generators': [30889, 30727, 38921], 'label': '128.734.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.h1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799341
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '32.i1.b1', '32.n1.a1', '32.n1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2835, -1, 3813, -1, 2834, -1, 3808, -1], 'generators': [4271, 30727, 38921], 'label': '128.734.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.i1.a1', 'projective_image': '32.27', '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': '2.1'}
  • id: 262799342
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.j1.a1', '8.m1.a1', '8.m1.b1', '8.m1.c1', '8.m1.d1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.j1.a1', '32.o1.a1', '32.o1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8665, -1, 9033, -1, 8665, -1, 9020, -1], 'generators': [49029, 30727, 38921], 'label': '128.734.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799343
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.l1.a1', '8.m1.a1', '8.m1.c1', '8.n1.a1', '8.n1.c1', '8.t1.a1'], 'contains': ['32.a1.a1', '32.p1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8889, -1, 8821, -1, 8889, -1, 8808, -1], 'generators': [4455, 38921], 'label': '128.734.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.k1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799344
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.l1.a1', '8.m1.b1', '8.m1.d1', '8.n1.b1', '8.n1.d1', '8.t1.a1'], 'contains': ['32.a1.a1', '32.p1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8889, -1, 8662, -1, 8889, -1, 8649, -1], 'generators': [4591, 38921], 'label': '128.734.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.k1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799345
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.j1.a1', '8.n1.a1', '8.n1.b1', '8.n1.c1', '8.n1.d1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8441, -1, 8104, -1, 8441, -1, 8092, -1], 'generators': [48909, 30727], 'label': '128.734.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.l1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799346
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.w1.a1', '8.x1.a1'], 'contains': ['32.b1.a1', '32.h1.a1', '32.q1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4463, -1, 3524, -1, 4462, -1, 3519, -1], 'generators': [13485, 61583, 38921], 'label': '128.734.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 262799347
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.w1.a1', '8.x1.a1'], 'contains': ['32.b1.a1', '32.h1.b1', '32.q1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4463, -1, 3909, -1, 4462, -1, 3904, -1], 'generators': [30889, 61583, 38921], 'label': '128.734.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 262799348
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.y1.a1', '8.z1.a1'], 'contains': ['32.b1.a1', '32.i1.a1', '32.i1.b1', '32.r1.a1', '32.r1.a2'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2201, -1, 3717, -1, 2201, -1, 3711, -1], 'generators': [4271, 61583, 38921], 'label': '128.734.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.n1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799349
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.b1.a1', '32.j1.a1', '32.k1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7520, -1, 7621, -1, 7520, -1, 7610, -1], 'generators': [49029, 61583], 'label': '128.734.16.o1.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.o1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799350
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.e1.b1', '8.l1.a1', '8.t1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7458, 1114, 8008, 8767, 7458, 1113, 7996, 8793], 'generators': [4455, 39049, 56453], 'label': '128.734.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.b1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '32.27', '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': '16.11'}
  • id: 262799351
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bd1.a1', '8.bd1.b1', '8.bd1.c1', '8.bd1.d1', '8.be1.a1', '8.bf1.a1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.s1.a1', '32.s1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3846, -1, 1919, -1, 3846, -1, 1917, -1], 'generators': [13485, 39049, 38921], 'label': '128.734.16.p1.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.p1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799352
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.bd1.e1', '8.bd1.f1', '8.bd1.g1', '8.bd1.h1', '8.be1.a1', '8.bf1.a1'], 'contains': ['32.c1.a1', '32.h1.b1', '32.s1.b1', '32.s1.b2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3846, -1, 3428, -1, 3846, -1, 3423, -1], 'generators': [30889, 39049, 38921], 'label': '128.734.16.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.p1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799353
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.i1.a1', '8.bd1.a1', '8.bd1.b1', '8.bd1.e1', '8.bd1.f1', '8.bg1.a1'], 'contains': ['32.c1.a1', '32.i1.a1', '32.t1.a1', '32.t1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1629, -1, 3044, -1, 1629, -1, 3039, -1], 'generators': [4271, 39049, 38921], 'label': '128.734.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.q1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799354
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.i1.a1', '8.bd1.c1', '8.bd1.d1', '8.bd1.g1', '8.bd1.h1', '8.bg1.a1'], 'contains': ['32.c1.a1', '32.i1.b1', '32.t1.b1', '32.t1.b2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1629, -1, 3140, -1, 1629, -1, 3135, -1], 'generators': [30825, 39049, 38921], 'label': '128.734.16.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.q1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799355
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.bh1.a1', '8.bi1.a1'], 'contains': ['32.c1.a1', '32.j1.a1', '32.k1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7371, -1, 7048, -1, 7372, -1, 7038, -1], 'generators': [49029, 39049], 'label': '128.734.16.r1.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.r1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799356
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.k1.a1', '8.bd1.a1', '8.bd1.c1', '8.bd1.e1', '8.bd1.g1', '8.bk1.a1'], 'contains': ['32.c1.a1', '32.u1.a1', '32.u1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1405, -1, 2132, -1, 1405, -1, 2129, -1], 'generators': [48323, 38921], 'label': '128.734.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.s1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799357
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '8.k1.a1', '8.bd1.b1', '8.bd1.d1', '8.bd1.f1', '8.bd1.h1', '8.bk1.a1'], 'contains': ['32.c1.a1', '32.u1.c1', '32.u1.d1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1405, -1, 1791, -1, 1405, -1, 1789, -1], 'generators': [56389, 38921], 'label': '128.734.16.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.s1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799358
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.w1.a1', '8.be1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.h1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5904, -1, 4413, -1, 5904, -1, 4406, -1], 'generators': [13485, 56453], 'label': '128.734.16.t1.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.t1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799359
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.w1.a1', '8.bf1.a1'], 'contains': ['32.e1.a1', '32.h1.a1', '32.h1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5477, -1, 4497, -1, 5476, -1, 4490, -1], 'generators': [13485, 13323], 'label': '128.734.16.u1.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.u1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799360
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.x1.a1', '8.bf1.a1'], 'contains': ['32.f1.a1', '32.h1.a1', '32.h1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4901, -1, 4581, -1, 4900, -1, 4575, -1], 'generators': [13485, 48259], 'label': '128.734.16.v1.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.v1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799361
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.f1.b1', '8.u1.a1', '8.bl1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4455, 3808, 5752, 911, 4454, 3806, 5766, 914], 'generators': [32621, 39049, 56453], 'label': '128.734.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799362
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.x1.a1', '8.be1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.h1.b1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5328, -1, 4328, -1, 5328, -1, 4322, -1], 'generators': [13485, 21517], 'label': '128.734.16.w1.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.w1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799363
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.y1.a1', '8.bg1.a1'], 'contains': ['32.d1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2992, -1, 4244, -1, 2992, -1, 4237, -1], 'generators': [4271, 56453], 'label': '128.734.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.x1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799365
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.r1.a1', '8.y1.a1'], 'contains': ['32.e1.a1', '32.i1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2676, -1, 4751, -1, 2676, -1, 4743, -1], 'generators': [21547, 13323], 'label': '128.734.16.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.y1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799366
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.q1.a1', '8.z1.a1', '8.bm1.a1', '8.bm1.b1', '8.bn1.a1', '8.bn1.b1'], 'contains': ['32.f1.a1', '32.i1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3141, -1, 6016, -1, 3140, -1, 6007, -1], 'generators': [4271, 48259], 'label': '128.734.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.z1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799367
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.q1.a1', '8.z1.a1', '8.bm1.c1', '8.bm1.d1', '8.bn1.c1', '8.bn1.d1'], 'contains': ['32.f1.a1', '32.i1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3141, -1, 6100, -1, 3140, -1, 6092, -1], 'generators': [56483, 48259], 'label': '128.734.16.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.z1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799368
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.z1.a1', '8.bg1.a1'], 'contains': ['32.g1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2528, -1, 4159, -1, 2528, -1, 4153, -1], 'generators': [4271, 21517], 'label': '128.734.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ba1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799369
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.ba1.a1', '8.bi1.a1'], 'contains': ['32.e1.a1', '32.j1.a1', '32.k1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8013, -1, 7499, -1, 8013, -1, 7488, -1], 'generators': [49029, 13323], 'label': '128.734.16.bb1.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.bb1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799370
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.bb1.a1', '8.bh1.a1'], 'contains': ['32.g1.a1', '32.j1.a1', '32.k1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7734, -1, 7255, -1, 7733, -1, 7244, -1], 'generators': [49029, 21517], 'label': '128.734.16.bc1.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.bc1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799371
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.ba1.a1', '8.bh1.a1'], 'contains': ['32.d1.a1', '32.j1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8227, -1, 7377, -1, 8227, -1, 7366, -1], 'generators': [49029, 56453], 'label': '128.734.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.bd1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799372
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.v1.a1', '8.bc1.a1', '8.bj1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5651, 5478, 4959, 4743, 5651, 5476, 4970, 4757], 'generators': [53583, 30727, 56453], 'label': '128.734.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799373
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.bb1.a1', '8.bi1.a1', '8.bm1.a1', '8.bm1.b1', '8.bm1.c1', '8.bm1.d1'], 'contains': ['32.f1.a1', '32.j1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6627, -1, 6804, -1, 6627, -1, 6794, -1], 'generators': [49029, 48259], 'label': '128.734.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.be1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799374
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.ba1.a1', '8.bh1.a1'], 'contains': ['32.d1.a1', '32.k1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7224, -1, 7133, -1, 7223, -1, 7122, -1], 'generators': [48909, 56453], 'label': '128.734.16.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.bf1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799375
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.bb1.a1', '8.bi1.a1', '8.bn1.a1', '8.bn1.b1', '8.bn1.c1', '8.bn1.d1'], 'contains': ['32.f1.a1', '32.k1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6480, -1, 6560, -1, 6479, -1, 6551, -1], 'generators': [48909, 48259], 'label': '128.734.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bg1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799376
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.u1.a1', '8.bl1.a1', '8.bm1.a1', '8.bm1.c1', '8.bn1.a1', '8.bn1.c1'], 'contains': ['32.f1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3611, -1, 6185, -1, 3597, -1, 6176, -1], 'generators': [32621], 'label': '128.734.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bh1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799377
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.u1.a1', '8.bl1.a1', '8.bm1.b1', '8.bm1.d1', '8.bn1.b1', '8.bn1.d1'], 'contains': ['32.f1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3611, -1, 6476, -1, 3597, -1, 6467, -1], 'generators': [32741], 'label': '128.734.16.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bh1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799378
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.bc1.a1', '8.bj1.a1'], 'contains': ['32.g1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6051, -1, 5154, -1, 6052, -1, 5146, -1], 'generators': [53583], 'label': '128.734.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.bi1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799379
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bo1.a1', '8.bo1.b1'], 'contains': ['32.l1.a1', '32.m1.a1', '32.q1.a1', '32.s1.a1', '32.s1.a2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2369, -1, 1312, -1, 2369, -1, 1310, -1], 'generators': [13485, 30727, 39049], 'label': '128.734.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bj1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799380
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.bo1.c1', '8.bo1.d1'], 'contains': ['32.l1.a1', '32.m1.b1', '32.q1.b1', '32.s1.b1', '32.s1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2369, -1, 3332, -1, 2369, -1, 3327, -1], 'generators': [30889, 30727, 39049], 'label': '128.734.16.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bj1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799381
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bo1.e1', '8.bo1.f1'], 'contains': ['32.l1.b1', '32.m1.c1', '32.q1.a1', '32.s1.a1', '32.s1.a2'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2369, -1, 1056, -1, 2369, -1, 1055, -1], 'generators': [13485, 61455, 39049], 'label': '128.734.16.bj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bj1.c1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799382
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.bo1.g1', '8.bo1.h1'], 'contains': ['32.l1.b1', '32.m1.d1', '32.q1.b1', '32.s1.b1', '32.s1.b2'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2369, -1, 3236, -1, 2369, -1, 3231, -1], 'generators': [30889, 61455, 39049], 'label': '128.734.16.bj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bj1.d1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799383
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.k1.a1', '8.bd1.a1', '8.bd1.b1', '8.bd1.c1', '8.bd1.d1', '8.bo1.a1', '8.bo1.b1', '8.bo1.e1', '8.bo1.f1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [830, -1, 955, -1, 830, -1, 953, -1], 'generators': [13485, 48323, 30727, 38921], 'label': '128.734.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799384
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bo1.a1', '8.bo1.b1'], 'contains': ['32.l1.a1', '32.n1.a1', '32.r1.a1', '32.t1.a1', '32.t1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1182, -1, 1504, -1, 1181, -1, 1502, -1], 'generators': [4271, 30727, 39049], 'label': '128.734.16.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bk1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799385
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bo1.c1', '8.bo1.d1'], 'contains': ['32.l1.a1', '32.n1.a1', '32.r1.a2', '32.t1.a2', '32.t1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1182, -1, 2947, -1, 1181, -1, 2943, -1], 'generators': [4271, 30727, 4225], 'label': '128.734.16.bk1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bk1.a2', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799386
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bo1.e1', '8.bo1.f1'], 'contains': ['32.l1.b1', '32.n1.b1', '32.r1.a2', '32.t1.a1', '32.t1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1182, -1, 1409, -1, 1181, -1, 1406, -1], 'generators': [4271, 61455, 39049], 'label': '128.734.16.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bk1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799387
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bo1.g1', '8.bo1.h1'], 'contains': ['32.l1.b1', '32.n1.b1', '32.r1.a1', '32.t1.a2', '32.t1.b2'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1182, -1, 2851, -1, 1181, -1, 2847, -1], 'generators': [4271, 61455, 4225], 'label': '128.734.16.bk1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bk1.b2', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799388
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.bo1.a1', '8.bo1.c1'], 'contains': ['32.l1.a1', '32.u1.a1', '32.u1.c1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [957, -1, 769, -1, 957, -1, 768, -1], 'generators': [48323, 30727], 'label': '128.734.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bl1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799389
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.bo1.b1', '8.bo1.d1'], 'contains': ['32.l1.a1', '32.u1.b1', '32.u1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [957, -1, 1632, -1, 957, -1, 1630, -1], 'generators': [13515, 30727], 'label': '128.734.16.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bl1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799390
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.bo1.e1', '8.bo1.g1'], 'contains': ['32.l1.b1', '32.u1.a1', '32.u1.d1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [957, -1, 928, -1, 957, -1, 927, -1], 'generators': [48323, 61455], 'label': '128.734.16.bl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bl1.c1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799391
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.bo1.f1', '8.bo1.h1'], 'contains': ['32.l1.b1', '32.u1.b1', '32.u1.c1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [957, -1, 1184, -1, 957, -1, 1183, -1], 'generators': [13515, 61455], 'label': '128.734.16.bl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bl1.d1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799392
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1'], 'contains': ['32.m1.a1', '32.o1.a1', '32.p1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9103, -1, 9208, -1, 9103, -1, 9195, -1], 'generators': [13485, 4455], 'label': '128.734.16.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '16.bm1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799393
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.c1'], 'contains': ['32.m1.b1', '32.o1.a1', '32.p1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9103, -1, 9292, -1, 9103, -1, 9279, -1], 'generators': [30889, 4455], 'label': '128.734.16.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.c1', 'old_label': '16.bm1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799394
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.b1', '8.i1.a1', '8.k1.a1', '8.bd1.e1', '8.bd1.f1', '8.bd1.g1', '8.bd1.h1', '8.bo1.c1', '8.bo1.d1', '8.bo1.g1', '8.bo1.h1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [830, -1, 2354, -1, 830, -1, 2357, -1], 'generators': [30889, 48323, 30727, 38921], 'label': '128.734.4.h1.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.h1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799395
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1'], 'contains': ['32.m1.c1', '32.o1.b1', '32.p1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9103, -1, 8943, -1, 9103, -1, 8930, -1], 'generators': [48165, 4591], 'label': '128.734.16.bm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.b1', 'old_label': '16.bm1.c1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799396
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.d1'], 'contains': ['32.m1.d1', '32.o1.b1', '32.p1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9103, -1, 9124, -1, 9103, -1, 9110, -1], 'generators': [61473, 4591], 'label': '128.734.16.bm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.d1', 'old_label': '16.bm1.d1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799397
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.bo1.a1', '8.bo1.e1'], 'contains': ['32.s1.a1', '32.t1.a1', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 140, -1, 743, -1, 140, -1], 'generators': [13485, 48323], 'label': '128.734.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799398
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.bo1.b1', '8.bo1.f1'], 'contains': ['32.s1.a1', '32.t1.a1', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 478, -1, 743, -1, 477, -1], 'generators': [13485, 13515], 'label': '128.734.16.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799399
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '8.bo1.a1', '8.bo1.f1'], 'contains': ['32.s1.a2', '32.t1.a1', '32.u1.c1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 56, -1, 743, -1, 56, -1], 'generators': [21611, 56389], 'label': '128.734.16.bn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.c1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799400
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1', '8.bo1.b1', '8.bo1.e1'], 'contains': ['32.s1.a2', '32.t1.a1', '32.u1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 309, -1, 743, -1, 309, -1], 'generators': [21611, 21581], 'label': '128.734.16.bn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.d1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799401
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.c1', '8.bo1.a1', '8.bo1.e1'], 'contains': ['32.s1.a2', '32.t1.b1', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 224, -1, 743, -1, 224, -1], 'generators': [21611, 48323], 'label': '128.734.16.bn1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.e1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799402
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.c1', '8.bo1.b1', '8.bo1.f1'], 'contains': ['32.s1.a2', '32.t1.b1', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 647, -1, 743, -1, 646, -1], 'generators': [21611, 13515], 'label': '128.734.16.bn1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.f1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799403
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.d1', '8.bo1.a1', '8.bo1.f1'], 'contains': ['32.s1.a1', '32.t1.b1', '32.u1.c1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 394, -1, 743, -1, 393, -1], 'generators': [13485, 56389], 'label': '128.734.16.bn1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.g1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799404
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.d1', '8.bo1.b1', '8.bo1.e1'], 'contains': ['32.s1.a1', '32.t1.b1', '32.u1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 563, -1, 743, -1, 562, -1], 'generators': [13485, 21581], 'label': '128.734.16.bn1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bn1.h1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799405
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.l1.a1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.n1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7820, -1, 8784, -1, 7820, -1, 8772, -1], 'generators': [13485, 4455, 39049], 'label': '128.734.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799406
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.e1', '8.bo1.c1', '8.bo1.g1'], 'contains': ['32.s1.b1', '32.t1.a2', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2339, -1, 743, -1, 2335, -1], 'generators': [4207, 48323], 'label': '128.734.16.bn1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.i1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799407
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.e1', '8.bo1.d1', '8.bo1.h1'], 'contains': ['32.s1.b1', '32.t1.a2', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2592, -1, 743, -1, 2588, -1], 'generators': [4207, 13515], 'label': '128.734.16.bn1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.j1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799408
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.f1', '8.bo1.c1', '8.bo1.h1'], 'contains': ['32.s1.b2', '32.t1.a2', '32.u1.c1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2010, -1, 743, -1, 2007, -1], 'generators': [30889, 56389], 'label': '128.734.16.bn1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.k1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799409
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.f1', '8.bo1.d1', '8.bo1.g1'], 'contains': ['32.s1.b2', '32.t1.a2', '32.u1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2254, -1, 743, -1, 2251, -1], 'generators': [30889, 21581], 'label': '128.734.16.bn1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.l1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799410
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.g1', '8.bo1.c1', '8.bo1.g1'], 'contains': ['32.s1.b2', '32.t1.b2', '32.u1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2423, -1, 743, -1, 2419, -1], 'generators': [30889, 48323], 'label': '128.734.16.bn1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.m1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799411
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.g1', '8.bo1.d1', '8.bo1.h1'], 'contains': ['32.s1.b2', '32.t1.b2', '32.u1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2761, -1, 743, -1, 2757, -1], 'generators': [30889, 13515], 'label': '128.734.16.bn1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.n1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799412
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.h1', '8.bo1.c1', '8.bo1.h1'], 'contains': ['32.s1.b1', '32.t1.b2', '32.u1.c1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2507, -1, 743, -1, 2504, -1], 'generators': [4207, 56389], 'label': '128.734.16.bn1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.o1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799413
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.h1', '8.bo1.d1', '8.bo1.g1'], 'contains': ['32.s1.b1', '32.t1.b2', '32.u1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T408', 'count': 4, 'diagramx': [743, -1, 2676, -1, 743, -1, 2673, -1], 'generators': [4207, 21581], 'label': '128.734.16.bn1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '16.bn1.p1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799414
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.h1.a1', '16.h1.b1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.k1.b1', '16.l1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.b1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6636, 7269, 7674, 5776, 6553, 7326, 7664, 5793], 'generators': [30727, 38921], 'label': '128.734.32.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.b1', '64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.27', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799415
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.m1.a1', '16.m1.b1', '16.n1.a1', '16.o1.a1'], 'contains': ['64.a1.a1', '64.c1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4576, 5493, 4400, 2557, 4575, 5551, 4394, 2564], 'generators': [61583, 38921], 'label': '128.734.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.e1.a1', '16.d1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799416
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.b1', '8.j1.a1', '8.l1.a1', '8.m1.c1', '8.m1.d1', '8.n1.c1', '8.n1.d1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7820, -1, 9123, -1, 7820, -1, 9109, -1], 'generators': [30889, 4455, 39049], 'label': '128.734.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799417
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '16.p1.a1', '16.p1.b1', '16.q1.a1', '16.q1.b1', '16.r1.a1', '16.s1.a1', '16.s1.b1'], 'contains': ['64.a1.a1', '64.d1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4183, 6110, 3344, 3653, 4181, 6168, 3339, 3664], 'generators': [39049, 38921], 'label': '128.734.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.g1.a1', '16.f1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799418
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '16.t1.a1', '16.x1.a1', '16.bd1.a1', '16.bf1.a1'], 'contains': ['64.a1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5793, 6689, 4715, 4714, 5797, 6747, 4752, 4729], 'generators': [56453], 'label': '128.734.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1', '16.d1.a1', '16.f1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.4', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799419
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '16.u1.a1', '16.y1.a1', '16.y1.b1', '16.bb1.a1'], 'contains': ['64.a1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5477, 3642, 4857, 5227, 5476, 3701, 4851, 5243], 'generators': [13323], 'label': '128.734.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.c1.a1', '16.d1.a1', '16.g1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799420
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.f1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '16.v1.a1', '16.z1.a1', '16.z1.b1', '16.be1.a1', '16.bg1.a1', '16.bh1.a1', '16.bh1.b1'], 'contains': ['64.a1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4901, 4914, 6100, 4202, 4900, 4972, 6092, 4214], 'generators': [48259], 'label': '128.734.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.b1.a1', '16.e1.a1', '16.g1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799421
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '32.g1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '16.w1.a1', '16.ba1.a1', '16.bc1.a1', '16.bi1.a1'], 'contains': ['64.a1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5328, 4372, 4601, 3106, 5328, 4430, 4638, 3114], 'generators': [21517], 'label': '128.734.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.c1.a1', '16.e1.a1', '16.f1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.73', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799422
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.m1.a1', '16.p1.a1', '16.t1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1'], 'contains': ['64.a1.a1', '64.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5170, -1, 4305, -1, 5170, -1, 4298, -1], 'generators': [13485, 38921], 'label': '128.734.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799443
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.bj1.a1', '16.bj1.c1'], 'contains': ['64.c1.a1', '64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1731', 'count': 8, 'diagramx': [4014, -1, 2381, -1, 4012, -1, 2378, -1], 'generators': [13485, 61583], 'label': '128.734.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '32.q1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799423
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.m1.b1', '16.p1.b1', '16.t1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1'], 'contains': ['64.a1.a1', '64.e1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5170, -1, 4497, -1, 5170, -1, 4490, -1], 'generators': [30889, 38921], 'label': '128.734.32.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.h1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799424
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.n1.a1', '16.q1.a1', '16.x1.a1', '16.y1.a1', '16.z1.a1', '16.ba1.a1'], 'contains': ['64.a1.a1', '64.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2876, -1, 4088, -1, 2875, -1, 4082, -1], 'generators': [4271, 38921], 'label': '128.734.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799425
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.n1.a1', '16.q1.b1', '16.x1.a1', '16.y1.b1', '16.z1.b1', '16.ba1.a1'], 'contains': ['64.a1.a1', '64.f1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2876, -1, 4184, -1, 2875, -1, 4178, -1], 'generators': [30825, 38921], 'label': '128.734.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.i1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799426
    {'ambient': '128.734', 'aut_centralizer_order': 256, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.o1.a1', '16.r1.a1', '16.bb1.a1', '16.bc1.a1', '16.bd1.a1', '16.be1.a1'], 'contains': ['64.a1.a1', '64.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7633, -1, 7290, -1, 7632, -1, 7279, -1], 'generators': [49029, 38921], 'label': '128.734.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799427
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493262', 'aut_weyl_index': 4, 'centralizer': '16.a1.a1', 'complements': ['64.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.h1.b1', '4.r1.a1', '4.r1.b1', '4.s1.a1', '4.s1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2094, 3393, 2736, 3390, 2094, 3392, 2752, 3400], 'generators': [13485, 48323, 30727, 56453], 'label': '128.734.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799428
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '8.m1.a1', '8.m1.c1', '8.n1.a1', '8.n1.c1', '8.p1.a1', '8.s1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9111, -1, 8954, -1, 9111, -1, 8941, -1], 'generators': [13485, 4455, 21517], 'label': '128.734.4.j1.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.j1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799429
    {'ambient': '128.734', 'aut_centralizer_order': 256, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.o1.a1', '16.r1.a1', '16.bb1.a1', '16.bc1.a1', '16.bf1.a1', '16.bg1.a1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7424, -1, 7167, -1, 7423, -1, 7156, -1], 'generators': [48909], 'label': '128.734.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799430
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bj1.a1', '16.bj1.b1', '16.bk1.a1', '16.bk1.a2', '16.bl1.a1', '16.bl1.b1'], 'contains': ['64.b1.a1', '64.c1.a1', '64.d1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2538, -1, 2478, -1, 2538, -1, 2474, -1], 'generators': [30727, 39049], 'label': '128.734.32.l1.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.l1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799431
    {'ambient': '128.734', 'aut_centralizer_order': 512, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bj1.c1', '16.bj1.d1', '16.bk1.b1', '16.bk1.b2', '16.bl1.c1', '16.bl1.d1'], 'contains': ['64.b1.b1', '64.c1.a1', '64.d1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2538, -1, 2232, -1, 2538, -1, 2065, -1], 'generators': [61455, 39049], 'label': '128.734.32.l1.b1', '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.l1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799432
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.bj1.a1', '16.bm1.a1'], 'contains': ['64.b1.a1', '64.e1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6056, -1, 7482, -1, 6261, -1, 7472, -1], 'generators': [13485, 30727], 'label': '128.734.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '32.m1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799433
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.bj1.b1', '16.bm1.b1'], 'contains': ['64.b1.a1', '64.e1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6056, -1, 7771, -1, 6261, -1, 7760, -1], 'generators': [30889, 30727], 'label': '128.734.32.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.b1', 'old_label': '32.m1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799434
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.bj1.c1', '16.bm1.c1'], 'contains': ['64.b1.b1', '64.e1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6056, -1, 7386, -1, 6261, -1, 7375, -1], 'generators': [13485, 61455], 'label': '128.734.32.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '32.m1.c1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799435
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.bj1.d1', '16.bm1.d1'], 'contains': ['64.b1.b1', '64.e1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6056, -1, 7578, -1, 6261, -1, 7568, -1], 'generators': [30889, 61455], 'label': '128.734.32.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.b1', 'old_label': '32.m1.d1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799436
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.bk1.a1', '16.bk1.a2'], 'contains': ['64.b1.a1', '64.f1.a1', '64.f1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2706, -1, 3248, -1, 2707, -1, 3243, -1], 'generators': [4271, 30727], 'label': '128.734.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.n1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799437
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.bk1.b1', '16.bk1.b2'], 'contains': ['64.b1.b1', '64.f1.a1', '64.f1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2706, -1, 3151, -1, 2707, -1, 3147, -1], 'generators': [4271, 61455], 'label': '128.734.32.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.n1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799438
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.bm1.a1', '16.bm1.b1'], 'contains': ['64.b1.a1', '64.g1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8665, -1, 9078, -1, 8665, -1, 9065, -1], 'generators': [49029, 30727], 'label': '128.734.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.o1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799439
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.b1', '8.m1.b1', '8.m1.d1', '8.n1.b1', '8.n1.d1', '8.p1.a1', '8.s1.a1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9111, -1, 8616, -1, 9111, -1, 8603, -1], 'generators': [13485, 20843, 21517], 'label': '128.734.4.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.j1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799440
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.bm1.c1', '16.bm1.d1'], 'contains': ['64.b1.b1', '64.g1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8665, -1, 8897, -1, 8665, -1, 8884, -1], 'generators': [49029, 61455], 'label': '128.734.32.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.b1', 'old_label': '32.o1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799441
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.bm1.a1', '16.bm1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8507, -1, 8988, -1, 8506, -1, 8974, -1], 'generators': [4455], 'label': '128.734.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '32.p1.a1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799442
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '16.bm1.c1', '16.bm1.d1'], 'contains': ['64.b1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8507, -1, 8712, -1, 8506, -1, 8743, -1], 'generators': [4591], 'label': '128.734.32.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '32.p1.b1', 'projective_image': '64.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799444
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '16.bj1.b1', '16.bj1.d1'], 'contains': ['64.c1.a1', '64.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T1731', 'count': 8, 'diagramx': [4014, -1, 3440, -1, 4012, -1, 3435, -1], 'generators': [30889, 61583], 'label': '128.734.32.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '32.q1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799445
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bk1.a1', '16.bk1.b2'], 'contains': ['64.c1.a1', '64.f1.a1', '64.f1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T1674', 'count': 8, 'diagramx': [2201, -1, 2959, -1, 2201, -1, 2955, -1], 'generators': [4271, 61583], 'label': '128.734.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.r1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799446
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bk1.a2', '16.bk1.b1'], 'contains': ['64.c1.a1', '64.f1.a1', '64.f1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T1674', 'count': 8, 'diagramx': [2201, -1, 3055, -1, 2201, -1, 3051, -1], 'generators': [4271, 30855], 'label': '128.734.32.r1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.r1.a2', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799447
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bj1.a1', '16.bj1.c1', '16.bn1.a1', '16.bn1.b1', '16.bn1.g1', '16.bn1.h1'], 'contains': ['64.d1.a1', '64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T906', 'count': 4, 'diagramx': [2369, -1, 1281, -1, 2369, -1, 1279, -1], 'generators': [13485, 39049], 'label': '128.734.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.s1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799448
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bj1.a1', '16.bj1.c1', '16.bn1.c1', '16.bn1.d1', '16.bn1.e1', '16.bn1.f1'], 'contains': ['64.d1.a1', '64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T906', 'count': 4, 'diagramx': [2369, -1, 1056, -1, 2369, -1, 1055, -1], 'generators': [13485, 4225], 'label': '128.734.32.s1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.s1.a2', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799449
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.bj1.b1', '16.bj1.d1', '16.bn1.i1', '16.bn1.j1', '16.bn1.o1', '16.bn1.p1'], 'contains': ['64.d1.a1', '64.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T906', 'count': 4, 'diagramx': [2369, -1, 2863, -1, 2369, -1, 2859, -1], 'generators': [30889, 4225], 'label': '128.734.32.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '32.s1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799450
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.m1.a1', '8.m1.b1', '8.m1.c1', '8.m1.d1', '8.o1.a1', '8.t1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8400, -1, 9370, -1, 8399, -1, 9375, -1], 'generators': [13485, 4455, 56453], 'label': '128.734.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799451
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.bj1.b1', '16.bj1.d1', '16.bn1.k1', '16.bn1.l1', '16.bn1.m1', '16.bn1.n1'], 'contains': ['64.d1.a1', '64.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T906', 'count': 4, 'diagramx': [2369, -1, 2766, -1, 2369, -1, 2763, -1], 'generators': [30889, 39049], 'label': '128.734.32.s1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '32.s1.b2', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799452
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bk1.a1', '16.bk1.b1', '16.bn1.a1', '16.bn1.b1', '16.bn1.c1', '16.bn1.d1'], 'contains': ['64.d1.a1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T908', 'count': 4, 'diagramx': [1629, -1, 1184, -1, 1629, -1, 1183, -1], 'generators': [4271, 39049], 'label': '128.734.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.t1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799453
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bk1.a2', '16.bk1.b2', '16.bn1.i1', '16.bn1.j1', '16.bn1.k1', '16.bn1.l1'], 'contains': ['64.d1.a1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T908', 'count': 4, 'diagramx': [1629, -1, 2574, -1, 1629, -1, 2571, -1], 'generators': [4271, 4225], 'label': '128.734.32.t1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '32.t1.a2', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799454
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.bk1.a1', '16.bk1.b1', '16.bn1.e1', '16.bn1.f1', '16.bn1.g1', '16.bn1.h1'], 'contains': ['64.d1.a1', '64.f1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T908', 'count': 4, 'diagramx': [1629, -1, 1409, -1, 1629, -1, 1406, -1], 'generators': [30825, 39049], 'label': '128.734.32.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.t1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799455
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.bk1.a2', '16.bk1.b2', '16.bn1.m1', '16.bn1.n1', '16.bn1.o1', '16.bn1.p1'], 'contains': ['64.d1.a1', '64.f1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T908', 'count': 4, 'diagramx': [1629, -1, 2671, -1, 1629, -1, 2667, -1], 'generators': [30825, 4225], 'label': '128.734.32.t1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.b1', 'old_label': '32.t1.b2', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799456
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.bl1.a1', '16.bl1.c1', '16.bn1.a1', '16.bn1.e1', '16.bn1.i1', '16.bn1.m1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T907', 'count': 2, 'diagramx': [1182, -1, 1660, -1, 1181, -1, 1673, -1], 'generators': [48323], 'label': '128.734.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.u1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799457
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.bl1.b1', '16.bl1.d1', '16.bn1.b1', '16.bn1.f1', '16.bn1.j1', '16.bn1.n1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T907', 'count': 2, 'diagramx': [1182, -1, 2050, -1, 1181, -1, 1899, -1], 'generators': [13515], 'label': '128.734.32.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.u1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799458
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.b1', '16.bl1.a1', '16.bl1.d1', '16.bn1.c1', '16.bn1.g1', '16.bn1.k1', '16.bn1.o1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T907', 'count': 2, 'diagramx': [1182, -1, 1561, -1, 1181, -1, 1527, -1], 'generators': [56389], 'label': '128.734.32.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.u1.c1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799459
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.b1', '16.bl1.b1', '16.bl1.c1', '16.bn1.d1', '16.bn1.h1', '16.bn1.l1', '16.bn1.p1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T907', 'count': 2, 'diagramx': [1182, -1, 1775, -1, 1181, -1, 1773, -1], 'generators': [21581], 'label': '128.734.32.u1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.u1.d1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799460
    {'ambient': '128.734', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1', '32.h1.b1', '32.i1.a1', '32.i1.b1', '32.j1.a1', '32.k1.a1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5250, 5801, 4557, 4459, 5248, 5859, 4564, 4472], 'generators': [38921], 'label': '128.734.64.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', '32.f1.a1', '32.d1.a1', '32.g1.a1', '32.e1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.73', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.73', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799461
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.d1.a1', '8.n1.a1', '8.n1.b1', '8.n1.c1', '8.n1.d1', '8.o1.a1', '8.t1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8094, -1, 8495, -1, 8093, -1, 8483, -1], 'generators': [48165, 4455, 56453], 'label': '128.734.4.l1.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.l1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799462
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.l1.a1', '32.m1.a1', '32.m1.b1', '32.n1.a1', '32.o1.a1', '32.p1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6056, 6809, 7578, 5263, 6261, 6860, 7568, 5279], 'generators': [30727], 'label': '128.734.64.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': '64.134', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.134', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799463
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.l1.b1', '32.m1.c1', '32.m1.d1', '32.n1.b1', '32.o1.b1', '32.p1.b1'], 'contains': ['128.a1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6056, 6809, 7440, 5776, 6261, 6860, 7429, 5793], 'generators': [61455], 'label': '128.734.64.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1.b1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.b1', 'projective_image': '64.134', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.134', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799464
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.l1.a1', '32.l1.b1', '32.q1.a1', '32.q1.b1', '32.r1.a1', '32.r1.a2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4014, -1, 2964, -1, 4012, -1, 2963, -1], 'generators': [61583], 'label': '128.734.64.c1.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.c1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799465
    {'ambient': '128.734', 'aut_centralizer_order': 1024, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.l1.a1', '32.l1.b1', '32.s1.a1', '32.s1.a2', '32.s1.b1', '32.s1.b2', '32.t1.a1', '32.t1.a2', '32.t1.b1', '32.t1.b2', '32.u1.a1', '32.u1.b1', '32.u1.c1', '32.u1.d1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2453, -1, 2089, -1, 2454, -1, 1942, -1], 'generators': [39049], 'label': '128.734.64.d1.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.d1.a1', 'projective_image': '128.734', '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: 262799466
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.m1.a1', '32.m1.c1', '32.q1.a1', '32.s1.a1', '32.s1.a2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4666, -1, 3830, -1, 4590, -1, 3824, -1], 'generators': [13485], 'label': '128.734.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.734', '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: 262799467
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.m1.b1', '32.m1.d1', '32.q1.b1', '32.s1.b1', '32.s1.b2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4666, -1, 3914, -1, 4590, -1, 3908, -1], 'generators': [30889], 'label': '128.734.64.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '64.e1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799468
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.n1.a1', '32.n1.b1', '32.r1.a1', '32.r1.a2', '32.t1.a1', '32.t1.a2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2706, -1, 3058, -1, 2707, -1, 3053, -1], 'generators': [4271], 'label': '128.734.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799469
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.n1.a1', '32.n1.b1', '32.r1.a1', '32.r1.a2', '32.t1.b1', '32.t1.b2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2706, -1, 3148, -1, 2707, -1, 3143, -1], 'generators': [30825], 'label': '128.734.64.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '64.f1.b1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799470
    {'ambient': '128.734', 'aut_centralizer_order': 256, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.o1.a1', '32.o1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7633, -1, 8237, -1, 7632, -1, 8311, -1], 'generators': [49029], 'label': '128.734.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.734', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262799471
    {'ambient': '128.734', '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.b1.b1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.e1.b1', '64.f1.a1', '64.f1.b1', '64.g1.a1'], 'contains': [], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4666, 6306, 3871, 5263, 4590, 6130, 3866, 5279], 'generators': [], 'label': '128.734.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.b1.b1', '64.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.734', '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: 262799472
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.q1.a1', '8.u1.a1', '8.bm1.a1', '8.bm1.b1', '8.bm1.c1', '8.bm1.d1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4084, -1, 6824, -1, 4084, -1, 6816, -1], 'generators': [4271, 32621, 56453], 'label': '128.734.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.m1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799473
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.q1.a1', '8.u1.a1', '8.bn1.a1', '8.bn1.b1', '8.bn1.c1', '8.bn1.d1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3716, -1, 6481, -1, 3716, -1, 6474, -1], 'generators': [38951, 32621, 56453], 'label': '128.734.4.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.n1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799474
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.e1.a1', '8.r1.a1', '8.v1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6429, -1, 5517, -1, 6428, -1, 5527, -1], 'generators': [4271, 4455], 'label': '128.734.4.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.o1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799475
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.e1.b1', '8.r1.a1', '8.v1.a1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6429, -1, 5410, -1, 6428, -1, 5419, -1], 'generators': [4271, 20843], 'label': '128.734.4.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.o1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799476
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.f1.a1', '8.x1.a1', '8.bc1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4800, -1, 5156, -1, 4800, -1, 5166, -1], 'generators': [13485, 32621], 'label': '128.734.4.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.p1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 262799477
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.f1.b1', '8.x1.a1', '8.bc1.a1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4800, -1, 5289, -1, 4800, -1, 5299, -1], 'generators': [13485, 16233], 'label': '128.734.4.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.p1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 262799478
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493668', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.f1.a1', '64.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.j1.a1', '4.j1.b1', '4.k1.a1', '4.l1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7639, 9322, 8554, 7663, 7639, 9319, 8542, 7686], 'generators': [13485, 4455, 39049, 56453], 'label': '128.734.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 262799479
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.a1', '8.z1.a1', '8.bb1.a1', '8.bm1.a1', '8.bm1.c1', '8.bn1.a1', '8.bn1.c1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3373, -1, 6021, -1, 3373, -1, 6013, -1], 'generators': [4271, 32621, 21517], 'label': '128.734.4.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.q1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799480
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.f1.b1', '8.z1.a1', '8.bb1.a1', '8.bm1.b1', '8.bm1.d1', '8.bn1.b1', '8.bn1.d1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3373, -1, 6677, -1, 3373, -1, 6669, -1], 'generators': [4271, 16233, 21517], 'label': '128.734.4.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.q1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799481
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.h1.a1', '8.bd1.a1', '8.bd1.c1', '8.bd1.e1', '8.bd1.g1', '8.be1.a1', '8.bg1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1837, -1, 2682, -1, 1837, -1, 2698, -1], 'generators': [13485, 48323, 56453], 'label': '128.734.4.r1.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.r1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799482
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.h1.b1', '8.bd1.b1', '8.bd1.d1', '8.bd1.f1', '8.bd1.h1', '8.be1.a1', '8.bg1.a1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1837, -1, 2574, -1, 1837, -1, 2590, -1], 'generators': [13485, 56389, 56453], 'label': '128.734.4.r1.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.r1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799483
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.g1.a1', '8.bd1.a1', '8.bd1.b1', '8.bd1.e1', '8.bd1.f1', '8.bf1.a1', '8.bk1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1629, -1, 2018, -1, 1629, -1, 2019, -1], 'generators': [13485, 48323, 48259], 'label': '128.734.4.s1.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.s1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799484
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.g1.b1', '8.bd1.c1', '8.bd1.d1', '8.bd1.g1', '8.bd1.h1', '8.bf1.a1', '8.bk1.a1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1629, -1, 2790, -1, 1629, -1, 2806, -1], 'generators': [30889, 48323, 48259], 'label': '128.734.4.s1.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.s1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799485
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.g1.a1', '8.bi1.a1', '8.bl1.a1', '8.bm1.a1', '8.bm1.b1', '8.bn1.a1', '8.bn1.b1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3141, -1, 6153, -1, 3140, -1, 6146, -1], 'generators': [4271, 32621, 39049], 'label': '128.734.4.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.t1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799486
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.g1.b1', '8.bi1.a1', '8.bl1.a1', '8.bm1.c1', '8.bm1.d1', '8.bn1.c1', '8.bn1.d1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3141, -1, 6286, -1, 3140, -1, 6278, -1], 'generators': [56483, 32621, 39049], 'label': '128.734.4.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.t1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799487
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.h1.a1', '8.bh1.a1', '8.bj1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6037, -1, 4552, -1, 6037, -1, 4549, -1], 'generators': [49029, 48323], 'label': '128.734.4.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.u1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799488
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1'], 'contains': ['8.h1.b1', '8.bh1.a1', '8.bj1.a1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6037, -1, 4361, -1, 6037, -1, 4366, -1], 'generators': [49029, 56389], 'label': '128.734.4.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.u1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799489
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493668', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.f1.a1', '64.f1.b1', '64.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '4.p1.a1', '4.p1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4956, 6148, 5170, 855, 5015, 6145, 5179, 857], 'generators': [13485, 32621, 56453], 'label': '128.734.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 262799490
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.m1.a1', '16.p1.a1', '16.bj1.a1', '16.bj1.c1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4193, 7345, 2891, 2820, 4193, 7402, 2887, 2829], 'generators': [13485, 30727, 39049, 38921], 'label': '128.734.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799491
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '8.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.b1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.h1.b1', '16.m1.b1', '16.p1.b1', '16.bj1.b1', '16.bj1.d1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4193, 7345, 3438, 3404, 4193, 7402, 3433, 3414], 'generators': [30889, 30727, 39049, 38921], 'label': '128.734.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799492
    {'ambient': '128.734', 'aut_centralizer_order': 256, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5285, 5485, 4982, 4258, 5285, 5483, 4975, 4272], 'generators': [30727, 39049, 56453], 'label': '128.734.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1', '16.d1.a1', '16.g1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799493
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.e1', '16.bn1.f1', '16.bn1.m1', '16.bn1.n1', '16.bn1.i1', '16.bn1.j1', '16.bn1.g1', '16.bn1.h1', '16.bn1.c1', '16.bn1.d1', '16.bn1.k1', '16.bn1.l1', '16.bn1.o1', '16.bn1.p1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.k1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.bd1.a1', '16.be1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8400, 9255, 8196, 8233, 8399, 9312, 8185, 8258], 'generators': [49029, 30727, 56453], 'label': '128.734.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799494
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.c1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.e1', '16.bn1.f1', '16.bn1.m1', '16.bn1.n1', '16.bn1.i1', '16.bn1.j1', '16.bn1.g1', '16.bn1.h1', '16.bn1.c1', '16.bn1.d1', '16.bn1.k1', '16.bn1.l1', '16.bn1.o1', '16.bn1.p1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.l1.a1', '16.bf1.a1', '16.bg1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7738, 8210, 7711, 7257, 7737, 8266, 7700, 7279], 'generators': [48909, 30727, 56453], 'label': '128.734.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799495
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.e1', '16.bn1.f1', '16.bn1.m1', '16.bn1.n1', '16.bn1.i1', '16.bn1.j1', '16.bn1.g1', '16.bn1.h1', '16.bn1.c1', '16.bn1.d1', '16.bn1.k1', '16.bn1.l1', '16.bn1.o1', '16.bn1.p1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.k1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9241, 1309, 8061, 9052, 9240, 1309, 8050, 9079], 'generators': [4455, 21517], 'label': '128.734.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799496
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.e1', '16.bn1.f1', '16.bn1.m1', '16.bn1.n1', '16.bn1.i1', '16.bn1.j1', '16.bn1.g1', '16.bn1.h1', '16.bn1.c1', '16.bn1.d1', '16.bn1.k1', '16.bn1.l1', '16.bn1.o1', '16.bn1.p1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.b1', '4.o1.b1'], 'contains': ['16.c1.a1', '16.k1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9241, 1309, 7954, 9708, 9240, 1309, 7942, 9736], 'generators': [20843, 21517], 'label': '128.734.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799497
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.i1', '16.bn1.j1', '16.bn1.m1', '16.bn1.n1', '16.bn1.e1', '16.bn1.f1', '16.bn1.d1', '16.bn1.c1', '16.bn1.l1', '16.bn1.k1', '16.bn1.p1', '16.bn1.o1', '16.bn1.h1', '16.bn1.g1', '16.bm1.c1', '16.bm1.d1', '16.bm1.a1', '16.bm1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.p1.a1', '4.q1.a1'], 'contains': ['16.e1.a1', '16.bh1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4006, 4138, 5572, 292, 4006, 4152, 5565, 293], 'generators': [32621, 21517], 'label': '128.734.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '64.73', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799498
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': ['16.bn1.a1', '16.bn1.b1', '16.bn1.i1', '16.bn1.j1', '16.bn1.m1', '16.bn1.n1', '16.bn1.e1', '16.bn1.f1', '16.bn1.d1', '16.bn1.c1', '16.bn1.l1', '16.bn1.k1', '16.bn1.p1', '16.bn1.o1', '16.bn1.h1', '16.bn1.g1', '16.bm1.a1', '16.bm1.b1', '16.bm1.c1', '16.bm1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.p1.b1', '4.q1.b1'], 'contains': ['16.e1.a1', '16.bh1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4006, 4138, 5852, 1005, 4006, 4152, 5843, 1007], 'generators': [16233, 21517], 'label': '128.734.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.f1.a1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '64.73', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799499
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': ['16.bm1.a1', '16.bm1.b1', '16.bm1.c1', '16.bm1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.s1.a1', '4.t1.a1'], 'contains': ['16.g1.a1', '16.q1.a1', '16.y1.a1', '16.z1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1629, 2807, 4489, 6282, 1629, 2813, 4482, 6300], 'generators': [4271, 48259, 39049], 'label': '128.734.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799500
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493668', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.e1.a1', '64.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.m1.a1', '4.n1.a1', '4.q1.a1', '4.q1.b1', '4.t1.a1', '4.t1.b1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3897, 4733, 6220, 4658, 3897, 4731, 6211, 4672], 'generators': [4271, 32621, 39049, 56453], 'label': '128.734.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 262799501
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': ['16.bm1.b1', '16.bm1.a1', '16.bm1.d1', '16.bm1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.s1.b1', '4.t1.b1'], 'contains': ['16.g1.a1', '16.q1.b1', '16.y1.b1', '16.z1.b1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1629, 2807, 4810, 5305, 1629, 2813, 4803, 5321], 'generators': [56483, 48259, 39049], 'label': '128.734.8.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.b1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799502
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': ['16.bm1.a1', '16.bm1.b1', '16.bm1.c1', '16.bm1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.r1.a1', '4.u1.a1'], 'contains': ['16.f1.a1', '16.s1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1856, 6621, 3180, 2236, 1855, 6679, 3175, 2243], 'generators': [48323, 56453], 'label': '128.734.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799503
    {'ambient': '128.734', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': ['16.bm1.a1', '16.bm1.b1', '16.bm1.c1', '16.bm1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.r1.b1', '4.u1.b1'], 'contains': ['16.f1.a1', '16.s1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1856, 6621, 3083, 1652, 1855, 6679, 3079, 1657], 'generators': [56389, 56453], 'label': '128.734.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '64.73', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799504
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.n1.a1', '16.q1.a1', '16.q1.b1', '16.bk1.a1', '16.bk1.a2', '16.bk1.b1', '16.bk1.b2'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [953, -1, 2987, -1, 953, -1, 2983, -1], 'generators': [4271, 30727, 39049, 38921], 'label': '128.734.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '32.27', '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': '4.2'}
  • id: 262799505
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.l1.a1', '16.o1.a1', '16.r1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8681, -1, 8542, -1, 8681, -1, 8529, -1], 'generators': [49029, 30727, 39049], 'label': '128.734.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.j1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799506
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '16.s1.a1', '16.s1.b1', '16.bl1.a1', '16.bl1.b1', '16.bl1.c1', '16.bl1.d1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [706, -1, 1367, -1, 706, -1, 1365, -1], 'generators': [48323, 30727, 38921], 'label': '128.734.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799507
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.k1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7199, -1, 9086, -1, 7199, -1, 9073, -1], 'generators': [4455, 39049], 'label': '128.734.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.l1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799508
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.k1.a1', '16.bm1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9878, -1, 9784, -1, 9878, -1, 9770, -1], 'generators': [13485, 4455, 38921], 'label': '128.734.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799509
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.j1.b1', '4.k1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.k1.b1', '16.bm1.c1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9878, -1, 9462, -1, 9878, -1, 9448, -1], 'generators': [48165, 4591, 38921], 'label': '128.734.8.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799510
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.h1.b1', '16.j1.a1', '16.k1.a1', '16.bm1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9878, -1, 9944, -1, 9878, -1, 9930, -1], 'generators': [30889, 4455, 38921], 'label': '128.734.8.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.c1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799511
    {'ambient': '128.734', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493668', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.e1.a1', '64.e1.b1', '64.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '4.o1.a1', '4.o1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5955, 678, 5410, 9080, 6015, 677, 5419, 9107], 'generators': [4271, 4455, 56453], 'label': '128.734.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 262799512
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.j1.b1', '4.k1.a1'], 'contains': ['16.h1.b1', '16.j1.a1', '16.k1.b1', '16.bm1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9878, -1, 9623, -1, 9878, -1, 9610, -1], 'generators': [61473, 4591, 38921], 'label': '128.734.8.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.d1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799513
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.h1.a1', '16.k1.a1', '16.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9621, -1, 8821, -1, 9621, -1, 8808, -1], 'generators': [48165, 4455], 'label': '128.734.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.n1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799514
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.j1.b1', '4.l1.a1'], 'contains': ['16.h1.a1', '16.k1.b1', '16.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9621, -1, 8688, -1, 9621, -1, 8676, -1], 'generators': [13485, 4591], 'label': '128.734.8.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.n1.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799515
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.j1.a1', '4.l1.a1'], 'contains': ['16.h1.b1', '16.k1.a1', '16.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9621, -1, 9316, -1, 9621, -1, 9303, -1], 'generators': [61473, 4455], 'label': '128.734.8.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.n1.c1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799516
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '4.j1.b1', '4.l1.a1'], 'contains': ['16.h1.b1', '16.k1.b1', '16.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9621, -1, 8954, -1, 9621, -1, 8941, -1], 'generators': [30889, 4591], 'label': '128.734.8.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.n1.d1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 262799517
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.k1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.h1.b1', '16.t1.a1', '16.v1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7456, -1, 7551, -1, 7456, -1, 7540, -1], 'generators': [13485, 30727, 56453], 'label': '128.734.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799518
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.h1.b1', '16.u1.a1', '16.w1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6282, -1, 7390, -1, 6282, -1, 7379, -1], 'generators': [13485, 30727, 21517], 'label': '128.734.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799519
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.m1.a1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.x1.a1', '16.z1.a1', '16.z1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2927, -1, 5712, -1, 2927, -1, 5704, -1], 'generators': [4271, 30727, 56453], 'label': '128.734.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.q1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799520
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.y1.a1', '16.y1.b1', '16.ba1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2645, -1, 4649, -1, 2645, -1, 4643, -1], 'generators': [4271, 30727, 21517], 'label': '128.734.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.r1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799521
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.j1.b1'], 'contains': ['16.c1.a1', '16.j1.a1', '16.l1.a1', '16.bb1.a1', '16.bc1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8983, -1, 8369, -1, 8983, -1, 8357, -1], 'generators': [49029, 30727, 21517], 'label': '128.734.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.s1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799522
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 8, 'centralizer': '16.c1.a1', 'complements': ['64.e1.a1', '64.e1.b1', '64.f1.a1', '64.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '4.u1.a1', '4.u1.b1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5518, 7712, 4733, 6139, 5577, 7710, 4742, 6157], 'generators': [49029, 48323, 30727], 'label': '128.734.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799523
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.k1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.k1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9420, -1, 9201, -1, 9419, -1, 9188, -1], 'generators': [4455, 56453], 'label': '128.734.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.t1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799524
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.m1.a1', '4.n1.a1'], 'contains': ['16.b1.a1', '16.bh1.a1', '16.bh1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3764, -1, 6820, -1, 3763, -1, 6811, -1], 'generators': [32621, 56453], 'label': '128.734.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.u1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799525
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.c1.a1', '16.bi1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6564, -1, 5434, -1, 6563, -1, 5426, -1], 'generators': [53583, 30727], 'label': '128.734.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.v1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262799526
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.d1.a1', '16.m1.a1', '16.m1.b1', '16.t1.a1', '16.u1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5587, -1, 3888, -1, 5587, -1, 3883, -1], 'generators': [13485, 61583, 56453], 'label': '128.734.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.w1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 262799527
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.p1.a1', '4.p1.b1'], 'contains': ['16.e1.a1', '16.m1.a1', '16.m1.b1', '16.v1.a1', '16.w1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4701, -1, 4049, -1, 4701, -1, 4043, -1], 'generators': [13485, 48259, 21517], 'label': '128.734.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.x1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 262799528
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.d1.a1', '16.n1.a1', '16.x1.a1', '16.y1.a1', '16.y1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2363, -1, 4209, -1, 2363, -1, 4203, -1], 'generators': [4271, 61583, 56453], 'label': '128.734.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.y1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799529
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.e1.a1', '16.n1.a1', '16.z1.a1', '16.z1.b1', '16.ba1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2081, -1, 5274, -1, 2082, -1, 5266, -1], 'generators': [4271, 48259, 21517], 'label': '128.734.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.z1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799530
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.d1.a1', '16.o1.a1', '16.bb1.a1', '16.bd1.a1', '16.bf1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8164, -1, 7846, -1, 8163, -1, 7835, -1], 'generators': [49029, 61583, 56453], 'label': '128.734.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.ba1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799531
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.q1.a1', '4.q1.b1'], 'contains': ['16.e1.a1', '16.o1.a1', '16.bc1.a1', '16.be1.a1', '16.bg1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6987, -1, 7255, -1, 6987, -1, 7244, -1], 'generators': [49029, 48259, 21517], 'label': '128.734.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bb1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799532
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.p1.a1', '4.p1.b1'], 'contains': ['16.e1.a1', '16.bi1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5832, -1, 5134, -1, 5832, -1, 5127, -1], 'generators': [53583, 48259], 'label': '128.734.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.bc1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799533
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55751', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': ['64.e1.a1', '64.e1.b1', '64.g1.a1', '64.f1.a1', '64.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4516, 2091, 5681, 2158, 4516, 2091, 5703, 2164], 'generators': [4455, 48323], 'label': '128.734.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799534
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.p1.a1', '16.q1.a1', '16.s1.a1', '16.bn1.a1', '16.bn1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 873, -1, 404, -1, 872, -1], 'generators': [13485, 48323, 38921], 'label': '128.734.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799535
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.r1.b1', '4.s1.a1'], 'contains': ['16.p1.a1', '16.q1.a1', '16.s1.b1', '16.bn1.c1', '16.bn1.d1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 713, -1, 404, -1, 712, -1], 'generators': [21611, 56389, 38921], 'label': '128.734.8.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799536
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.r1.a1', '4.s1.b1'], 'contains': ['16.p1.a1', '16.q1.b1', '16.s1.a1', '16.bn1.e1', '16.bn1.f1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 1194, -1, 404, -1, 1193, -1], 'generators': [21611, 48323, 38921], 'label': '128.734.8.bd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.c1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799537
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.r1.b1', '4.s1.b1'], 'contains': ['16.p1.a1', '16.q1.b1', '16.s1.b1', '16.bn1.g1', '16.bn1.h1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 1034, -1, 404, -1, 1033, -1], 'generators': [13485, 56389, 38921], 'label': '128.734.8.bd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.d1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799538
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.p1.b1', '16.q1.a1', '16.s1.a1', '16.bn1.i1', '16.bn1.j1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 2440, -1, 404, -1, 2437, -1], 'generators': [4207, 48323, 38921], 'label': '128.734.8.bd1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.e1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799539
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.r1.b1', '4.s1.a1'], 'contains': ['16.p1.b1', '16.q1.a1', '16.s1.b1', '16.bn1.k1', '16.bn1.l1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 1540, -1, 404, -1, 1537, -1], 'generators': [30889, 56389, 38921], 'label': '128.734.8.bd1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.f1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799540
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.r1.a1', '4.s1.b1'], 'contains': ['16.p1.b1', '16.q1.b1', '16.s1.a1', '16.bn1.m1', '16.bn1.n1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 2762, -1, 404, -1, 2758, -1], 'generators': [30889, 48323, 38921], 'label': '128.734.8.bd1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.g1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799541
    {'ambient': '128.734', 'aut_centralizer_order': 8, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.r1.b1', '4.s1.b1'], 'contains': ['16.p1.b1', '16.q1.b1', '16.s1.b1', '16.bn1.o1', '16.bn1.p1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [404, -1, 2601, -1, 404, -1, 2598, -1], 'generators': [4207, 56389, 38921], 'label': '128.734.8.bd1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bd1.h1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799542
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.r1.a1', '4.r1.b1'], 'contains': ['16.f1.a1', '16.p1.a1', '16.p1.b1', '16.t1.a1', '16.w1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4983, -1, 3567, -1, 4983, -1, 3562, -1], 'generators': [13485, 39049, 56453], 'label': '128.734.8.be1.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.be1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799543
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.s1.a1', '4.s1.b1'], 'contains': ['16.g1.a1', '16.p1.a1', '16.p1.b1', '16.u1.a1', '16.v1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4419, -1, 3727, -1, 4419, -1, 3722, -1], 'generators': [13485, 48259, 39049], 'label': '128.734.8.bf1.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.bf1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799544
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2326', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.o1.a1', '8.p1.a1', '8.w1.a1', '8.x1.a1', '8.be1.a1', '8.bf1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5079, 8096, 3969, 3390, 5079, 8093, 3963, 3400], 'generators': [13485, 30727, 39049, 56453], 'label': '128.734.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.b1', '8.a1.a1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799545
    {'ambient': '128.734', 'aut_centralizer_order': 32, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.r1.a1', '4.r1.b1'], 'contains': ['16.f1.a1', '16.q1.a1', '16.q1.b1', '16.x1.a1', '16.ba1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1348, -1, 3309, -1, 1348, -1, 3304, -1], 'generators': [4271, 39049, 56453], 'label': '128.734.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bg1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799546
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.u1.a1', '4.u1.b1'], 'contains': ['16.f1.a1', '16.r1.a1', '16.bc1.a1', '16.bd1.a1', '16.bf1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7974, -1, 7146, -1, 7974, -1, 7137, -1], 'generators': [49029, 39049, 56453], 'label': '128.734.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.bh1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799547
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.t1.a1', '4.t1.b1'], 'contains': ['16.g1.a1', '16.r1.a1', '16.bb1.a1', '16.be1.a1', '16.bg1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6799, -1, 7039, -1, 6798, -1, 7029, -1], 'generators': [49029, 48259, 39049], 'label': '128.734.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bi1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799548
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.u1.a1', '4.u1.b1'], 'contains': ['16.f1.a1', '16.bi1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6037, -1, 4350, -1, 6037, -1, 4343, -1], 'generators': [53583, 56453], 'label': '128.734.8.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.bj1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 262799549
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.s1.a1', '4.s1.b1'], 'contains': ['16.g1.a1', '16.s1.a1', '16.s1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1121, -1, 1829, -1, 1121, -1, 1827, -1], 'generators': [48323, 48259], 'label': '128.734.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bk1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262799550
    {'ambient': '128.734', 'aut_centralizer_order': 64, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.t1.a1', '4.t1.b1'], 'contains': ['16.g1.a1', '16.bh1.a1', '16.bh1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3521, -1, 5969, -1, 3521, -1, 5961, -1], 'generators': [32621, 39049], 'label': '128.734.8.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bl1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 262799551
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.a1', '4.t1.a1'], 'contains': ['16.z1.a1', '16.be1.a1', '16.bh1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3344, -1, 6185, -1, 3344, -1, 6176, -1], 'generators': [4271, 32621], 'label': '128.734.8.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bm1.a1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799552
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.b1', '4.t1.a1'], 'contains': ['16.z1.a1', '16.be1.a1', '16.bh1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3344, -1, 6698, -1, 3344, -1, 6689, -1], 'generators': [38951, 32741], 'label': '128.734.8.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bm1.b1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799553
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.a1', '4.t1.b1'], 'contains': ['16.z1.b1', '16.be1.a1', '16.bh1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3344, -1, 6385, -1, 3344, -1, 6375, -1], 'generators': [56483, 32621], 'label': '128.734.8.bm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bm1.c1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 262799554
    {'ambient': '128.734', 'aut_centralizer_order': 16, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.q1.b1', '4.t1.b1'], 'contains': ['16.z1.b1', '16.be1.a1', '16.bh1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3344, -1, 6942, -1, 3344, -1, 6933, -1], 'generators': [21547, 32741], 'label': '128.734.8.bm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bm1.d1', 'projective_image': '64.73', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}