Abstract group data - 128.850

Formats: - HTML - YAML - JSON - 2025-10-01T05:51:30.694291

• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 2, 4, 4, 2, 2], 'aut_gens': [[420006, 126720, 1, 142584, 889560, 126774, 1229808], [430231, 1134000, 1, 1219680, 970974, 1149264, 1229808], [1679190, 1134000, 1, 1219680, 889560, 1149264, 1229808], [420006, 1229784, 1229809, 1134054, 889560, 126774, 1229808], [1558446, 55, 1229809, 1134054, 2436168, 126774, 1229808], [1832689, 126720, 1, 1219680, 2395824, 126774, 1229808], [420007, 126720, 1, 142584, 889560, 126774, 1229808], [586951, 54, 1, 1134054, 2436168, 126774, 1229808]], 'aut_group': '1024.dly', 'aut_hash': 1735459185383964265, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 20, 'aut_perms': [881984129862941416, 122784084868762800, 269038337945505854, 1007084588962724049, 933053778746006416, 2156717159550016, 14950828822018456], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 4, 1, 4], [2, 4, 4, 1], [4, 4, 1, 2], [4, 8, 2, 1], [4, 8, 4, 1], [8, 8, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_4^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '32.27', 'autcentquo_hash': 27, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 8], [4, 4, 2], [4, 8, 6], [8, 8, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '32.6', 'commutator_count': 1, 'commutator_label': '8.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 850, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['64.32', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 8], [4, 4, 1, 2], [4, 8, 1, 2], [4, 8, 2, 2], [8, 8, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 672, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.11', 'frattini_quotient': '8.5', 'hash': 850, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 2, 1, 2, 2, 2, 1], 'inner_gens': [[420006, 21024, 1, 21048, 889560, 1149264, 1229808], [1674126, 126720, 1, 142584, 970974, 126774, 1229808], [420006, 126720, 1, 142584, 889560, 126774, 1229808], [1558446, 126720, 1, 142584, 2436168, 126774, 1229808], [420006, 54, 1, 1134054, 889560, 126774, 1229808], [1679190, 126720, 1, 142584, 889560, 126774, 1229808], [420006, 126720, 1, 142584, 889560, 126774, 1229808]], 'inner_hash': 6, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': True, 'inner_tex': 'C_2^3:C_4', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 6]], 'label': '128.850', 'linC_count': 32, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 16, 'linQ_dim': 5, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:C4', 'ngens': 7, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 26, 'number_divisions': 22, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 125, 'number_subgroup_classes': 219, 'number_subgroups': 660, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 56], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 126774, 0], 'outer_gens': [[1817400, 1149288, 1, 1219680, 889560, 126774, 1229808], [1817401, 1149288, 1, 1219680, 889560, 126774, 1229808], [2678449, 1149288, 1229809, 1219680, 889560, 126774, 1229808], [2678449, 1149289, 1229809, 1219680, 889560, 126774, 1229808]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [7, 23, 11527, 16560], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 6]], 'representations': {'PC': {'code': 302840343827298100751649, 'gens': [1, 3, 4, 5, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 14, 2019, 346, 2357, 2028, 278, 124, 3926]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706304316028, 706461441026]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [32713795, 4562006, 7292993, 5128257, 20225089, 6210625, 18750531]}, 'Perm': {'d': 10, 'gens': [420006, 126720, 1, 142584, 889560, 126774, 1229808]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:C_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: 43449941
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 850, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 43449952
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 850, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 1, 'size': 1}
  • id: 43449960
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 850, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 1229809, 'size': 1}
  • id: 43449961
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 850, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 1229808, 'size': 1}
  • id: 43449962
    {'aut_label': '2D', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 850, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 126775, 'size': 2}
  • id: 43449963
    {'aut_label': '2E', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 850, 'group_order': 128, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 126774, 'size': 2}
  • id: 43449964
    {'aut_label': '2F', 'centralizer': '4.a1.a1', 'counter': 7, 'group_counter': 850, 'group_order': 128, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 54, 'size': 4}
  • id: 43449965
    {'aut_label': '2F', 'centralizer': '4.a1.a1', 'counter': 8, 'group_counter': 850, 'group_order': 128, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 55, 'size': 4}
  • id: 43449966
    {'aut_label': '2H', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 850, 'group_order': 128, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 21048, 'size': 4}
  • id: 43449942
    {'aut_label': '2I', 'centralizer': '4.a1.a1', 'counter': 10, 'group_counter': 850, 'group_order': 128, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 21049, 'size': 4}
  • id: 43449943
    {'aut_label': '2F', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 850, 'group_order': 128, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 142608, 'size': 4}
  • id: 43449944
    {'aut_label': '2F', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 850, 'group_order': 128, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 142609, 'size': 4}
  • id: 43449945
    {'aut_label': '2L', 'centralizer': '4.j1.a1', 'counter': 13, 'group_counter': 850, 'group_order': 128, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 889561, 'size': 4}
  • id: 43449946
    {'aut_label': '2M', 'centralizer': '4.j1.a1', 'counter': 14, 'group_counter': 850, 'group_order': 128, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 889560, 'size': 4}
  • id: 43449947
    {'aut_label': '4A', 'centralizer': '4.k1.a1', 'counter': 15, 'group_counter': 850, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [4], 'representative': 899689, 'size': 4}
  • id: 43449948
    {'aut_label': '4B', 'centralizer': '4.k1.a1', 'counter': 16, 'group_counter': 850, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [4], 'representative': 899688, 'size': 4}
  • id: 43449949
    {'aut_label': '4C', 'centralizer': '8.m1.a1', 'counter': 17, 'group_counter': 850, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [6], 'representative': 889614, 'size': 8}
  • id: 43449950
    {'aut_label': '4C', 'centralizer': '8.m1.a1', 'counter': 18, 'group_counter': 850, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [6], 'representative': 889615, 'size': 8}
  • id: 43449951
    {'aut_label': '4E1', 'centralizer': '8.p1.a1', 'counter': 19, 'group_counter': 850, 'group_order': 128, 'label': '4E1', 'order': 4, 'powers': [14], 'representative': 420006, 'size': 8}
  • id: 43449953
    {'aut_label': '4E1', 'centralizer': '8.p1.a1', 'counter': 20, 'group_counter': 850, 'group_order': 128, 'label': '4E-1', 'order': 4, 'powers': [14], 'representative': 1817400, 'size': 8}
  • id: 43449954
    {'aut_label': '4E1', 'centralizer': '8.p1.a1', 'counter': 21, 'group_counter': 850, 'group_order': 128, 'label': '4F1', 'order': 4, 'powers': [14], 'representative': 420007, 'size': 8}
  • id: 43449955
    {'aut_label': '4E1', 'centralizer': '8.p1.a1', 'counter': 22, 'group_counter': 850, 'group_order': 128, 'label': '4F-1', 'order': 4, 'powers': [14], 'representative': 1817401, 'size': 8}
  • id: 43449956
    {'aut_label': '8A1', 'centralizer': '8.q1.a1', 'counter': 23, 'group_counter': 850, 'group_order': 128, 'label': '8A1', 'order': 8, 'powers': [16], 'representative': 420030, 'size': 8}
  • id: 43449957
    {'aut_label': '8A1', 'centralizer': '8.q1.a1', 'counter': 24, 'group_counter': 850, 'group_order': 128, 'label': '8A-1', 'order': 8, 'powers': [16], 'representative': 1817454, 'size': 8}
  • id: 43449958
    {'aut_label': '8A1', 'centralizer': '8.q1.a1', 'counter': 25, 'group_counter': 850, 'group_order': 128, 'label': '8B1', 'order': 8, 'powers': [16], 'representative': 420031, 'size': 8}
  • id: 43449959
    {'aut_label': '8A1', 'centralizer': '8.q1.a1', 'counter': 26, 'group_counter': 850, 'group_order': 128, 'label': '8B-1', 'order': 8, 'powers': [16], 'representative': 1817455, '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: 108431
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1a', '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: 108442
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1b', '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: 108446
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1c', '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: 108447
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1d', '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: 108448
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1e', '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: 108449
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1f', '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: 108450
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1g', '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: 108451
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1h', '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: 108452
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108432
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108433
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108434
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108435
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 0, 0, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108436
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 0, 0, -2, 2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108437
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108438
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108439
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4a', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108440
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4b', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108441
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4c', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108443
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4d', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108444
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4e', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 108445
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '128.850', 'group_order': 128, 'image': None, 'label': '128.850.4f', 'multiplicity': 1, 'nt': [8, 27], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 105899
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 128, 'label': '128.850.1a', '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: 105910
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 64, 'label': '128.850.1b', '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: 105918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 64, 'label': '128.850.1c', '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: 105919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 64, 'label': '128.850.1d', '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: 105920
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 64, 'label': '128.850.1e', '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: 105921
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 64, 'label': '128.850.1f', '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: 105922
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 64, 'label': '128.850.1g', '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: 105923
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 64, 'label': '128.850.1h', '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: 105924
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 32, 'label': '128.850.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 105900
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 32, 'label': '128.850.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 105901
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.b1', 'kernel_order': 32, 'label': '128.850.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 105902
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.b1', 'kernel_order': 32, 'label': '128.850.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 105903
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 32, 'label': '128.850.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 105904
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 32, 'label': '128.850.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 105905
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 32, 'label': '128.850.1l1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 105906
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 128, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 32, 'label': '128.850.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 105907
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1.a1', 'kernel_order': 16, 'label': '128.850.2a', '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]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105908
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1.a1', 'kernel_order': 16, 'label': '128.850.2b', '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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105909
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 16, 'label': '128.850.2c', '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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105911
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 16, 'label': '128.850.2d', '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]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105912
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1.a1', 'kernel_order': 4, 'label': '128.850.4a', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105913
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 4, 'label': '128.850.4b', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105914
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.b1', 'kernel_order': 2, 'label': '128.850.4c', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105915
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.b1', 'kernel_order': 2, 'label': '128.850.4d', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105916
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 2, 'label': '128.850.4e', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 105917
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.850', 'group_counter': 850, 'group_order': 128, 'image': None, 'image_isoclass': '64.32', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 2, 'label': '128.850.4f', 'nt': [8, 27], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 8214845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.850.1.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': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 2}
  • id: 8214956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.2.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.2.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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.2.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: 8215009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '128.850.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '128.850.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '128.850.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.c1', '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': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '128.850.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.d1', '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': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215053
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 8214846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.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': ['U1'], '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: 8214857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.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': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.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': True, '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: 8214945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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: 8214968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8214981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.4.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': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 8214986
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8214988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8214990
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8214991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 8214994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 8214995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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: 8214999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.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: 8215001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.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: 8215002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215008
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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: 8215011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8215013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 8215017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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: 8215021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 8215026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 8215027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8215030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.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: 8215032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.8.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8215033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['U2'], '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: 8215034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215038
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.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': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.16.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: 8215040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215043
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8215044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8215045
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8215046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.h2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8215047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215052
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8215054
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215055
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8215056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.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: 8215057
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.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: 8215058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8215059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l2.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: 8215060
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l2.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: 8215061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.l2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l2.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: 8215062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8215063
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214863
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.y1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.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: 8214864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 8214871
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 8214872
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.16.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214876
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.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: 8214877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.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: 8214878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.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: 8214881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bf1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.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: 8214885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.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: 8214886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bh1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.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: 8214889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bh1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.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: 8214891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 8214892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 8214893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.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: 8214894
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.bi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.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: 8214895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.16.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: 8214899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.32.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': '32.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 8214902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.850.32.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': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.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: 8214908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1.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: 8214909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8214914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214920
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214921
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8214926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8214927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.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: 8214933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.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: 8214935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.r2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r2.a1', 'outer_equivalence': False, 'perfect': False, '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: 8214936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.r2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r2.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: 8214937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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: 8214939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214941
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214942
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8214943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.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: 8214947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.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: 8214948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 8214949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x2.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: 8214950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x2.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: 8214951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.x2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x2.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: 8214952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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: 8214954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 8214955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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: 8214958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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: 8214959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.c2', 'outer_equivalence': False, 'perfect': False, '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: 8214960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.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: 8214961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.850.32.y1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.d2', 'outer_equivalence': False, 'perfect': False, '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: 8214962
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214963
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.32.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 8214964
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '128.850.64.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': '64.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214965
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '128.850.64.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 208, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.850.64.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': '64.90', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 90, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:C_4', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 8214967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214970
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214971
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214972
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 8214973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 8214974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214975
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.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: 8214976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 8214977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.850.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 8214978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.850', 'ambient_counter': 850, 'ambient_order': 128, 'ambient_tex': 'C_2^5:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 219, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.850.128.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': '128.850', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 850, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 8214845
    {'ambient': '128.850', '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.d1.b1', '2.d1.c1', '2.d1.d1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2542, 3019, 2018, 3570, 2565, 3123, 2026, 3687], 'generators': [889560, 1229808, 126720, 1, 126774, 142584, 420006], 'label': '128.850.1.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.d1', '2.d1.c1', '2.d1.b1', '2.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8214846
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', '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.b1.a1', '8.c1.a1', '8.e1.a1', '8.f1.a1', '8.h1.a1', '8.i1.a1', '8.o1.a1', '8.s1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3251, 3565, 2246, 778, 3325, 3700, 2254, 803], 'generators': [889560, 1229808, 1, 126774, 142584], 'label': '128.850.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.b1.a1', '8.a1.a1', '8.c1.a1', '8.f1.a1', '8.i1.a1', '8.e1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214847
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.n1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.e1.b1', '32.e1.c1', '32.e1.d1', '32.h1.a1', '32.h1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8051, -1, 6848, -1, 8133, -1, 6875, -1], 'generators': [1229808, 126720, 1], 'label': '128.850.16.n1.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.n1.a1', 'projective_image': '32.6', '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': '1.1'}
  • id: 8214848
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.f1.b1', '32.i1.a1', '32.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6950, -1, 5433, -1, 7021, -1, 5454, -1], 'generators': [1229808, 1, 142584], 'label': '128.850.16.o1.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.o1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8214849
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.o1.a1', '8.p1.a1'], 'contains': ['32.a1.a1', '32.g1.a1', '32.g1.b1', '32.k1.a1', '32.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1615, -1, 1210, -1, 1632, -1, 1214, -1], 'generators': [889560, 1229808, 1], 'label': '128.850.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.p1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8214850
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.o1.a1', '8.q1.a1'], 'contains': ['32.a1.a1', '32.m1.a1', '32.n1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3128, -1, 1484, -1, 3160, -1, 1490, -1], 'generators': [1229808, 1, 2380014], 'label': '128.850.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.q1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8214851
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.r1.a1'], 'contains': ['32.b1.a1', '32.h1.a1', '32.h1.b1', '32.o1.a1', '32.o1.b1', '32.o1.c1', '32.o1.d1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7611, -1, 6258, -1, 7688, -1, 6283, -1], 'generators': [1229808, 126775, 126720], 'label': '128.850.16.r1.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.r1.a1', 'projective_image': '64.90', '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': '1.1'}
  • id: 8214852
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.b1.a1', '32.i1.a1', '32.j1.a1', '32.p1.a1', '32.p1.a2'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6729, -1, 5314, -1, 6798, -1, 5336, -1], 'generators': [1229808, 126775, 142584], 'label': '128.850.16.s1.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.s1.a1', 'projective_image': '64.90', '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: 8214853
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.s1.a1', '8.t1.a1'], 'contains': ['32.b1.a1', '32.k1.a1', '32.l1.a1', '32.q1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1836, -1, 1327, -1, 1855, -1, 1333, -1], 'generators': [889560, 1229808, 126775], 'label': '128.850.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.t1.a1', 'projective_image': '64.90', '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: 8214854
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.s1.a1', '8.u1.a1'], 'contains': ['32.b1.a1', '32.m1.a1', '32.n1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2763, -1, 1680, -1, 2791, -1, 1687, -1], 'generators': [1229808, 126775, 2380014], 'label': '128.850.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.u1.a1', 'projective_image': '64.90', '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: 8214855
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.l1.a1', '8.v1.a1', '8.w1.a1', '8.x1.a1', '8.y1.a1', '8.z1.a1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.r1.a1', '32.r1.c1', '32.r2.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7170, -1, 5078, -1, 7243, -1, 5099, -1], 'generators': [1229808, 126720, 126774], 'label': '128.850.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.v1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8214856
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.l1.a1', '8.v1.b1', '8.w1.b1', '8.x1.b1', '8.y1.b1', '8.z1.a1'], 'contains': ['32.c1.a1', '32.h1.b1', '32.r1.b1', '32.r1.d1', '32.r2.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7170, -1, 5197, -1, 7243, -1, 5217, -1], 'generators': [1229808, 126721, 126774], 'label': '128.850.16.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.v1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214857
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': ['32.z1.a1', '32.z1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.g1.b1', '8.m1.a1', '8.ba1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7694, 5093, 4363, 6603, 7772, 5284, 4380, 6819], 'generators': [1229808, 970920, 1, 126774, 142584], 'label': '128.850.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.g1.a1', '8.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '32.6', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214858
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.m1.a1', '8.v1.b1', '8.w1.a1', '8.x1.b1', '8.y1.a1', '8.ba1.a1'], 'contains': ['32.c1.a1', '32.w1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5776, -1, 3112, -1, 5835, -1, 3125, -1], 'generators': [1229808, 970920, 126774], 'label': '128.850.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.w1.a1', 'projective_image': '64.90', '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: 8214859
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.b1', '8.m1.a1', '8.v1.a1', '8.w1.b1', '8.x1.a1', '8.y1.b1', '8.ba1.a1'], 'contains': ['32.c1.a1', '32.w1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5776, -1, 2917, -1, 5835, -1, 2929, -1], 'generators': [970921, 1229808, 126774], 'label': '128.850.16.w1.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.w1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214860
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.n1.a1', '8.r1.a1'], 'contains': ['32.h1.a1', '32.i1.a1', '32.x1.a1', '32.x1.c1', '32.x2.a1', '32.x2.a2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7556, -1, 8578, -1, 7585, -1], 'generators': [1229808, 126720, 142584], 'label': '128.850.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.x1.a1', 'projective_image': '64.90', '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': '1.1'}
  • id: 8214861
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.n1.a1', '8.r1.a1'], 'contains': ['32.h1.b1', '32.i1.a1', '32.x1.b1', '32.x1.d1', '32.x2.b1', '32.x2.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 8500, -1, 8578, -1, 8533, -1], 'generators': [1229808, 126721, 142584], 'label': '128.850.16.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.x1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214862
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.r1.a1', '8.z1.a1'], 'contains': ['32.h1.a1', '32.h1.b1', '32.j1.a1', '32.y1.a1', '32.y1.b2', '32.y1.c1', '32.y1.d2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 7792, -1, 8801, -1, 7822, -1], 'generators': [1229808, 126720, 142585], 'label': '128.850.16.y1.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.y1.a1', 'projective_image': '64.90', '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': '1.1'}
  • id: 8214863
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.r1.a1', '8.z1.a1'], 'contains': ['32.h1.a1', '32.h1.b1', '32.j1.a1', '32.y1.a2', '32.y1.b1', '32.y1.c2', '32.y1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 7673, -1, 8801, -1, 7704, -1], 'generators': [21024, 1229808, 142585], 'label': '128.850.16.y1.a2', '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.y1.a2', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214864
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.o1.a1', '8.s1.a1'], 'contains': ['32.i1.a1', '32.k1.a1', '32.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4160, -1, 2140, -1, 4202, -1, 2149, -1], 'generators': [1229808, 889561, 142584], 'label': '128.850.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.z1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214865
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.o1.a1', '8.s1.a1'], 'contains': ['32.i1.a1', '32.l1.a1', '32.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2262, -1, 1830, -1, 2286, -1, 1837, -1], 'generators': [889560, 1229808, 142584], 'label': '128.850.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ba1.a1', 'projective_image': '64.90', '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: 8214866
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.o1.a1', '8.s1.a1'], 'contains': ['32.j1.a1', '32.k1.a1', '32.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3773, -1, 2037, -1, 3811, -1, 2045, -1], 'generators': [1229808, 142585, 2380014], 'label': '128.850.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.bb1.a1', 'projective_image': '64.90', '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': '4.2'}
  • id: 8214867
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.o1.a1', '8.s1.a1'], 'contains': ['32.j1.a1', '32.l1.a1', '32.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3966, -1, 1933, -1, 4006, -1, 1941, -1], 'generators': [889560, 1229808, 142585], 'label': '128.850.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.bc1.a1', 'projective_image': '64.90', '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': '4.2'}
  • id: 8214868
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.z1.a1', '32.z1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.g1.b1', '8.v1.a1', '8.x1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6740, 8226, 3351, 7685, 6809, 8534, 3365, 7937], 'generators': [1229808, 126720, 889561, 126774, 142584], 'label': '128.850.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214869
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.t1.a1', '8.bb1.a1'], 'contains': ['32.l1.a1', '32.z1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [853, -1, 671, -1, 861, -1, 674, -1], 'generators': [889560, 1229808, 420006], 'label': '128.850.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bd1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8214870
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.t1.a1', '8.bb1.b1'], 'contains': ['32.l1.a1', '32.z1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [853, -1, 476, -1, 861, -1, 478, -1], 'generators': [889560, 1229808, 420007], 'label': '128.850.16.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bd1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214871
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.u1.a1', '8.bc1.a1'], 'contains': ['32.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1408, -1, 977, -1, 1423, -1, 982, -1], 'generators': [1229808, 2380014, 1548246], 'label': '128.850.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.be1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8214872
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.u1.a1', '8.bc1.b1'], 'contains': ['32.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1408, -1, 1087, -1, 1423, -1, 1098, -1], 'generators': [1229808, 1548247, 2380014], 'label': '128.850.16.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.be1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214873
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.c1', '8.r1.a1'], 'contains': ['32.o1.a1', '32.o1.c1', '32.p1.a1', '32.x1.b1', '32.x2.a1', '32.y1.a1', '32.y1.c2'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 9207, -1, 9468, -1, 9243, -1], 'generators': [1229784, 1149265, 142584], 'label': '128.850.16.bf1.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.bf1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214874
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.c1', '8.r1.a1'], 'contains': ['32.o1.a1', '32.o1.c1', '32.p1.a2', '32.x1.b1', '32.x2.a2', '32.y1.a2', '32.y1.c1'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 9089, -1, 9468, -1, 9125, -1], 'generators': [126775, 142584, 54], 'label': '128.850.16.bf1.a2', '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.bf1.a2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214875
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.d1', '8.r1.a1'], 'contains': ['32.o1.b1', '32.o1.d1', '32.p1.a2', '32.x1.d1', '32.x2.a1', '32.y1.b2', '32.y1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 7320, -1, 9468, -1, 7349, -1], 'generators': [1229784, 126775, 142584], 'label': '128.850.16.bf1.b1', '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.bf1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214876
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.d1', '8.r1.a1'], 'contains': ['32.o1.b1', '32.o1.d1', '32.p1.a1', '32.x1.d1', '32.x2.a2', '32.y1.b1', '32.y1.d2'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 7437, -1, 9468, -1, 7467, -1], 'generators': [1149265, 142584, 54], 'label': '128.850.16.bf1.b2', '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.bf1.b2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214877
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.d1', '8.r1.a1'], 'contains': ['32.o1.a1', '32.o1.b1', '32.p1.a1', '32.x1.a1', '32.x2.b1', '32.y1.a2', '32.y1.b2'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 8264, -1, 9468, -1, 8296, -1], 'generators': [1149265, 126720, 142584], 'label': '128.850.16.bf1.c1', '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.bf1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214878
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.d1', '8.r1.a1'], 'contains': ['32.o1.a1', '32.o1.b1', '32.p1.a2', '32.x1.a1', '32.x2.b2', '32.y1.a1', '32.y1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 8145, -1, 9468, -1, 8178, -1], 'generators': [126775, 126720, 142584], 'label': '128.850.16.bf1.c2', '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.bf1.c2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214879
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.z1.a1', '32.z1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.b1', '8.e1.a1', '8.g1.a1', '8.v1.b1', '8.x1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6740, 8226, 4623, 8726, 6809, 8534, 4641, 9012], 'generators': [1229808, 970920, 889561, 126774, 142584], 'label': '128.850.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.d1.b1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214880
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.c1', '8.r1.a1'], 'contains': ['32.o1.c1', '32.o1.d1', '32.p1.a2', '32.x1.c1', '32.x2.b1', '32.y1.c2', '32.y1.d2'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 8735, -1, 9468, -1, 8770, -1], 'generators': [1149288, 126775, 142584], 'label': '128.850.16.bf1.d1', '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.bf1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214881
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.c1', '8.r1.a1'], 'contains': ['32.o1.c1', '32.o1.d1', '32.p1.a1', '32.x1.c1', '32.x2.b2', '32.y1.c1', '32.y1.d1'], 'core': '128.a1.a1', 'coset_action_label': '16T259', 'count': 4, 'diagramx': [9372, -1, 8617, -1, 9468, -1, 8651, -1], 'generators': [1149265, 1149288, 142584], 'label': '128.850.16.bf1.d2', '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.bf1.d2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214882
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.j1.c1', '8.v1.a1'], 'contains': ['32.r1.a1', '32.u1.a1', '32.w1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T227', 'count': 4, 'diagramx': [5131, -1, 4059, -1, 5184, -1, 4075, -1], 'generators': [126720, 889561, 126774], 'label': '128.850.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bg1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214883
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.j1.d1', '8.v1.b1'], 'contains': ['32.r1.b1', '32.u1.a1', '32.w1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T227', 'count': 4, 'diagramx': [5131, -1, 4968, -1, 5184, -1, 4988, -1], 'generators': [970920, 889561, 126774], 'label': '128.850.16.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bg1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214884
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.j1.d1', '8.v1.a1'], 'contains': ['32.r1.c1', '32.u1.a1', '32.w1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T227', 'count': 4, 'diagramx': [5131, -1, 4266, -1, 5184, -1, 4283, -1], 'generators': [1149288, 889561, 126774], 'label': '128.850.16.bg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bg1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214885
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.j1.c1', '8.v1.b1'], 'contains': ['32.r1.d1', '32.u1.a1', '32.w1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T227', 'count': 4, 'diagramx': [5131, -1, 3956, -1, 5184, -1, 3971, -1], 'generators': [970920, 126774, 2436169], 'label': '128.850.16.bg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bg1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214886
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.j1.c1', '8.w1.a1'], 'contains': ['32.r1.a1', '32.v1.a1', '32.w1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T283', 'count': 4, 'diagramx': [4938, -1, 4162, -1, 4988, -1, 4179, -1], 'generators': [889560, 126720, 126774], 'label': '128.850.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bh1.a1', 'projective_image': '128.850', '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: 8214887
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.j1.d1', '8.w1.b1'], 'contains': ['32.r1.b1', '32.v1.a1', '32.w1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T283', 'count': 4, 'diagramx': [4938, -1, 4370, -1, 4988, -1, 4387, -1], 'generators': [889560, 126721, 126774], 'label': '128.850.16.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bh1.b1', 'projective_image': '128.850', '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: 8214888
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.j1.d1', '8.w1.a1'], 'contains': ['32.r1.c1', '32.v1.a1', '32.w1.a1'], 'core': '128.a1.a1', 'coset_action_label': '16T283', 'count': 4, 'diagramx': [4938, -1, 4865, -1, 4988, -1, 4884, -1], 'generators': [889560, 1149288, 126774], 'label': '128.850.16.bh1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bh1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214889
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.j1.c1', '8.w1.b1'], 'contains': ['32.r1.d1', '32.v1.a1', '32.w1.b1'], 'core': '128.a1.a1', 'coset_action_label': '16T283', 'count': 4, 'diagramx': [4938, -1, 3734, -1, 4988, -1, 3749, -1], 'generators': [889560, 1149289, 126774], 'label': '128.850.16.bh1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bh1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8214890
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.d1.a1', '8.f1.a1', '8.g1.a1', '8.w1.a1', '8.y1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5301, 6690, 3852, 5521, 5355, 6941, 3867, 5701], 'generators': [889560, 1229808, 126720, 126774, 142584], 'label': '128.850.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.b1', '2.d1.a1'], 'normal_contains': ['8.d1.a1', '8.f1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '64.90', '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': '16.3'}
  • id: 8214891
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.k1.a1', '8.k1.c1'], 'contains': ['32.r1.c1', '32.r2.a1', '32.s1.a1', '32.x1.c1', '32.x2.a1', '32.x2.a2'], 'core': '128.a1.a1', 'coset_action_label': '16T261', 'count': 4, 'diagramx': [8933, -1, 7084, -1, 9023, -1, 7112, -1], 'generators': [1149288, 126774, 142584], 'label': '128.850.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bi1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214892
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.k1.b1', '8.k1.d1'], 'contains': ['32.r1.a1', '32.r2.a1', '32.s1.a1', '32.x1.a1', '32.x2.a1', '32.x2.a2'], 'core': '128.a1.a1', 'coset_action_label': '16T261', 'count': 4, 'diagramx': [8933, -1, 6730, -1, 9023, -1, 6757, -1], 'generators': [126720, 126774, 142584], 'label': '128.850.16.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bi1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214893
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.k1.a1', '8.k1.d1'], 'contains': ['32.r1.d1', '32.r2.b1', '32.s1.a1', '32.x1.d1', '32.x2.b1', '32.x2.b2'], 'core': '128.a1.a1', 'coset_action_label': '16T261', 'count': 4, 'diagramx': [8933, -1, 6966, -1, 9023, -1, 6993, -1], 'generators': [1149289, 126774, 142584], 'label': '128.850.16.bi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bi1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214894
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.k1.b1', '8.k1.c1'], 'contains': ['32.r1.b1', '32.r2.b1', '32.s1.a1', '32.x1.b1', '32.x2.b1', '32.x2.b2'], 'core': '128.a1.a1', 'coset_action_label': '16T261', 'count': 4, 'diagramx': [8933, -1, 8028, -1, 9023, -1, 8059, -1], 'generators': [126721, 126774, 142584], 'label': '128.850.16.bi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bi1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214895
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.c1', '8.z1.a1'], 'contains': ['32.r1.b1', '32.r2.a1', '32.t1.a1', '32.y1.a1', '32.y1.a2', '32.y1.c1', '32.y1.c2'], 'core': '128.a1.a1', 'coset_action_label': '16T273', 'count': 4, 'diagramx': [9152, -1, 8971, -1, 9246, -1, 9006, -1], 'generators': [21024, 142585, 126774], 'label': '128.850.16.bj1.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.bj1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214896
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.d1', '8.z1.a1'], 'contains': ['32.r1.d1', '32.r2.a1', '32.t1.a1', '32.y1.b1', '32.y1.b2', '32.y1.d1', '32.y1.d2'], 'core': '128.a1.a1', 'coset_action_label': '16T273', 'count': 4, 'diagramx': [9152, -1, 6494, -1, 9246, -1, 6520, -1], 'generators': [142585, 126774, 1219734], 'label': '128.850.16.bj1.b1', '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.bj1.b1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214897
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.k1.d1', '8.z1.a1'], 'contains': ['32.r1.a1', '32.r2.b1', '32.t1.a1', '32.y1.a1', '32.y1.a2', '32.y1.b1', '32.y1.b2'], 'core': '128.a1.a1', 'coset_action_label': '16T273', 'count': 4, 'diagramx': [9152, -1, 7202, -1, 9246, -1, 7230, -1], 'generators': [126720, 142585, 126774], 'label': '128.850.16.bj1.c1', '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.bj1.c1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214898
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.c1', '8.z1.a1'], 'contains': ['32.r1.c1', '32.r2.b1', '32.t1.a1', '32.y1.c1', '32.y1.c2', '32.y1.d1', '32.y1.d2'], 'core': '128.a1.a1', 'coset_action_label': '16T273', 'count': 4, 'diagramx': [9152, -1, 7909, -1, 9246, -1, 7941, -1], 'generators': [1149288, 142585, 126774], 'label': '128.850.16.bj1.d1', '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.bj1.d1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214899
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.o1.a1', '16.p1.a1', '16.q1.a1'], 'contains': ['64.a1.a1', '64.a1.b1', '64.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6069, 6055, 4259, 1017, 6131, 6282, 4276, 1050], 'generators': [1229808, 1], 'label': '128.850.32.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.b1.a1', '64.a1.a1', '64.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.6', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214900
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.r1.a1', '16.s1.a1', '16.t1.a1', '16.u1.a1'], 'contains': ['64.b1.a1', '64.c1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5849, 5332, 4141, 1507, 5908, 5531, 4157, 1557], 'generators': [1229808, 126775], 'label': '128.850.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.90', '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: 8214901
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.d1.b1', '8.f1.a1', '8.g1.b1', '8.w1.b1', '8.y1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5301, 6690, 2831, 4479, 5355, 6941, 2842, 4626], 'generators': [889560, 1229808, 126721, 126774, 142584], 'label': '128.850.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.d1', '2.d1.c1'], 'normal_contains': ['8.d1.b1', '8.f1.a1', '8.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214902
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.v1.a1', '16.v1.b1', '16.w1.a1', '16.w1.b1'], 'contains': ['64.b1.a1', '64.d1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5628, 4369, 3505, 2644, 5686, 4533, 3519, 2730], 'generators': [1229808, 126774], 'label': '128.850.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.e1.a1', '16.d1.a1', '16.b1.a1', '16.c1.a1', '16.g1.a1', '16.f1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.90', '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: 8214903
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.h1.b1', '16.h2.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '64.c1.a1', '64.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6729, -1, 5197, -1, 6798, -1, 5217, -1], 'generators': [1, 126774], 'label': '128.850.32.d1.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.d1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214904
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.c1', '16.h1.d1', '16.h2.b1', '16.i1.b1', '16.j1.b1', '16.k1.b1'], 'contains': ['64.a1.b1', '64.c1.a1', '64.d1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6729, -1, 5078, -1, 6798, -1, 5099, -1], 'generators': [126774, 1229809], 'label': '128.850.32.d1.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.d1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214905
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.h2.a1', '16.l1.a1', '16.l2.a1', '16.l2.a2', '16.n1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.e1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 8617, -1, 8801, -1, 8651, -1], 'generators': [126720, 1], 'label': '128.850.32.e1.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': '32.e1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214906
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.h2.a1', '16.l1.b1', '16.l2.a1', '16.l2.a2', '16.n1.a1'], 'contains': ['64.a1.a1', '64.e1.c1', '64.e1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 7673, -1, 8801, -1, 7704, -1], 'generators': [1, 142608], 'label': '128.850.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.e1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214907
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.c1', '16.h2.b1', '16.l1.c1', '16.l2.b1', '16.l2.b2', '16.n1.a1'], 'contains': ['64.a1.b1', '64.e1.a1', '64.e1.d1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 7084, -1, 8801, -1, 7112, -1], 'generators': [126720, 1229809], 'label': '128.850.32.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.e1.c1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214908
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.d1', '16.h2.b1', '16.l1.d1', '16.l2.b1', '16.l2.b2', '16.n1.a1'], 'contains': ['64.a1.b1', '64.e1.b1', '64.e1.c1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 7556, -1, 8801, -1, 7585, -1], 'generators': [142608, 1229809], 'label': '128.850.32.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.e1.d1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214909
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.l1.a1', '16.l1.b1', '16.l2.a1', '16.l2.a2', '16.o1.a1'], 'contains': ['64.a1.a1', '64.f1.a1', '64.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8271, -1, 9443, -1, 8356, -1, 9480, -1], 'generators': [1, 142584], 'label': '128.850.32.f1.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.f1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214910
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.l1.c1', '16.l1.d1', '16.l2.b1', '16.l2.b2', '16.o1.a1'], 'contains': ['64.a1.b1', '64.f1.a1', '64.g1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8271, -1, 8500, -1, 8356, -1, 8533, -1], 'generators': [142584, 1229809], 'label': '128.850.32.f1.b1', '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.f1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214911
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.m1.a1', '16.p1.a1'], 'contains': ['64.a1.a1', '64.h1.a1', '64.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2043, -1, 1704, -1, 2063, -1, 1711, -1], 'generators': [889560, 1], 'label': '128.850.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214912
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.e1.a1', '32.e1.b1', '32.e1.d1', '32.e1.c1', '32.o1.a1', '32.o1.d1', '32.o1.c1', '32.o1.b1', '32.y1.a1', '32.y1.d2', '32.y1.c1', '32.y1.b2', '32.y1.b1', '32.y1.c2', '32.y1.d1', '32.y1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.f1.a1', '8.bb1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1487, 750, 1887, 3618, 1502, 778, 1895, 3737], 'generators': [889560, 1229808, 126774, 142584, 420006], 'label': '128.850.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.c1', '2.d1.a1'], 'normal_contains': ['8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '64.90', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8214913
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.m1.b1', '16.p1.a1'], 'contains': ['64.a1.b1', '64.h1.a1', '64.i1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2043, -1, 1587, -1, 2063, -1, 1593, -1], 'generators': [889560, 1229809], 'label': '128.850.32.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '32.g1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214914
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.r1.a1', '16.v1.a1', '16.x1.a1', '16.y1.a1', '16.y1.a2'], 'contains': ['64.b1.a1', '64.e1.a1', '64.e1.c1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7830, -1, 6141, -1, 7911, -1, 6165, -1], 'generators': [1229808, 126720], 'label': '128.850.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214915
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.r1.a1', '16.v1.b1', '16.x1.b1', '16.y1.a1', '16.y1.a2'], 'contains': ['64.b1.a1', '64.e1.b1', '64.e1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7830, -1, 6494, -1, 7911, -1, 6520, -1], 'generators': [1229808, 126721], 'label': '128.850.32.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.h1.b1', 'projective_image': '64.90', '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': '1.1'}
  • id: 8214916
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.o1.a1', '16.s1.a1', '16.x1.a1', '16.x1.b1', '16.z1.a1', '16.ba1.a1'], 'contains': ['64.b1.a1', '64.f1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6289, -1, 4961, -1, 6353, -1, 4981, -1], 'generators': [1229808, 142584], 'label': '128.850.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.90', '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: 8214917
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.o1.a1', '16.s1.a1', '16.y1.a1', '16.y1.a2', '16.bb1.a1', '16.bc1.a1'], 'contains': ['64.b1.a1', '64.g1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6510, -1, 4843, -1, 6576, -1, 4862, -1], 'generators': [1229808, 142585], 'label': '128.850.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.90', '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: 8214918
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.p1.a1', '16.t1.a1', '16.z1.a1', '16.bb1.a1'], 'contains': ['64.b1.a1', '64.h1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3732, -1, 2044, -1, 3770, -1, 2052, -1], 'generators': [1229808, 889561], 'label': '128.850.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.90', '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: 8214919
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.p1.a1', '16.t1.a1', '16.ba1.a1', '16.bc1.a1', '16.bd1.a1', '16.bd1.b1'], 'contains': ['64.b1.a1', '64.i1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2262, -1, 1822, -1, 2286, -1, 1830, -1], 'generators': [889560, 1229808], 'label': '128.850.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.l1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8214920
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.q1.a1', '16.u1.a1', '16.z1.a1', '16.bc1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4160, -1, 2155, -1, 4202, -1, 2163, -1], 'generators': [2380015, 1229808], 'label': '128.850.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.m1.a1', 'projective_image': '64.90', '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: 8214921
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.q1.a1', '16.u1.a1', '16.ba1.a1', '16.bb1.a1', '16.be1.a1', '16.be1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3128, -1, 1933, -1, 3160, -1, 1941, -1], 'generators': [1229808, 2380014], 'label': '128.850.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.n1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8214922
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.h2.b1', '16.r1.a1', '16.bf1.a1', '16.bf1.a2', '16.bf1.c1', '16.bf1.c2'], 'contains': ['64.c1.a1', '64.e1.a1', '64.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T595', 'count': 4, 'diagramx': [8492, -1, 6966, -1, 8578, -1, 6993, -1], 'generators': [126775, 126720], 'label': '128.850.32.o1.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': '32.o1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214923
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.e1.a1', '32.e1.c1', '32.e1.d1', '32.e1.b1', '32.o1.a1', '32.o1.b1', '32.o1.c1', '32.o1.d1', '32.y1.a1', '32.y1.b2', '32.y1.c1', '32.y1.d2', '32.y1.b1', '32.y1.a2', '32.y1.d1', '32.y1.c2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.f1.a1', '8.bb1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1487, 750, 1389, 2266, 1502, 778, 1395, 2341], 'generators': [889560, 1229808, 420007, 126774, 142584], 'label': '128.850.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.d1', '2.d1.b1'], 'normal_contains': ['8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '64.90', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8214924
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.c1', '16.h2.a1', '16.r1.a1', '16.bf1.b1', '16.bf1.b2', '16.bf1.c1', '16.bf1.c2'], 'contains': ['64.c1.a1', '64.e1.a1', '64.e1.d1'], 'core': '128.a1.a1', 'coset_action_label': '32T595', 'count': 4, 'diagramx': [8492, -1, 6376, -1, 8578, -1, 6401, -1], 'generators': [21024, 126775], 'label': '128.850.32.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.o1.b1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214925
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.d1', '16.h2.a1', '16.r1.a1', '16.bf1.a1', '16.bf1.a2', '16.bf1.d1', '16.bf1.d2'], 'contains': ['64.c1.a1', '64.e1.b1', '64.e1.c1'], 'core': '128.a1.a1', 'coset_action_label': '32T595', 'count': 4, 'diagramx': [8492, -1, 7437, -1, 8578, -1, 7467, -1], 'generators': [126775, 142608], 'label': '128.850.32.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.o1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214926
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.h2.b1', '16.r1.a1', '16.bf1.b1', '16.bf1.b2', '16.bf1.d1', '16.bf1.d2'], 'contains': ['64.c1.a1', '64.e1.c1', '64.e1.d1'], 'core': '128.a1.a1', 'coset_action_label': '32T595', 'count': 4, 'diagramx': [8492, -1, 6612, -1, 8578, -1, 6638, -1], 'generators': [1149288, 126775], 'label': '128.850.32.o1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.o1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214927
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.i1.b1', '16.s1.a1', '16.bf1.a1', '16.bf1.b2', '16.bf1.c1', '16.bf1.d2'], 'contains': ['64.c1.a1', '64.f1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T597', 'count': 4, 'diagramx': [7611, -1, 6848, -1, 7688, -1, 6875, -1], 'generators': [1149265, 142584], 'label': '128.850.32.p1.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.p1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214928
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.i1.b1', '16.s1.a1', '16.bf1.a2', '16.bf1.b1', '16.bf1.c2', '16.bf1.d1'], 'contains': ['64.c1.a1', '64.f1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T597', 'count': 4, 'diagramx': [7611, -1, 6730, -1, 7688, -1, 6757, -1], 'generators': [126775, 142584], 'label': '128.850.32.p1.a2', '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.p1.a2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214929
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.j1.b1', '16.t1.a1'], 'contains': ['64.c1.a1', '64.h1.a1', '64.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1796', 'count': 8, 'diagramx': [2483, -1, 2764, -1, 2508, -1, 2783, -1], 'generators': [889560, 126775], 'label': '128.850.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '32.q1.a1', 'projective_image': '128.850', '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: 8214930
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.h1.c1', '16.v1.a1', '16.bg1.a1', '16.bh1.a1', '16.bi1.b1', '16.bj1.c1'], 'contains': ['64.d1.a1', '64.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T508', 'count': 2, 'diagramx': [7170, -1, 5433, -1, 7243, -1, 5454, -1], 'generators': [126720, 126774], 'label': '128.850.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.a1', 'projective_image': '128.850', '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': '2.1'}
  • id: 8214931
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.h1.d1', '16.v1.b1', '16.bg1.b1', '16.bh1.b1', '16.bi1.d1', '16.bj1.a1'], 'contains': ['64.d1.a1', '64.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': '32T508', 'count': 2, 'diagramx': [7170, -1, 5669, -1, 7243, -1, 5691, -1], 'generators': [126721, 126774], 'label': '128.850.32.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214932
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.h1.d1', '16.v1.a1', '16.bg1.c1', '16.bh1.c1', '16.bi1.a1', '16.bj1.d1'], 'contains': ['64.d1.a1', '64.e1.c1'], 'core': '128.a1.a1', 'coset_action_label': '32T508', 'count': 2, 'diagramx': [7170, -1, 5550, -1, 7243, -1, 5573, -1], 'generators': [1149288, 126774], 'label': '128.850.32.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214933
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '16.h1.c1', '16.v1.b1', '16.bg1.d1', '16.bh1.d1', '16.bi1.c1', '16.bj1.b1'], 'contains': ['64.d1.a1', '64.e1.d1'], 'core': '128.a1.a1', 'coset_action_label': '32T508', 'count': 2, 'diagramx': [7170, -1, 5314, -1, 7243, -1, 5336, -1], 'generators': [1149289, 126774], 'label': '128.850.32.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214934
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.e1.a1', '32.e1.b1', '32.e1.d1', '32.e1.c1', '32.o1.a1', '32.o1.d1', '32.o1.c1', '32.o1.b1', '32.y1.a1', '32.y1.d2', '32.y1.c1', '32.y1.b2', '32.y1.b1', '32.y1.c2', '32.y1.d1', '32.y1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.f1.a1', '8.bc1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2389, 2259, 1724, 1591, 2413, 2344, 1731, 1643], 'generators': [889560, 1229808, 126774, 586926, 142584], 'label': '128.850.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.d1', '2.d1.a1'], 'normal_contains': ['8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '64.90', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8214935
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h2.a1', '16.h2.b1', '16.v1.a1', '16.bi1.a1', '16.bi1.b1', '16.bj1.a1', '16.bj1.b1'], 'contains': ['64.d1.a1', '64.e1.a1', '64.e1.c1'], 'core': '128.a1.a1', 'coset_action_label': '32T602', 'count': 4, 'diagramx': [8051, -1, 6022, -1, 8133, -1, 6046, -1], 'generators': [21024, 126774], 'label': '128.850.32.r2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.r2.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214936
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.r2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h2.a1', '16.h2.b1', '16.v1.b1', '16.bi1.c1', '16.bi1.d1', '16.bj1.c1', '16.bj1.d1'], 'contains': ['64.d1.a1', '64.e1.b1', '64.e1.d1'], 'core': '128.a1.a1', 'coset_action_label': '32T602', 'count': 4, 'diagramx': [8051, -1, 6258, -1, 8133, -1, 6283, -1], 'generators': [126774, 21025], 'label': '128.850.32.r2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.r2.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214937
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.i1.a1', '16.i1.b1', '16.bi1.a1', '16.bi1.b1', '16.bi1.c1', '16.bi1.d1'], 'contains': ['64.d1.a1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T601', 'count': 4, 'diagramx': [6950, -1, 5786, -1, 7021, -1, 5809, -1], 'generators': [126774, 142584], 'label': '128.850.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.s1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214938
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a1', '16.i1.b1', '16.bj1.a1', '16.bj1.b1', '16.bj1.c1', '16.bj1.d1'], 'contains': ['64.d1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T633', 'count': 4, 'diagramx': [7391, -1, 5905, -1, 7466, -1, 5928, -1], 'generators': [142585, 126774], 'label': '128.850.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.t1.a1', 'projective_image': '128.850', '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': '1.1'}
  • id: 8214939
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.j1.a1', '16.j1.b1', '16.bg1.a1', '16.bg1.b1', '16.bg1.c1', '16.bg1.d1'], 'contains': ['64.d1.a1', '64.h1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T506', 'count': 4, 'diagramx': [4366, -1, 3956, -1, 4410, -1, 3971, -1], 'generators': [889561, 126774], 'label': '128.850.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.u1.a1', 'projective_image': '128.850', '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: 8214940
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.j1.a1', '16.j1.b1', '16.bh1.a1', '16.bh1.b1', '16.bh1.c1', '16.bh1.d1'], 'contains': ['64.d1.a1', '64.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T657', 'count': 4, 'diagramx': [3952, -1, 3734, -1, 3993, -1, 3749, -1], 'generators': [889560, 126774], 'label': '128.850.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.v1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214941
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.k1.b1', '16.w1.a1', '16.bg1.b1', '16.bg1.d1', '16.bh1.a1', '16.bh1.c1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T507', 'count': 4, 'diagramx': [5411, -1, 4617, -1, 5466, -1, 4635, -1], 'generators': [970920, 126774], 'label': '128.850.32.w1.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.w1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214942
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.k1.b1', '16.w1.b1', '16.bg1.a1', '16.bg1.c1', '16.bh1.b1', '16.bh1.d1'], 'contains': ['64.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T507', 'count': 4, 'diagramx': [5411, -1, 4370, -1, 5466, -1, 4387, -1], 'generators': [970921, 126774], 'label': '128.850.32.w1.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.w1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8214943
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.l1.c1', '16.x1.a1', '16.bf1.c1', '16.bf1.c2', '16.bi1.b1'], 'contains': ['64.e1.a1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T599', 'count': 4, 'diagramx': [9152, -1, 8381, -1, 9246, -1, 8414, -1], 'generators': [126720, 142584], 'label': '128.850.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214944
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.l1.d1', '16.x1.b1', '16.bf1.a1', '16.bf1.a2', '16.bi1.d1'], 'contains': ['64.e1.b1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T599', 'count': 4, 'diagramx': [9152, -1, 9679, -1, 9246, -1, 9717, -1], 'generators': [126721, 142584], 'label': '128.850.32.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214945
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.e1.a1', '32.e1.c1', '32.e1.b1', '32.e1.d1', '32.o1.a1', '32.o1.b1', '32.o1.d1', '32.o1.c1', '32.y1.a2', '32.y1.b1', '32.y1.d1', '32.y1.c2', '32.y1.c1', '32.y1.d2', '32.y1.b2', '32.y1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.f1.a1', '8.bc1.b1'], 'core': '4.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2389, 2259, 2049, 2942, 2413, 2344, 2058, 3039], 'generators': [889560, 1229808, 586927, 126774, 142584], 'label': '128.850.4.g1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.c1', '2.d1.b1'], 'normal_contains': ['8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.b1', 'projective_image': '64.90', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8214946
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.l1.d1', '16.x1.a1', '16.bf1.d1', '16.bf1.d2', '16.bi1.a1'], 'contains': ['64.e1.c1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T599', 'count': 4, 'diagramx': [9152, -1, 8971, -1, 9246, -1, 9006, -1], 'generators': [1149288, 142584], 'label': '128.850.32.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214947
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.l1.c1', '16.x1.b1', '16.bf1.b1', '16.bf1.b2', '16.bi1.c1'], 'contains': ['64.e1.d1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T599', 'count': 4, 'diagramx': [9152, -1, 7909, -1, 9246, -1, 7941, -1], 'generators': [1149289, 142584], 'label': '128.850.32.x1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214948
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l2.a1', '16.l2.b2', '16.x1.a1', '16.bf1.a1', '16.bf1.b1', '16.bi1.a1', '16.bi1.b1'], 'contains': ['64.e1.a1', '64.e1.c1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T598', 'count': 4, 'diagramx': [8933, -1, 7792, -1, 9023, -1, 7822, -1], 'generators': [1229784, 142584], 'label': '128.850.32.x2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x2.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214949
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l2.a2', '16.l2.b1', '16.x1.a1', '16.bf1.a2', '16.bf1.b2', '16.bi1.a1', '16.bi1.b1'], 'contains': ['64.e1.a1', '64.e1.c1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T598', 'count': 4, 'diagramx': [8933, -1, 8028, -1, 9023, -1, 8059, -1], 'generators': [142584, 54], 'label': '128.850.32.x2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x2.a2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214950
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l2.a1', '16.l2.b1', '16.x1.b1', '16.bf1.c1', '16.bf1.d1', '16.bi1.c1', '16.bi1.d1'], 'contains': ['64.e1.b1', '64.e1.d1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T598', 'count': 4, 'diagramx': [8933, -1, 8853, -1, 9023, -1, 8888, -1], 'generators': [1229785, 142584], 'label': '128.850.32.x2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x2.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214951
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.x2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l2.a2', '16.l2.b2', '16.x1.b1', '16.bf1.c2', '16.bf1.d2', '16.bi1.c1', '16.bi1.d1'], 'contains': ['64.e1.b1', '64.e1.d1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T598', 'count': 4, 'diagramx': [8933, -1, 8735, -1, 9023, -1, 8770, -1], 'generators': [55, 142584], 'label': '128.850.32.x2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.x2.b2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x2.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214952
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.l2.b1', '16.y1.a1', '16.bf1.a1', '16.bf1.c2', '16.bj1.a1', '16.bj1.c1'], 'contains': ['64.e1.a1', '64.e1.b1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 9207, -1, 9468, -1, 9243, -1], 'generators': [126720, 142585], 'label': '128.850.32.y1.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': '32.y1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214953
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.l2.b2', '16.y1.a2', '16.bf1.a2', '16.bf1.c1', '16.bj1.a1', '16.bj1.c1'], 'contains': ['64.e1.a1', '64.e1.b1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 9089, -1, 9468, -1, 9125, -1], 'generators': [21024, 142585], 'label': '128.850.32.y1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.a2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214954
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.c1', '16.l2.a1', '16.y1.a2', '16.bf1.b2', '16.bf1.c2', '16.bj1.b1', '16.bj1.c1'], 'contains': ['64.e1.a1', '64.e1.d1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 7202, -1, 9468, -1, 7230, -1], 'generators': [1134000, 142585], 'label': '128.850.32.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214955
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.c1', '16.l2.a2', '16.y1.a1', '16.bf1.b1', '16.bf1.c1', '16.bj1.b1', '16.bj1.c1'], 'contains': ['64.e1.a1', '64.e1.d1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 7320, -1, 9468, -1, 7349, -1], 'generators': [142585, 54], 'label': '128.850.32.y1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.b2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214956
    {'ambient': '128.850', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29080', 'aut_weyl_index': 4, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1', '4.h1.a1', '4.i1.a1', '4.l1.a1', '4.m1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6029, 6249, 3727, 6603, 6090, 6374, 3741, 6819], 'generators': [889560, 1229808, 126720, 1, 126774, 142584], 'label': '128.850.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.e1.b1', '4.e1.a1', '4.d1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214957
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.j1.b1', '8.j1.c1', '8.j1.d1', '8.l1.a1', '8.m1.a1', '8.v1.a1', '8.v1.b1', '8.w1.a1', '8.w1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4855, -1, 4882, -1, 4904, -1, 4911, -1], 'generators': [889560, 1229808, 126720, 1, 126774], 'label': '128.850.4.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': '32.6', '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: 8214958
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.d1', '16.l2.a1', '16.y1.a1', '16.bf1.a2', '16.bf1.d2', '16.bj1.a1', '16.bj1.d1'], 'contains': ['64.e1.b1', '64.e1.c1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 9325, -1, 9468, -1, 9362, -1], 'generators': [1229784, 142585], 'label': '128.850.32.y1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214959
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.d1', '16.l2.a2', '16.y1.a2', '16.bf1.a1', '16.bf1.d1', '16.bj1.a1', '16.bj1.d1'], 'contains': ['64.e1.b1', '64.e1.c1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 9561, -1, 9468, -1, 9598, -1], 'generators': [142585, 142608], 'label': '128.850.32.y1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.c2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214960
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.l2.b1', '16.y1.a2', '16.bf1.b1', '16.bf1.d2', '16.bj1.b1', '16.bj1.d1'], 'contains': ['64.e1.c1', '64.e1.d1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 8145, -1, 9468, -1, 8178, -1], 'generators': [142585, 1219734], 'label': '128.850.32.y1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214961
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.l2.b2', '16.y1.a1', '16.bf1.b2', '16.bf1.d1', '16.bj1.b1', '16.bj1.d1'], 'contains': ['64.e1.c1', '64.e1.d1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T596', 'count': 4, 'diagramx': [9372, -1, 8264, -1, 9468, -1, 8296, -1], 'generators': [1149288, 142585], 'label': '128.850.32.y1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.y1.d2', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214962
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.m1.b1', '16.bd1.a1'], 'contains': ['64.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1130', 'count': 8, 'diagramx': [853, -1, 577, -1, 861, -1, 628, -1], 'generators': [889560, 420006], 'label': '128.850.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.z1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214963
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.m1.b1', '16.bd1.b1'], 'contains': ['64.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': '32T1130', 'count': 8, 'diagramx': [853, -1, 379, -1, 861, -1, 380, -1], 'generators': [889560, 420007], 'label': '128.850.32.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '32.z1.b1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214964
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': ['2.d1.a1', '2.d1.b1', '2.d1.d1', '2.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '32.e1.b1', '32.f1.a1', '32.g1.a1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6923, 6011, 7098, 646, 6994, 6254, 7126, 667], 'generators': [1], 'label': '128.850.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.32', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.32', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214965
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': ['2.d1.a1', '2.d1.b1', '2.d1.d1', '2.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.b1', '32.e1.c1', '32.e1.d1', '32.f1.b1', '32.g1.b1'], 'contains': ['128.a1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6923, 6011, 6995, 1076, 6994, 6254, 7022, 1112], 'generators': [1229809], 'label': '128.850.64.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.b1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.b1', 'projective_image': '64.32', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.32', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214966
    {'ambient': '128.850', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.h1.a1', '32.h1.b1', '32.i1.a1', '32.j1.a1', '32.k1.a1', '32.l1.a1', '32.m1.a1', '32.n1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5849, 5357, 4200, 1507, 5908, 5577, 4217, 1557], 'generators': [1229808], 'label': '128.850.64.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.90', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214967
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.d1.a1', '32.d1.b1', '32.o1.a1', '32.o1.b1', '32.o1.c1', '32.o1.d1', '32.p1.a1', '32.p1.a2', '32.q1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6729, -1, 6612, -1, 6798, -1, 6638, -1], 'generators': [126775], 'label': '128.850.64.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': '128.850', '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: 8214968
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.l1.a1', '8.m1.a1', '8.x1.a1', '8.x1.b1', '8.y1.a1', '8.y1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5787, -1, 3091, -1, 5846, -1, 3103, -1], 'generators': [1229808, 126720, 1, 2380014, 126774], 'label': '128.850.4.i1.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.i1.a1', 'projective_image': '32.6', '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': '8.5'}
  • id: 8214969
    {'ambient': '128.850', 'aut_centralizer_order': 512, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.d1.a1', '32.d1.b1', '32.r1.a1', '32.r1.b1', '32.r1.c1', '32.r1.d1', '32.r2.a1', '32.r2.b1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.v1.a1', '32.w1.a1', '32.w1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6536, -1, 5374, -1, 6603, -1, 5395, -1], 'generators': [126774], 'label': '128.850.64.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': '128.850', '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: 8214970
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.e1.c1', '32.h1.a1', '32.o1.a1', '32.o1.b1', '32.r1.a1', '32.r2.a1', '32.x1.a1', '32.x2.a1', '32.x2.a2', '32.y1.a1', '32.y1.a2', '32.y1.b1', '32.y1.b2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7306, -1, 8578, -1, 7334, -1], 'generators': [126720], 'label': '128.850.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.850', '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: 8214971
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.e1.d1', '32.h1.b1', '32.o1.a1', '32.o1.c1', '32.r1.b1', '32.r2.b1', '32.x1.b1', '32.x2.b1', '32.x2.b2', '32.y1.a1', '32.y1.a2', '32.y1.c1', '32.y1.c2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 8617, -1, 8578, -1, 8651, -1], 'generators': [126721], 'label': '128.850.64.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.e1.b1', 'projective_image': '128.850', '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: 8214972
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '32.e1.d1', '32.h1.a1', '32.o1.c1', '32.o1.d1', '32.r1.c1', '32.r2.a1', '32.x1.c1', '32.x2.a1', '32.x2.a2', '32.y1.c1', '32.y1.c2', '32.y1.d1', '32.y1.d2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7673, -1, 8578, -1, 7704, -1], 'generators': [142608], 'label': '128.850.64.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.e1.c1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214973
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '32.e1.c1', '32.h1.b1', '32.o1.b1', '32.o1.d1', '32.r1.d1', '32.r2.b1', '32.x1.d1', '32.x2.b1', '32.x2.b2', '32.y1.b1', '32.y1.b2', '32.y1.d1', '32.y1.d2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7202, -1, 8578, -1, 7230, -1], 'generators': [142609], 'label': '128.850.64.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.e1.d1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214974
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.f1.b1', '32.i1.a1', '32.p1.a1', '32.p1.a2', '32.s1.a1', '32.x1.a1', '32.x1.b1', '32.x1.c1', '32.x1.d1', '32.x2.a1', '32.x2.a2', '32.x2.b1', '32.x2.b2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7611, -1, 8028, -1, 7688, -1, 8059, -1], 'generators': [142584], 'label': '128.850.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.850', '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: 8214975
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.f1.b1', '32.j1.a1', '32.p1.a1', '32.p1.a2', '32.t1.a1', '32.y1.a1', '32.y1.a2', '32.y1.b1', '32.y1.b2', '32.y1.c1', '32.y1.c2', '32.y1.d1', '32.y1.d2'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7404, -1, 8145, -1, 7479, -1, 8178, -1], 'generators': [142585], 'label': '128.850.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.850', '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: 8214976
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.g1.b1', '32.k1.a1', '32.q1.a1', '32.u1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3732, -1, 2401, -1, 3770, -1, 2422, -1], 'generators': [889561], 'label': '128.850.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214977
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.g1.b1', '32.l1.a1', '32.q1.a1', '32.v1.a1', '32.z1.a1', '32.z1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2373, -1, 1764, -1, 2397, -1, 1770, -1], 'generators': [889560], 'label': '128.850.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '64.i1.a1', 'projective_image': '128.850', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8214978
    {'ambient': '128.850', '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.a1.b1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.e1.b1', '64.e1.c1', '64.e1.d1', '64.f1.a1', '64.g1.a1', '64.h1.a1', '64.i1.a1'], 'contains': [], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6729, 5685, 7098, 1076, 6798, 5906, 7126, 1112], 'generators': [], 'label': '128.850.128.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.b1.a1', '64.a1.a1', '64.a1.b1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.850', '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: 8214979
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.p1.a1', '8.t1.a1', '8.bb1.a1', '8.bb1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [778, -1, 541, -1, 785, -1, 543, -1], 'generators': [889560, 1229808, 1, 126774, 420006], 'label': '128.850.4.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': '32.6', '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': '8.3'}
  • id: 8214980
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.264', 'aut_weyl_index': 16, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.q1.a1', '8.u1.a1', '8.bc1.a1', '8.bc1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1938, -1, 1129, -1, 1958, -1, 1131, -1], 'generators': [1229808, 1, 2380014, 126774, 586926], 'label': '128.850.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.k1.a1', 'projective_image': '32.6', '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': '8.3'}
  • id: 8214981
    {'ambient': '128.850', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.h1.a1', '8.v1.a1', '8.v1.b1', '8.y1.a1', '8.y1.b1', '8.z1.a1', '8.ba1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6273, -1, 4102, -1, 6337, -1, 4118, -1], 'generators': [1229808, 126720, 142585, 2380014, 126774], 'label': '128.850.4.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8214982
    {'ambient': '128.850', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.i1.a1', '8.w1.a1', '8.w1.b1', '8.x1.a1', '8.x1.b1', '8.z1.a1', '8.ba1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7208, -1, 3601, -1, 7281, -1, 3616, -1], 'generators': [889560, 1229808, 126720, 142585, 126774], 'label': '128.850.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8214983
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.h1.a1', '8.bc1.a1', '8.bc1.b1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2771, -1, 1552, -1, 2799, -1, 1558, -1], 'generators': [1229808, 142585, 2380014, 126774, 1548246], 'label': '128.850.4.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.n1.a1', 'projective_image': '64.90', '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': '16.3'}
  • id: 8214984
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.i1.a1', '8.bb1.a1', '8.bb1.b1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1183, -1, 848, -1, 1195, -1, 825, -1], 'generators': [889560, 1229808, 142585, 126774, 1674126], 'label': '128.850.4.o1.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.o1.a1', 'projective_image': '64.90', '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': '16.3'}
  • id: 8214985
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.i1.a1', '16.i1.b1', '16.o1.a1', '16.s1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7611, 7361, 5858, 4456, 7688, 7637, 5882, 4633], 'generators': [1229808, 1, 126774, 142584], 'label': '128.850.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8214986
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.j1.a1', '16.j1.b1', '16.p1.a1', '16.t1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2019, 1615, 2208, 1496, 2039, 1676, 2217, 1544], 'generators': [889560, 1229808, 1, 126774], 'label': '128.850.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.6', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8214987
    {'ambient': '128.850', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.e1.a1', '64.e1.c1', '64.e1.b1', '64.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.f1.a1', '4.f1.b1', '4.j1.a1', '4.o1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1487, 750, 1282, 1633, 1502, 778, 1287, 1686], 'generators': [889560, 1229808, 1, 126774, 142584, 420006], 'label': '128.850.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.f1.b1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.6', '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': '32.6'}
  • id: 8214988
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '16.q1.a1', '16.u1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3444, 5093, 1839, 778, 3480, 5284, 1845, 803], 'generators': [1229808, 1, 2380014, 126774], 'label': '128.850.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '32.6', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8214989
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.v1.a1', '16.x1.a1', '16.bi1.a1', '16.bi1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8051, 9092, 6323, 7667, 8133, 9432, 6348, 7931], 'generators': [1229808, 126720, 126774, 142584], 'label': '128.850.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.e1.a1', '4.d1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8214990
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.b1', '4.e1.b1'], 'contains': ['16.b1.a1', '16.v1.b1', '16.x1.b1', '16.bi1.c1', '16.bi1.d1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8051, 9092, 6790, 7165, 8133, 9432, 6904, 7424], 'generators': [1229808, 126721, 126774, 142584], 'label': '128.850.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.a1.a1', '4.e1.b1', '4.d1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8214991
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '16.z1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4576, 6391, 2760, 5132, 4622, 6630, 2771, 5330], 'generators': [1229808, 889561, 126774, 142584], 'label': '128.850.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.b1', '4.d1.a1'], 'normal_contains': ['16.d1.a1', '16.b1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214992
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.f1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.a1', '4.e1.b1', '4.f1.a1', '4.f1.b1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '16.ba1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2314, 644, 2049, 3792, 2337, 668, 2058, 3916], 'generators': [889560, 1229808, 126774, 142584], 'label': '128.850.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1', '4.e1.b1', '4.e1.a1', '4.f1.b1', '4.f1.a1', '4.g1.a1', '4.g1.b1'], 'normal_contains': ['16.e1.a1', '16.b1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214993
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.b1', '4.e1.a1'], 'contains': ['16.b1.a1', '16.w1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7044, 8226, 4113, 6567, 7116, 8534, 4128, 6813], 'generators': [1229808, 970920, 126774, 142584], 'label': '128.850.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.e1.a1', '4.d1.b1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214994
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': ['16.m1.a1', '16.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.e1.b1'], 'contains': ['16.b1.a1', '16.w1.b1'], 'core': '8.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7044, 8226, 3265, 5886, 7116, 8534, 3278, 6109], 'generators': [970921, 1229808, 126774, 142584], 'label': '128.850.8.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.b1', 'normal_contained_in': ['4.c1.a1', '4.e1.b1', '4.d1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.b1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214995
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.n1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '16.bb1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3839, 2587, 2564, 2972, 3879, 2683, 2573, 3070], 'generators': [1229808, 142585, 2380014, 126774], 'label': '128.850.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.d1.a1', '16.c1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214996
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.m1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.f1.a1', '16.bc1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4208, 3795, 2366, 2153, 4250, 3938, 2375, 2224], 'generators': [889560, 1229808, 142585, 126774], 'label': '128.850.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.e1.a1', '16.c1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 8214997
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.k1.a1', '16.bg1.a1', '16.bg1.b1', '16.bh1.a1', '16.bh1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4943, -1, 5503, -1, 4994, -1, 5525, -1], 'generators': [889560, 126720, 1, 126774], 'label': '128.850.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.j1.a1', 'projective_image': '64.32', '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': '4.2'}
  • id: 8214998
    {'ambient': '128.850', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['64.e1.a1', '64.e1.c1', '64.e1.b1', '64.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.g1.a1', '4.g1.b1', '4.k1.a1', '4.n1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2771, 3769, 1552, 509, 2799, 3910, 1558, 525], 'generators': [889560, 1229808, 1, 126774, 586926, 142584], 'label': '128.850.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.g1.a1', '4.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '32.6', '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': '32.6'}
  • id: 8214999
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.b1', '16.j1.a1', '16.k1.a1', '16.bg1.c1', '16.bg1.d1', '16.bh1.c1', '16.bh1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4943, -1, 5306, -1, 4994, -1, 5327, -1], 'generators': [889560, 1149288, 1, 126774], 'label': '128.850.8.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.j1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8215000
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.c1', '16.j1.b1', '16.k1.b1', '16.bg1.a1', '16.bg1.d1', '16.bh1.a1', '16.bh1.d1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4943, -1, 5109, -1, 4994, -1, 5129, -1], 'generators': [889560, 126720, 126774, 1229809], 'label': '128.850.8.j1.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': '8.j1.c1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8215001
    {'ambient': '128.850', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.d1', '16.j1.b1', '16.k1.b1', '16.bg1.b1', '16.bg1.c1', '16.bh1.b1', '16.bh1.c1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4943, -1, 5700, -1, 4994, -1, 5723, -1], 'generators': [889560, 1149288, 126774, 1229809], 'label': '128.850.8.j1.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': '8.j1.d1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 8215002
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.b1', '16.h2.a1', '16.i1.a1', '16.l1.b1', '16.l2.a1', '16.l2.a2', '16.bf1.b1', '16.bf1.b2', '16.bf1.d1', '16.bf1.d2', '16.bi1.a1', '16.bi1.c1', '16.bj1.b1', '16.bj1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8933, -1, 7320, -1, 9023, -1, 7349, -1], 'generators': [1149288, 1, 126774, 142584], 'label': '128.850.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '64.32', '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': '1.1'}
  • id: 8215003
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.a1', '16.h2.a1', '16.i1.a1', '16.l1.a1', '16.l2.a1', '16.l2.a2', '16.bf1.a1', '16.bf1.a2', '16.bf1.c1', '16.bf1.c2', '16.bi1.b1', '16.bi1.d1', '16.bj1.a1', '16.bj1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8933, -1, 8204, -1, 9023, -1, 8237, -1], 'generators': [126720, 1, 126774, 142584], 'label': '128.850.8.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.k1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215004
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.d1', '16.h2.b1', '16.i1.b1', '16.l1.d1', '16.l2.b1', '16.l2.b2', '16.bf1.a1', '16.bf1.a2', '16.bf1.d1', '16.bf1.d2', '16.bi1.a1', '16.bi1.d1', '16.bj1.a1', '16.bj1.d1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8933, -1, 8086, -1, 9023, -1, 8118, -1], 'generators': [1149288, 126774, 142584, 1229809], 'label': '128.850.8.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.k1.c1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215005
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.c1', '16.h2.b1', '16.i1.b1', '16.l1.c1', '16.l2.b1', '16.l2.b2', '16.bf1.b1', '16.bf1.b2', '16.bf1.c1', '16.bf1.c2', '16.bi1.b1', '16.bi1.c1', '16.bj1.b1', '16.bj1.c1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8933, -1, 7202, -1, 9023, -1, 7230, -1], 'generators': [126720, 126774, 142584, 1229809], 'label': '128.850.8.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.k1.d1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215006
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.h1.b1', '16.h1.c1', '16.h1.d1', '16.h2.a1', '16.h2.b1', '16.n1.a1', '16.r1.a1', '16.v1.a1', '16.v1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 5977, -1, 7911, -1, 6000, -1], 'generators': [1229808, 126720, 1, 126774], 'label': '128.850.8.l1.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.l1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8215007
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.k1.b1', '16.w1.a1', '16.w1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6378, -1, 4503, -1, 6443, -1, 4521, -1], 'generators': [1229808, 970920, 1, 126774], 'label': '128.850.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.6', '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': '4.2'}
  • id: 8215008
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.l1.a1', '16.l1.b1', '16.l1.c1', '16.l1.d1', '16.l2.a1', '16.l2.a2', '16.l2.b1', '16.l2.b2', '16.n1.a1', '16.o1.a1', '16.x1.a1', '16.x1.b1', '16.y1.a1', '16.y1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8712, -1, 8500, -1, 8801, -1, 8533, -1], 'generators': [1229808, 126720, 1, 142584], 'label': '128.850.8.n1.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': '8.n1.a1', 'projective_image': '32.6', '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': '1.1'}
  • id: 8215009
    {'ambient': '128.850', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['64.a1.a1', '64.a1.b1', '64.c1.a1', '64.g1.a1', '64.h1.a1', '64.e1.b1', '64.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2311, 2259, 2018, 3570, 2335, 2344, 2026, 3687], 'generators': [889560, 1229808, 126720, 126774, 142584, 420006], 'label': '128.850.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '64.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8215010
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.o1.a1', '16.p1.a1', '16.q1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3050, -1, 1430, -1, 3081, -1, 1435, -1], 'generators': [889560, 1229808, 1, 142584], 'label': '128.850.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.6', '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': '4.2'}
  • id: 8215011
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.m1.a1', '16.m1.b1', '16.p1.a1', '16.bd1.a1', '16.bd1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [187, -1, 102, -1, 189, -1, 103, -1], 'generators': [889560, 1229808, 1, 420006], 'label': '128.850.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8215012
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.q1.a1', '16.be1.a1', '16.be1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1457, -1, 801, -1, 1472, -1, 804, -1], 'generators': [1229808, 1, 2380014, 1548246], 'label': '128.850.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '8.q1.a1', 'projective_image': '32.6', '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': '2.1'}
  • id: 8215013
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.r1.a1', '16.s1.a1', '16.x1.a1', '16.x1.b1', '16.y1.a1', '16.y1.a2', '16.bf1.a1', '16.bf1.a2', '16.bf1.b1', '16.bf1.b2', '16.bf1.c1', '16.bf1.c2', '16.bf1.d1', '16.bf1.d2'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7792, -1, 8578, -1, 7822, -1], 'generators': [1229808, 126775, 126720, 142584], 'label': '128.850.8.r1.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': '8.r1.a1', 'projective_image': '64.90', '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': '1.1'}
  • id: 8215014
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 128, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.s1.a1', '16.t1.a1', '16.u1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2682, -1, 1627, -1, 2709, -1, 1633, -1], 'generators': [889560, 1229808, 126775, 142584], 'label': '128.850.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.s1.a1', 'projective_image': '64.90', '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: 8215015
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.t1.a1', '16.bd1.a1', '16.bd1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [549, -1, 297, -1, 555, -1, 297, -1], 'generators': [1229808, 126775, 970974, 1674126], 'label': '128.850.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.t1.a1', 'projective_image': '64.90', '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: 8215016
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.u1.a1', '16.be1.a1', '16.be1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1140, -1, 971, -1, 1152, -1, 975, -1], 'generators': [2420280, 1229808, 126775, 586926], 'label': '128.850.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '8.u1.a1', 'projective_image': '64.90', '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: 8215017
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.v1.a1', '16.w1.b1', '16.bg1.a1', '16.bg1.c1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5983, -1, 4292, -1, 6044, -1, 4309, -1], 'generators': [1229808, 126720, 889561, 126774], 'label': '128.850.8.v1.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.v1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8215018
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.d1.a1', '16.v1.b1', '16.w1.a1', '16.bg1.b1', '16.bg1.d1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5983, -1, 4912, -1, 6044, -1, 4931, -1], 'generators': [1229808, 970920, 889561, 126774], 'label': '128.850.8.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.v1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8215019
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.m1.a1'], 'contains': ['16.e1.a1', '16.v1.a1', '16.w1.a1', '16.bh1.a1', '16.bh1.c1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5312, -1, 4715, -1, 5366, -1, 4734, -1], 'generators': [889560, 1229808, 126720, 126774], 'label': '128.850.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.w1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8215020
    {'ambient': '128.850', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['64.a1.a1', '64.a1.b1', '64.c1.a1', '64.g1.a1', '64.h1.a1', '64.e1.b1', '64.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.b1', '4.g1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2311, 2259, 2239, 4486, 2335, 2344, 2247, 4633], 'generators': [889560, 1229808, 126720, 420007, 126774, 142584], 'label': '128.850.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.b1', '4.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '64.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8215021
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.h1.a1', '4.m1.a1'], 'contains': ['16.e1.a1', '16.v1.b1', '16.w1.b1', '16.bh1.b1', '16.bh1.d1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5312, -1, 3932, -1, 5366, -1, 3948, -1], 'generators': [889560, 1229808, 126721, 126774], 'label': '128.850.8.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.w1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8215022
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.f1.a1', '16.v1.a1', '16.w1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6740, -1, 3102, -1, 6809, -1, 3115, -1], 'generators': [2380015, 1229808, 126720, 126774], 'label': '128.850.8.x1.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.x1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8215023
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.f1.a1', '16.v1.b1', '16.w1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6740, -1, 3590, -1, 6809, -1, 3604, -1], 'generators': [2380015, 1229808, 970920, 126774], 'label': '128.850.8.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.x1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8215024
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.l1.a1'], 'contains': ['16.g1.a1', '16.v1.a1', '16.w1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5648, -1, 3427, -1, 5705, -1, 3441, -1], 'generators': [1229808, 126720, 2380014, 126774], 'label': '128.850.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.y1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8215025
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.i1.a1', '4.l1.a1'], 'contains': ['16.g1.a1', '16.v1.b1', '16.w1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5648, -1, 2940, -1, 5705, -1, 2952, -1], 'generators': [1229808, 126721, 2380014, 126774], 'label': '128.850.8.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.y1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 8215026
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.c1.a1', '16.v1.a1', '16.v1.b1', '16.y1.a1', '16.y1.a2', '16.bj1.a1', '16.bj1.b1', '16.bj1.c1', '16.bj1.d1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8271, -1, 6582, -1, 8356, -1, 6608, -1], 'generators': [1229808, 126720, 142585, 126774], 'label': '128.850.8.z1.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.z1.a1', 'projective_image': '64.90', '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': '2.1'}
  • id: 8215027
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.c1.a1', '16.w1.a1', '16.w1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7348, -1, 3753, -1, 7422, -1, 3767, -1], 'generators': [1229808, 970920, 142585, 126774], 'label': '128.850.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ba1.a1', 'projective_image': '64.90', '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': '8.5'}
  • id: 8215028
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.j1.a1', '4.o1.a1'], 'contains': ['16.e1.a1', '16.bd1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [853, -1, 622, -1, 861, -1, 624, -1], 'generators': [889560, 1229808, 126774, 420006], 'label': '128.850.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bb1.a1', 'projective_image': '64.90', '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: 8215029
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '4.j1.a1', '4.o1.a1'], 'contains': ['16.e1.a1', '16.bd1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [853, -1, 459, -1, 861, -1, 461, -1], 'generators': [889560, 1229808, 420007, 126774], 'label': '128.850.8.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bb1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215030
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.be1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1774, -1, 1115, -1, 1792, -1, 1119, -1], 'generators': [1229808, 2380014, 126774, 586926], 'label': '128.850.8.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': '64.90', '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: 8215031
    {'ambient': '128.850', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['64.a1.a1', '64.a1.b1', '64.c1.a1', '64.g1.a1', '64.h1.a1', '64.e1.a1', '64.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.b1', '4.f1.a1', '4.g1.b1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2311, 2259, 2458, 5401, 2335, 2344, 2468, 5578], 'generators': [889560, 1229808, 126721, 126774, 142584, 420006], 'label': '128.850.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.b1', '4.f1.a1', '4.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '64.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8215032
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '4.k1.a1', '4.n1.a1'], 'contains': ['16.g1.a1', '16.be1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1774, -1, 1258, -1, 1792, -1, 1264, -1], 'generators': [1229808, 586927, 2380014, 126774], 'label': '128.850.8.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.bc1.b1', 'projective_image': '64.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215033
    {'ambient': '128.850', 'aut_centralizer_order': 256, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6069, 6055, 3505, 1017, 6131, 6282, 3519, 1050], 'generators': [1229808, 1, 126774], 'label': '128.850.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1', '8.a1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215034
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.g1.b1'], 'contains': ['32.c1.a1', '32.i1.a1', '32.s1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6289, 7070, 3844, 5508, 6353, 7335, 3860, 5720], 'generators': [1229808, 126774, 142584], 'label': '128.850.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.b1', '8.d1.a1', '8.f1.a1', '8.e1.a1', '8.g1.a1', '8.g1.b1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8215035
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.z1.a1', '8.ba1.a1'], 'contains': ['32.c1.a1', '32.j1.a1', '32.t1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6510, 4130, 3624, 3625, 6576, 4286, 3638, 3743], 'generators': [1229808, 142585, 126774], 'label': '128.850.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.i1.a1', '8.h1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '64.90', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8215036
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.h1.a1', '8.v1.a1', '8.v1.b1'], 'contains': ['32.c1.a1', '32.k1.a1', '32.u1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4366, 3407, 2760, 4114, 4410, 3535, 2771, 4250], 'generators': [1229808, 889561, 126774], 'label': '128.850.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.h1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '64.90', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215037
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.i1.a1', '8.w1.a1', '8.w1.b1', '8.bb1.a1', '8.bb1.b1'], 'contains': ['32.c1.a1', '32.l1.a1', '32.v1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2056, 1483, 2447, 2320, 2077, 1538, 2456, 2397], 'generators': [889560, 1229808, 126774], 'label': '128.850.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.f1.a1', '8.i1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '64.90', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215038
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.i1.a1', '8.x1.a1', '8.x1.b1'], 'contains': ['32.c1.a1', '32.m1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4659, 5093, 2603, 1668, 4706, 5284, 2614, 1723], 'generators': [2380015, 1229808, 126774], 'label': '128.850.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.c1.a1', '8.i1.a1', '8.e1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '64.90', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215039
    {'ambient': '128.850', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.f1.a1', '8.h1.a1', '8.y1.a1', '8.y1.b1', '8.bc1.a1', '8.bc1.b1'], 'contains': ['32.c1.a1', '32.n1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3493, 2445, 2290, 2972, 3529, 2537, 2299, 3070], 'generators': [1229808, 2380014, 126774], 'label': '128.850.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1', '8.f1.a1', '8.h1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '64.90', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 8215040
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.k1.b1', '8.l1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.o1.a1', '32.r1.a1', '32.r1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 5905, -1, 7911, -1, 5928, -1], 'generators': [126720, 1, 126774], 'label': '128.850.16.h1.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': '16.h1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215041
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.d1.a1', '32.e1.b1', '32.o1.d1', '32.r1.c1', '32.r1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 5669, -1, 7911, -1, 5691, -1], 'generators': [1149288, 1, 126774], 'label': '128.850.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215042
    {'ambient': '128.850', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['64.a1.a1', '64.a1.b1', '64.c1.a1', '64.g1.a1', '64.h1.a1', '64.e1.a1', '64.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.b1', '4.f1.b1', '4.g1.a1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2311, 2259, 1798, 2655, 2335, 2344, 1805, 2742], 'generators': [889560, 1229808, 126721, 420007, 126774, 142584], 'label': '128.850.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.b1', '4.f1.b1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '64.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
  • id: 8215043
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.c1', '8.k1.d1', '8.l1.a1'], 'contains': ['32.d1.b1', '32.e1.c1', '32.o1.b1', '32.r1.a1', '32.r1.d1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 5550, -1, 7911, -1, 5573, -1], 'generators': [126720, 126774, 1229809], 'label': '128.850.16.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.c1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215044
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.d1', '8.k1.c1', '8.l1.a1'], 'contains': ['32.d1.b1', '32.e1.d1', '32.o1.c1', '32.r1.b1', '32.r1.c1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 5786, -1, 7911, -1, 5809, -1], 'generators': [1149288, 126774, 1229809], 'label': '128.850.16.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.h1.d1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215045
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.b1', '8.l1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.e1.b1', '32.o1.b1', '32.o1.c1', '32.r2.a1', '32.r2.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8271, -1, 6612, -1, 8356, -1, 6638, -1], 'generators': [21024, 1, 126774], 'label': '128.850.16.h2.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.h2.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215046
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.h2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.c1', '8.k1.d1', '8.l1.a1'], 'contains': ['32.d1.b1', '32.e1.c1', '32.e1.d1', '32.o1.a1', '32.o1.d1', '32.r2.a1', '32.r2.b1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8271, -1, 6376, -1, 8356, -1, 6401, -1], 'generators': [21024, 126774, 1229809], 'label': '128.850.16.h2.b1', '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.h2.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215047
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.k1.a1', '8.k1.b1'], 'contains': ['32.d1.a1', '32.f1.a1', '32.p1.a1', '32.p1.a2', '32.s1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7391, -1, 6141, -1, 7466, -1, 6165, -1], 'generators': [1, 126774, 142584], 'label': '128.850.16.i1.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': '16.i1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215048
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.k1.c1', '8.k1.d1'], 'contains': ['32.d1.b1', '32.f1.b1', '32.p1.a1', '32.p1.a2', '32.s1.a1', '32.t1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7391, -1, 6022, -1, 7466, -1, 6046, -1], 'generators': [126774, 142584, 1229809], 'label': '128.850.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.i1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215049
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.d1.a1', '32.g1.a1', '32.q1.a1', '32.u1.a1', '32.v1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2470, -1, 3388, -1, 2495, -1, 3401, -1], 'generators': [889560, 1, 126774], 'label': '128.850.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215050
    {'ambient': '128.850', 'aut_centralizer_order': 64, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.j1.c1', '8.j1.d1'], 'contains': ['32.d1.b1', '32.g1.b1', '32.q1.a1', '32.u1.a1', '32.v1.a1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2470, -1, 3269, -1, 2495, -1, 3282, -1], 'generators': [889560, 126774, 1229809], 'label': '128.850.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.j1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 8215051
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.j1.b1', '8.m1.a1'], 'contains': ['32.d1.a1', '32.w1.a1', '32.w1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5411, -1, 4715, -1, 5466, -1, 4734, -1], 'generators': [970920, 1, 126774], 'label': '128.850.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.32', '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': '2.1'}
  • id: 8215052
    {'ambient': '128.850', 'aut_centralizer_order': 32, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.c1', '8.j1.d1', '8.m1.a1'], 'contains': ['32.d1.b1', '32.w1.a1', '32.w1.b1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5411, -1, 4520, -1, 5466, -1, 4537, -1], 'generators': [970920, 126774, 1229809], 'label': '128.850.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.k1.b1', 'projective_image': '64.32', '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': '2.1'}
  • id: 8215053
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.226', 'aut_weyl_index': 16, 'centralizer': '4.a1.a1', 'complements': ['32.z1.a1', '32.z1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.k1.a1', '8.k1.b1', '8.k1.c1', '8.k1.d1', '8.l1.a1', '8.n1.a1', '8.r1.a1', '8.z1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8164, 9356, 6995, 9491, 8247, 9707, 7067, 9803], 'generators': [1229808, 126720, 1, 126774, 142584], 'label': '128.850.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.b1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.6', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 8215054
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.f1.a1', '32.x1.a1', '32.x1.b1', '32.y1.a1', '32.y1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 9915, -1, 9913, -1, 9954, -1], 'generators': [126720, 1, 142584], 'label': '128.850.16.l1.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.l1.a1', 'projective_image': '64.32', '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': '1.1'}
  • id: 8215055
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.n1.a1'], 'contains': ['32.e1.b1', '32.f1.a1', '32.x1.c1', '32.x1.d1', '32.y1.d1', '32.y1.d2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 9561, -1, 9913, -1, 9598, -1], 'generators': [1149288, 1, 142584], 'label': '128.850.16.l1.b1', '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.l1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215056
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.d1', '8.n1.a1'], 'contains': ['32.e1.c1', '32.f1.b1', '32.x1.a1', '32.x1.d1', '32.y1.b1', '32.y1.b2'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 8381, -1, 9913, -1, 8414, -1], 'generators': [126720, 142584, 1229809], 'label': '128.850.16.l1.c1', '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.l1.c1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215057
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.c1', '8.n1.a1'], 'contains': ['32.e1.d1', '32.f1.b1', '32.x1.b1', '32.x1.c1', '32.y1.c1', '32.y1.c2'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 9796, -1, 9913, -1, 9835, -1], 'generators': [1149288, 142584, 1229809], 'label': '128.850.16.l1.d1', '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.l1.d1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215058
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.b1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.e1.b1', '32.f1.a1', '32.x2.a1', '32.x2.b1', '32.y1.b1', '32.y1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9593, -1, 9443, -1, 9691, -1, 9480, -1], 'generators': [1229784, 1, 142584], 'label': '128.850.16.l2.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.l2.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215059
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.k1.b1', '8.n1.a1'], 'contains': ['32.e1.a1', '32.e1.b1', '32.f1.a1', '32.x2.a2', '32.x2.b2', '32.y1.b2', '32.y1.c2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9593, -1, 9679, -1, 9691, -1, 9717, -1], 'generators': [1, 142584, 54], 'label': '128.850.16.l2.a2', '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.l2.a2', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l2.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215060
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.c1', '8.k1.d1', '8.n1.a1'], 'contains': ['32.e1.c1', '32.e1.d1', '32.f1.b1', '32.x2.a2', '32.x2.b1', '32.y1.a1', '32.y1.d1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9593, -1, 9325, -1, 9691, -1, 9362, -1], 'generators': [142584, 54, 1229809], 'label': '128.850.16.l2.b1', '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.l2.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215061
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.l2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.c1', '8.k1.d1', '8.n1.a1'], 'contains': ['32.e1.c1', '32.e1.d1', '32.f1.b1', '32.x2.a1', '32.x2.b2', '32.y1.a2', '32.y1.d2'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9593, -1, 8853, -1, 9691, -1, 8888, -1], 'generators': [1229784, 142584, 1229809], 'label': '128.850.16.l2.b2', '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.l2.b2', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l2.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215062
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.g1.a1', '32.z1.a1', '32.z1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [488, -1, 280, -1, 492, -1, 282, -1], 'generators': [889560, 1, 420006], 'label': '128.850.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 8215063
    {'ambient': '128.850', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1'], 'contains': ['32.g1.b1', '32.z1.a1', '32.z1.b1'], 'core': '64.a1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [488, -1, 85, -1, 492, -1, 85, -1], 'generators': [970974, 1674126, 1229809], 'label': '128.850.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.p1.a1', 'old_label': '16.m1.b1', 'projective_image': '64.32', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}