Abstract group data - 256.53382

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 8, 12, 4, 4], 'aut_gens': [[2917963830, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [1445590947628801, 2579612544196686, 921165952518414, 3823657107099840, 1558053575931241, 1551513286714440, 1453437518158944, 1558053575931240], [9247650618384, 3088183538852665, 4703819281996567, 1179824713041960, 1558053575931241, 1453437518158944, 9250089176568, 1558053575931240], [1445590947628801, 795533299969728, 2336089854875761, 3823657107099841, 1558053575931241, 1453437518158944, 1551513286714440, 1558053575931240], [1445590947628800, 5276679855650928, 1954500251745624, 3823657107099841, 1, 1453437518158944, 1445593386585990, 1558053575931240], [1445590947628800, 2586153351610447, 4111100098343694, 1179824713041961, 1, 1551513286714440, 1445593386585990, 1558053575931240], [1445590947628800, 3150956575154455, 2340017666867790, 3823657107099840, 1, 1453437518158944, 1551513286714440, 1558053575931240]], 'aut_group': None, 'aut_hash': 7735405136427890832, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 98304, 'aut_permdeg': 64, 'aut_perms': [34309139634969365981206112012634495549483438818444807225243993943429811457245602870562437, 61635431537104094074133613662722631394012391493983849128992965175879438072139288041265753, 26411852157599395273883073401174719639122731808994141807311288203189992981803858462625412, 69592840527483731970102639200026660633361208495375109537313398309371907359560177769313231, 8648937249262665097580014337936455758612900613968156787940063183404539773828069560054065, 82554400999610121666416767310374788972856578509692589731421206342980613244772824705564921], 'aut_phi_ratio': 768.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 3, 2], [2, 4, 4, 1], [2, 4, 12, 1], [4, 1, 4, 1], [4, 2, 6, 1], [4, 4, 4, 1], [4, 4, 12, 1], [4, 8, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.C_6.C_2^5.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '512.6249567', 'autcent_hash': 6452065007057432321, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '192.1538', 'autcentquo_hash': 1538, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^3:S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 16], [4, 1, 4], [4, 2, 6], [4, 4, 16], [4, 8, 12]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '32.27', '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', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 53382, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['128.1757', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 16], [4, 1, 2, 2], [4, 2, 1, 6], [4, 4, 1, 12], [4, 4, 2, 2], [4, 8, 1, 12]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 3333120, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 53382, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 1, 1, 2, 2, 1], 'inner_gens': [[2917963830, 367832559810630, 921165952518414, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [9247650618384, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 1453437518158944, 1558053575931240], [126938577836280, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 1551513286714440, 126940973252046, 1558053575931240], [2917963830, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [2917963830, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [2917963830, 359890668724326, 3416619631436328, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [2917963830, 2586153351610446, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240], [2917963830, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240]], 'inner_hash': 27, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^2\\wr C_2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 24], [4, 8]], 'label': '256.53382', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3.C2^5', 'ngens': 8, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 64, 'number_divisions': 60, 'number_normal_subgroups': 559, 'number_subgroup_autclasses': 207, 'number_subgroup_classes': 2543, 'number_subgroups': 5199, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 79], [4, 176]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [4, 6, 4, 6, 4], 'outer_gen_pows': [0, 0, 0, 0, 126940973252046], 'outer_gens': [[1558052138927760, 795533299969728, 359890668724326, 3823657107099841, 1, 126940973252046, 9250089176568, 1558053575931240], [1558052138927760, 3088183538852664, 5636576220456535, 3823657107099840, 1, 126940973252046, 1445593386585990, 1558053575931240], [1558052138927761, 359890668724326, 4450960814410087, 1179824713041960, 1, 9250089176568, 1445593386585990, 1558053575931240], [1558052138927760, 4549036146743568, 2336089854875761, 3823657107099841, 1558053575931241, 1445593386585990, 9250089176568, 1558053575931240], [2917963831, 1822424990425975, 5234836874185584, 3823657107099841, 1558053575931241, 1445593386585990, 126940973252046, 1558053575931240]], 'outer_group': None, 'outer_hash': 4177889693200194196, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 16, 'outer_perms': [1327353731830, 8195797249919, 374659119815, 9434415525864, 5499501200236], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4.(C_6\\times D_4).C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 24], [8, 4]], 'representations': {'PC': {'code': 9711696554077757657677904, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2187, 972, 260, 748, 116, 1941, 166]}, 'Perm': {'d': 18, 'gens': [2917963830, 359890668724326, 795533299969728, 1179824713041960, 1558053575931241, 9250089176568, 126940973252046, 1558053575931240]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.C_2^5', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 103351420
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 53382, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 103351431
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 53382, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 1, 'size': 1}
  • id: 103351442
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 53382, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 1558053575931241, 'size': 1}
  • id: 103351453
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 53382, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 1558053575931240, 'size': 1}
  • id: 103351464
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 53382, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 9250089176569, 'size': 2}
  • id: 103351475
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 53382, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 126940973252047, 'size': 2}
  • id: 103351481
    {'aut_label': '2D', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 53382, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 134878510137841, 'size': 2}
  • id: 103351482
    {'aut_label': '2G', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 53382, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 9250089176568, 'size': 2}
  • id: 103351483
    {'aut_label': '2G', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 53382, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 126940973252046, 'size': 2}
  • id: 103351421
    {'aut_label': '2G', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 53382, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 1445593386585990, 'size': 2}
  • id: 103351422
    {'aut_label': '2J', 'centralizer': '4.b1', 'counter': 11, 'group_counter': 53382, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 2917963830, 'size': 4}
  • id: 103351423
    {'aut_label': '2J', 'centralizer': '4.b1', 'counter': 12, 'group_counter': 53382, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 2917963831, 'size': 4}
  • id: 103351424
    {'aut_label': '2J', 'centralizer': '4.b1', 'counter': 13, 'group_counter': 53382, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 134880426147960, 'size': 4}
  • id: 103351425
    {'aut_label': '2J', 'centralizer': '4.b1', 'counter': 14, 'group_counter': 53382, 'group_order': 256, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 134880426147961, 'size': 4}
  • id: 103351426
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 15, 'group_counter': 53382, 'group_order': 256, 'label': '2N', 'order': 2, 'powers': [1], 'representative': 359890668724326, 'size': 4}
  • id: 103351427
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 16, 'group_counter': 53382, 'group_order': 256, 'label': '2O', 'order': 2, 'powers': [1], 'representative': 359890668724327, 'size': 4}
  • id: 103351428
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 17, 'group_counter': 53382, 'group_order': 256, 'label': '2P', 'order': 2, 'powers': [1], 'representative': 795533299969728, 'size': 4}
  • id: 103351429
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 18, 'group_counter': 53382, 'group_order': 256, 'label': '2Q', 'order': 2, 'powers': [1], 'representative': 795533299969729, 'size': 4}
  • id: 103351430
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 19, 'group_counter': 53382, 'group_order': 256, 'label': '2R', 'order': 2, 'powers': [1], 'representative': 1822424990425974, 'size': 4}
  • id: 103351432
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 20, 'group_counter': 53382, 'group_order': 256, 'label': '2S', 'order': 2, 'powers': [1], 'representative': 1822424990425975, 'size': 4}
  • id: 103351433
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 21, 'group_counter': 53382, 'group_order': 256, 'label': '2T', 'order': 2, 'powers': [1], 'representative': 2336089854875760, 'size': 4}
  • id: 103351434
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 22, 'group_counter': 53382, 'group_order': 256, 'label': '2U', 'order': 2, 'powers': [1], 'representative': 2336089854875761, 'size': 4}
  • id: 103351435
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 23, 'group_counter': 53382, 'group_order': 256, 'label': '2V', 'order': 2, 'powers': [1], 'representative': 3088183538852664, 'size': 4}
  • id: 103351436
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 24, 'group_counter': 53382, 'group_order': 256, 'label': '2W', 'order': 2, 'powers': [1], 'representative': 3088183538852665, 'size': 4}
  • id: 103351437
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 25, 'group_counter': 53382, 'group_order': 256, 'label': '2X', 'order': 2, 'powers': [1], 'representative': 4450960814410086, 'size': 4}
  • id: 103351438
    {'aut_label': '2N', 'centralizer': '4.q1', 'counter': 26, 'group_counter': 53382, 'group_order': 256, 'label': '2Y', 'order': 2, 'powers': [1], 'representative': 4450960814410087, 'size': 4}
  • id: 103351439
    {'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 27, 'group_counter': 53382, 'group_order': 256, 'label': '4A1', 'order': 4, 'powers': [4], 'representative': 1179824713041960, 'size': 1}
  • id: 103351440
    {'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 28, 'group_counter': 53382, 'group_order': 256, 'label': '4A-1', 'order': 4, 'powers': [4], 'representative': 3823657107099840, 'size': 1}
  • id: 103351441
    {'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 29, 'group_counter': 53382, 'group_order': 256, 'label': '4B1', 'order': 4, 'powers': [4], 'representative': 1179824713041961, 'size': 1}
  • id: 103351443
    {'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 30, 'group_counter': 53382, 'group_order': 256, 'label': '4B-1', 'order': 4, 'powers': [4], 'representative': 3823657107099841, 'size': 1}
  • id: 103351444
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 31, 'group_counter': 53382, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 1187678429726520, 'size': 2}
  • id: 103351445
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 32, 'group_counter': 53382, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 1187678429726521, 'size': 2}
  • id: 103351446
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 33, 'group_counter': 53382, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [4], 'representative': 1327599450054864, 'size': 2}
  • id: 103351447
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 34, 'group_counter': 53382, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 1327599450054865, 'size': 2}
  • id: 103351448
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 35, 'group_counter': 53382, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 1334143568704710, 'size': 2}
  • id: 103351449
    {'aut_label': '4C', 'centralizer': '2.a1', 'counter': 36, 'group_counter': 53382, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 1334143568704711, 'size': 2}
  • id: 103351450
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 37, 'group_counter': 53382, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 422661114061446, 'size': 4}
  • id: 103351451
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 38, 'group_counter': 53382, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [4], 'representative': 422661114061447, 'size': 4}
  • id: 103351452
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 39, 'group_counter': 53382, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [4], 'representative': 799458240531168, 'size': 4}
  • id: 103351454
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 40, 'group_counter': 53382, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 799458240531169, 'size': 4}
  • id: 103351455
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 41, 'group_counter': 53382, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [4], 'representative': 1827657125950614, 'size': 4}
  • id: 103351456
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 42, 'group_counter': 53382, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [4], 'representative': 1827657125950615, 'size': 4}
  • id: 103351457
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 43, 'group_counter': 53382, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [4], 'representative': 2210464151530206, 'size': 4}
  • id: 103351458
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 44, 'group_counter': 53382, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [4], 'representative': 2210464151530207, 'size': 4}
  • id: 103351459
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 45, 'group_counter': 53382, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [4], 'representative': 3080248359646008, 'size': 4}
  • id: 103351460
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 46, 'group_counter': 53382, 'group_order': 256, 'label': '4R', 'order': 4, 'powers': [4], 'representative': 3080248359646009, 'size': 4}
  • id: 103351461
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 47, 'group_counter': 53382, 'group_order': 256, 'label': '4S', 'order': 4, 'powers': [4], 'representative': 4444332311929374, 'size': 4}
  • id: 103351462
    {'aut_label': '4I', 'centralizer': '4.q1', 'counter': 48, 'group_counter': 53382, 'group_order': 256, 'label': '4T', 'order': 4, 'powers': [4], 'representative': 4444332311929375, 'size': 4}
  • id: 103351463
    {'aut_label': '4U1', 'centralizer': '4.b1', 'counter': 49, 'group_counter': 53382, 'group_order': 256, 'label': '4U1', 'order': 4, 'powers': [4], 'representative': 1179826153715760, 'size': 4}
  • id: 103351465
    {'aut_label': '4U1', 'centralizer': '4.b1', 'counter': 50, 'group_counter': 53382, 'group_order': 256, 'label': '4U-1', 'order': 4, 'powers': [4], 'representative': 1334144047705920, 'size': 4}
  • id: 103351466
    {'aut_label': '4U1', 'centralizer': '4.b1', 'counter': 51, 'group_counter': 53382, 'group_order': 256, 'label': '4V1', 'order': 4, 'powers': [4], 'representative': 1179826153715761, 'size': 4}
  • id: 103351467
    {'aut_label': '4U1', 'centralizer': '4.b1', 'counter': 52, 'group_counter': 53382, 'group_order': 256, 'label': '4V-1', 'order': 4, 'powers': [4], 'representative': 1334144047705921, 'size': 4}
  • id: 103351468
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 53, 'group_counter': 53382, 'group_order': 256, 'label': '4W', 'order': 4, 'powers': [8], 'representative': 359892628275870, 'size': 8}
  • id: 103351469
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 54, 'group_counter': 53382, 'group_order': 256, 'label': '4X', 'order': 4, 'powers': [8], 'representative': 359892628275871, 'size': 8}
  • id: 103351470
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 55, 'group_counter': 53382, 'group_order': 256, 'label': '4Y', 'order': 4, 'powers': [9], 'representative': 795535216378854, 'size': 8}
  • id: 103351471
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 56, 'group_counter': 53382, 'group_order': 256, 'label': '4Z', 'order': 4, 'powers': [9], 'representative': 795535216378855, 'size': 8}
  • id: 103351472
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 57, 'group_counter': 53382, 'group_order': 256, 'label': '4AA', 'order': 4, 'powers': [10], 'representative': 1822425948428574, 'size': 8}
  • id: 103351473
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 58, 'group_counter': 53382, 'group_order': 256, 'label': '4AB', 'order': 4, 'powers': [10], 'representative': 1822425948428575, 'size': 8}
  • id: 103351474
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 59, 'group_counter': 53382, 'group_order': 256, 'label': '4AC', 'order': 4, 'powers': [8], 'representative': 2210466071527320, 'size': 8}
  • id: 103351476
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 60, 'group_counter': 53382, 'group_order': 256, 'label': '4AD', 'order': 4, 'powers': [8], 'representative': 2210466071527321, 'size': 8}
  • id: 103351477
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 61, 'group_counter': 53382, 'group_order': 256, 'label': '4AE', 'order': 4, 'powers': [9], 'representative': 3080250315608544, 'size': 8}
  • id: 103351478
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 62, 'group_counter': 53382, 'group_order': 256, 'label': '4AF', 'order': 4, 'powers': [9], 'representative': 3080250315608545, 'size': 8}
  • id: 103351479
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 63, 'group_counter': 53382, 'group_order': 256, 'label': '4AG', 'order': 4, 'powers': [10], 'representative': 4444334747220984, 'size': 8}
  • id: 103351480
    {'aut_label': '4W', 'centralizer': '8.z1', 'counter': 64, 'group_counter': 53382, 'group_order': 256, 'label': '4AH', 'order': 4, 'powers': [10], 'representative': 4444334747220985, '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: 2173963
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2173974
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2173985
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2173996
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2174007
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 2174018
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 2174020
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2174021
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2174022
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2173964
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 2173965
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2173966
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2173967
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2173968
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2173969
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 2173970
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2173971
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1q', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 2173972
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1r', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2173973
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1s', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2173975
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1t', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2173976
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1u', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2173977
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1v', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2173978
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1w', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2173979
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1x', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2173980
    {'cdim': 1, 'counter': 25, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1y', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2173981
    {'cdim': 1, 'counter': 26, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1z', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2173982
    {'cdim': 1, 'counter': 27, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1aa', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2173983
    {'cdim': 1, 'counter': 28, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1ab', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2173984
    {'cdim': 1, 'counter': 29, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1ac', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2173986
    {'cdim': 1, 'counter': 30, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1ad', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2173987
    {'cdim': 1, 'counter': 31, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1ae', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2173988
    {'cdim': 1, 'counter': 32, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.1af', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2173989
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173990
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173991
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173992
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173993
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173994
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173995
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173997
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173998
    {'cdim': 2, 'counter': 41, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -2, 2, 0, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2173999
    {'cdim': 2, 'counter': 42, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, -2, 0, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174000
    {'cdim': 2, 'counter': 43, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174001
    {'cdim': 2, 'counter': 44, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, -2, 0, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174002
    {'cdim': 2, 'counter': 45, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2m', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174003
    {'cdim': 2, 'counter': 46, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2n', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174004
    {'cdim': 2, 'counter': 47, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2o', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174005
    {'cdim': 2, 'counter': 48, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2p', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174006
    {'cdim': 2, 'counter': 49, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2q', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174008
    {'cdim': 2, 'counter': 50, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2r', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174009
    {'cdim': 2, 'counter': 51, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2s', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174010
    {'cdim': 2, 'counter': 52, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2t', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174011
    {'cdim': 2, 'counter': 53, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2u', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174012
    {'cdim': 2, 'counter': 54, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2v', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174013
    {'cdim': 2, 'counter': 55, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2w', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174014
    {'cdim': 2, 'counter': 56, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.2x', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2174015
    {'cdim': 4, 'counter': 57, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.4a', 'multiplicity': 2, 'nt': [16, 223], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 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, 0], 'schur_index': 1}
  • id: 2174016
    {'cdim': 4, 'counter': 58, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.4b', 'multiplicity': 2, 'nt': [16, 223], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -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, 0], 'schur_index': 1}
  • id: 2174017
    {'cdim': 4, 'counter': 59, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.4c', 'multiplicity': 2, 'nt': [16, 223], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -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, 0], 'schur_index': 1}
  • id: 2174019
    {'cdim': 4, 'counter': 60, 'faithful': False, 'group': '256.53382', 'group_order': 256, 'image': None, 'label': '256.53382.4d', 'multiplicity': 2, 'nt': [16, 223], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 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, 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: 2757518
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 256, 'label': '256.53382.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 2757537
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 27, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.53382.1aa', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757538
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 28, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.53382.1ab', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757539
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.53382.1ac', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757541
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.53382.1ad', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 2757542
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.53382.1ae', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757543
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 128, 'label': '256.53382.1af', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757529
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757540
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757551
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757562
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757573
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 2757579
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757580
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757581
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 2757519
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757520
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 2757521
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 2757522
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757523
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757524
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757525
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757526
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 17, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 128, 'label': '256.53382.1q', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757527
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 18, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.53382.1r', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757528
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 19, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.53382.1s', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 2757530
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 20, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.53382.1t', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 2757531
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 21, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.53382.1u', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 2757532
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 22, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.53382.1v', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757533
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 23, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.53382.1w', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757534
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 24, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.53382.1x', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757535
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 25, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.53382.1y', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 2757536
    {'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 26, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 128, 'label': '256.53382.1z', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 2757544
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757545
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757546
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757547
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757548
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757549
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757550
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 39, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757552
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 40, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757553
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 41, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2i', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757554
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 42, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2j', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757555
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 43, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2k', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757556
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 44, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 32, 'label': '256.53382.2l', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757557
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 45, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 32, 'label': '256.53382.2m', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757558
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 46, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2n', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757559
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 47, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2o', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757560
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 48, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 32, 'label': '256.53382.2p', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757561
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 49, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 32, 'label': '256.53382.2q', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757563
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 50, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2r', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757564
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 51, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2s', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757565
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 52, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 32, 'label': '256.53382.2t', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 2757566
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 53, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1', 'kernel_order': 32, 'label': '256.53382.2u', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757567
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 54, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2v', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757568
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 55, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 32, 'label': '256.53382.2w', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757569
    {'center': '4.e1', 'center_index': 4, 'center_order': 64, 'counter': 56, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 32, 'label': '256.53382.2x', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 2757570
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 57, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4a1', 'nt': [16, 223], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[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]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[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: 2757571
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 58, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4a2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[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]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[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: 2757572
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 59, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4b1', 'nt': [16, 223], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[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]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[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: 2757574
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 60, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4b2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[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]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[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: 2757575
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 61, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4c1', 'nt': [16, 223], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[4, 1]], [[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]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[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: 2757576
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 62, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[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]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[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: 2757577
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 63, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4d1', 'nt': [16, 223], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[4, 1]], [[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]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[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: 2757578
    {'center': '32.b1', 'center_index': 32, 'center_order': 8, 'counter': 64, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '256.53382', 'group_counter': 53382, 'group_order': 256, 'image': None, 'image_isoclass': '128.1757', 'image_order': 128, 'indicator': 0, 'kernel': '128.a1', 'kernel_order': 2, 'label': '256.53382.4d2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[4, 1]], [[-4, 1]], [[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]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[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: 48821986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.53382.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '256.53382', 'subgroup_hash': 53382, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 2}
  • id: 48822097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': '128.2167', 'subgroup_hash': 2167, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, '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': '128.1614', 'subgroup_hash': 1614, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, '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': '128.1756', 'subgroup_hash': 1756, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, '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': '128.2325', 'subgroup_hash': 2325, 'subgroup_order': 128, 'subgroup_tex': 'C_4.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 48822160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '256.53382.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, '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': '128.1757', 'subgroup_hash': 1757, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, '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': '64.260', 'subgroup_hash': 260, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, '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': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, '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': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, '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': '64.263', 'subgroup_hash': 263, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, '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': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, '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': '64.195', 'subgroup_hash': 195, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, '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': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, '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': '64.91', 'subgroup_hash': 91, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, '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': '64.139', 'subgroup_hash': 139, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, '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': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, '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': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, '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': '64.203', 'subgroup_hash': 203, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, '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': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, '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': '64.265', 'subgroup_hash': 265, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.q1', 'outer_equivalence': True, 'perfect': False, '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': '64.263', 'subgroup_hash': 263, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.r1', 'outer_equivalence': True, 'perfect': False, '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': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.s1', 'outer_equivalence': True, 'perfect': False, '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': '64.206', 'subgroup_hash': 206, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.4.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.t1', 'outer_equivalence': True, 'perfect': False, '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': '64.266', 'subgroup_hash': 266, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822118
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 48822119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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': [], '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: 48822120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, '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': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822121
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, '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': [], 'split': False, '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: 48822123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1', 'outer_equivalence': True, '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': ['C3'], '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: 48822125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1', 'outer_equivalence': True, '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': [], '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: 48822129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1', 'outer_equivalence': True, 'perfect': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1', 'outer_equivalence': True, 'perfect': False, '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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1', 'outer_equivalence': True, 'perfect': False, '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': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1', 'outer_equivalence': True, 'perfect': False, '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1', 'outer_equivalence': True, 'perfect': False, '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1', 'outer_equivalence': True, 'perfect': False, '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822146
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1', 'outer_equivalence': True, 'perfect': False, '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd2', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1', 'outer_equivalence': True, 'perfect': False, '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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1', 'outer_equivalence': True, 'perfect': False, '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': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bh1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bi1', 'outer_equivalence': True, 'perfect': False, '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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bj1', 'outer_equivalence': True, 'perfect': False, '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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822155
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1', 'outer_equivalence': True, 'perfect': False, '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': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1', 'outer_equivalence': True, 'perfect': False, '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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1', 'outer_equivalence': True, 'perfect': False, '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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1', 'outer_equivalence': True, 'perfect': False, '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bp1', 'outer_equivalence': True, 'perfect': False, '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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bq1', 'outer_equivalence': True, 'perfect': False, '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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.br1', 'outer_equivalence': True, 'perfect': False, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bs1', 'outer_equivalence': True, 'perfect': False, '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': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bt1', 'outer_equivalence': True, 'perfect': False, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.8.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bu1', 'outer_equivalence': True, 'perfect': False, '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': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822170
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', '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: 48822173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1', 'outer_equivalence': True, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1', 'outer_equivalence': True, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822175
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1', 'outer_equivalence': True, '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': True, '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: 48822176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 48822179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', '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: 48822180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', '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: 48822181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', '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: 48822183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 48822184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822188
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822189
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822192
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821988
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821992
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48821993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1', 'outer_equivalence': True, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48821994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1', 'outer_equivalence': True, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48821995
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821996
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821997
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48821999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh2', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1', 'outer_equivalence': True, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1', 'outer_equivalence': True, 'perfect': False, '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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 48822006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1', 'outer_equivalence': True, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1', 'outer_equivalence': True, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1', 'outer_equivalence': True, 'perfect': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1', 'outer_equivalence': True, 'perfect': False, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1', 'outer_equivalence': True, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc1', 'outer_equivalence': True, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cd1', 'outer_equivalence': True, 'perfect': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1', 'outer_equivalence': True, 'perfect': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.ce2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce2', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1', 'outer_equivalence': True, 'perfect': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 48822027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.16.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1', 'outer_equivalence': True, 'perfect': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], '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: 48822030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822032
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822038
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\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: 48822039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.51', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C5'], '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: 48822040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l2', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822043
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822045
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822051
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822054
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822055
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822057
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822060
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822063
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822065
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1', 'outer_equivalence': True, 'perfect': False, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1', 'outer_equivalence': True, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1', 'outer_equivalence': True, 'perfect': False, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 48822072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1', 'outer_equivalence': True, 'perfect': False, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.32.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 48822076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 48822077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': 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: 48822078
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53382.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.261', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 261, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 48822079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.53382.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.53382.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822081
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822087
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.64.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822088
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.64.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.p2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822095
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.64.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 48822096
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.53382.64.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 48822100
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '256.53382.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.1757', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1757, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.C_2^4', '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: 48822101
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 202, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.53382.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2163', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2163, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C7'], '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: 48822102
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 48822103
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.128.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 48822104
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.128.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 48822105
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.53382.128.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 48822106
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.53382', 'ambient_counter': 53382, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 207, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.53382.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '256.53382', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 53382, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C8'], '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: 48822004
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '8.bg1', '8.bm1'], 'contains': ['32.e1', '32.x1', '32.bl1'], 'core': '32.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [5915, -1, 5922, -1], 'generators': [3411380306487624, 1187678429726520, 1453437518158945, 1558053575931240], 'label': '256.53382.16.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bm1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48821986
    {'ambient': '256.53382', '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.b1', 'complements': ['256.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5189, 6083, 5193, 6038], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 359890668724326, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48821987
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '512.7577399', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': ['64.t1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.e1', '8.g1', '8.h1', '8.l1', '8.x1', '8.bb1', '8.bl1'], 'core': '4.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3580, 4265, 3585, 4233], 'generators': [1558053575931241, 126940973252046, 795535216378854, 3080248359646008, 9250089176568, 1558053575931240], 'label': '256.53382.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.e1', '8.g1', '8.h1', '8.l1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48821988
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.v1', '8.bc1', '8.be1', '8.bf1'], 'contains': ['32.c1', '32.r1', '32.s1', '32.bg1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7658, -1, 7668, -1], 'generators': [1558053575931241, 795533299969728, 1327599450054864, 1558053575931240], 'label': '256.53382.16.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.y1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821989
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.w1', '8.y1', '8.bc1', '8.bd1', '8.be1'], 'contains': ['32.r1', '32.s1', '32.bh1'], 'core': '64.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9297, -1, 9308, -1], 'generators': [1558053575931241, 795533299969728, 2210464151530206, 1558053575931240], 'label': '256.53382.16.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.z1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821990
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '8.u1', '8.v1', '8.be1', '8.bf1'], 'contains': ['32.c1', '32.r1', '32.bi1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7470, -1, 7479, -1], 'generators': [1558053575931241, 795533299969728, 1187678429726520, 1558053575931240], 'label': '256.53382.16.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.ba1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821991
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.w1', '8.y1', '8.bd2', '8.be1', '8.bf1'], 'contains': ['32.r1', '32.s1', '32.bj1'], 'core': '64.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9109, -1, 9119, -1], 'generators': [1558053575931241, 795533299969728, 2214395799564366, 1558053575931240], 'label': '256.53382.16.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bb1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821992
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 512, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.y1', '8.bd1', '8.bf1'], 'contains': ['32.p1', '32.r1', '32.bk1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9771, -1, 9783, -1], 'generators': [1558053575931241, 795533299969728, 4703819281996566, 1558053575931240], 'label': '256.53382.16.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bc1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821993
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '8.u1', '8.v1', '8.bc1', '8.be1'], 'contains': ['32.c1', '32.s1', '32.bl1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7118, -1, 7127, -1], 'generators': [3411380306487624, 1558053575931241, 1187678429726520, 1558053575931240], 'label': '256.53382.16.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bd1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821994
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 512, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.w1', '8.bc1', '8.bd2'], 'contains': ['32.s1', '32.bm1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9911, -1, 9923, -1], 'generators': [3411380306487624, 1558053575931241, 2214395799564366, 1558053575931240], 'label': '256.53382.16.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.be1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821995
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.r1', '8.bk1'], 'contains': ['32.d1', '32.u1', '32.y1', '32.bd1', '32.be1'], 'core': '32.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [492, -1, 493, -1], 'generators': [1179824713041960, 1453437518158945, 2917963830, 1558053575931240], 'label': '256.53382.16.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.bf1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48821996
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.s1', '8.bk1'], 'contains': ['32.e1', '32.u1', '32.y1', '32.be1'], 'core': '32.e1', 'coset_action_label': None, 'count': 24, 'diagramx': [694, -1, 694, -1], 'generators': [1551513286714441, 2917963830, 1327599450054864, 1558053575931240], 'label': '256.53382.16.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.bg1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48821997
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.a1', '8.bh1', '8.bm1'], 'contains': ['32.d1', '32.w1', '32.x1', '32.bf1', '32.bg1'], 'core': '32.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [6574, -1, 6582, -1], 'generators': [795533299969728, 1179824713041960, 1453437518158945, 1558053575931240], 'label': '256.53382.16.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bh1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48821998
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 12, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 192, 'centralizer': '32.b1', 'complements': ['64.t1'], 'conjugacy_class_count': 12, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.e1', '8.h1', '8.m1'], 'core': '4.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [4930, 6114, 4935, 6069], 'generators': [1558053575931241, 126940973252046, 3080248359646008, 359892628275870, 9250089176568, 1558053575931240], 'label': '256.53382.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.e1', '8.h1', '8.m1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48821999
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bh2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.i1', '8.u1', '8.bh1', '8.bm1'], 'contains': ['32.d1', '32.v1', '32.bf1', '32.bi1', '32.bl1'], 'core': '32.d1', 'coset_action_label': None, 'count': 48, 'diagramx': [6853, -1, 6861, -1], 'generators': [1551513286714441, 795533299969728, 1179824713041960, 1558053575931240], 'label': '256.53382.16.bh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bh2', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822000
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.i1', '8.v1', '8.bg1', '8.bi1', '8.bm1'], 'contains': ['32.e1', '32.v1', '32.bg1', '32.bi1', '32.bl1'], 'core': '32.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [6971, -1, 6979, -1], 'generators': [1551513286714441, 795533299969728, 1327599450054864, 1558053575931240], 'label': '256.53382.16.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bi1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822001
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.w1', '8.bg1', '8.bh1', '8.bn1'], 'contains': ['32.v1', '32.x1', '32.bh1', '32.bj1', '32.bm1'], 'core': '64.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [8610, -1, 8620, -1], 'generators': [1551513286714441, 795533299969728, 2210464151530206, 1558053575931240], 'label': '256.53382.16.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bj1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822002
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '8.bi1', '8.bm1'], 'contains': ['32.e1', '32.w1', '32.bi1'], 'core': '32.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [6266, -1, 6274, -1], 'generators': [795533299969728, 1187678429726520, 1453437518158945, 1558053575931240], 'label': '256.53382.16.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bk1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822003
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.y1', '8.bh1', '8.bi1', '8.bn1'], 'contains': ['32.v1', '32.w1', '32.bh1', '32.bj1', '32.bk1'], 'core': '64.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [8461, -1, 8472, -1], 'generators': [795533299969728, 2210464151530206, 1453437518158945, 1558053575931240], 'label': '256.53382.16.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bl1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822096
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16384, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1', '32.o1', '32.bp1'], 'contains': ['128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3418, -1, 3422, -1], 'generators': [126940973252046, 9250089176568], 'label': '256.53382.64.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.s1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822005
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '8.bj1', '8.bk1'], 'contains': ['32.f1', '32.u1', '32.z1', '32.bn1'], 'core': '32.f1', 'coset_action_label': None, 'count': 6, 'diagramx': [1462, -1, 1464, -1], 'generators': [1551513286714441, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.16.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bn1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822006
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.e1', '8.bm1', '8.bn1'], 'contains': ['32.f1', '32.v1', '32.w1', '32.x1', '32.ba1'], 'core': '32.f1', 'coset_action_label': None, 'count': 24, 'diagramx': [6090, -1, 6098, -1], 'generators': [3080248359646008, 1453437518158945, 134878510137840, 1558053575931240], 'label': '256.53382.16.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bo1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822007
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.g1', '8.bk1', '8.bl1'], 'contains': ['32.f1', '32.y1', '32.bb1'], 'core': '32.f1', 'coset_action_label': None, 'count': 6, 'diagramx': [1993, -1, 1996, -1], 'generators': [1551513286714441, 126940973252046, 1179826153715760, 1558053575931240], 'label': '256.53382.16.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bp1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822008
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.h1', '8.bj1', '8.bl1', '8.bo1'], 'contains': ['32.f1', '32.bc1'], 'core': '32.f1', 'coset_action_label': None, 'count': 12, 'diagramx': [3591, -1, 3595, -1], 'generators': [1551513286714441, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.16.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bq1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822009
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 96, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.c1', '2.e1'], 'contains': ['8.a1', '8.b1', '8.c1', '8.e1', '8.f1', '8.i1', '8.n1', '8.u1', '8.v1', '8.bm1'], 'core': '4.e1', 'coset_action_label': None, 'count': 3, 'diagramx': [5906, 1795, 5913, 1782], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.c1', '2.e1'], 'normal_contains': ['8.a1', '8.b1', '8.c1', '8.e1', '8.f1', '8.i1', '8.n1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822010
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.j1', '8.q1', '8.bj1', '8.bp1', '8.bq1'], 'contains': ['32.g1', '32.z1', '32.bc1', '32.bo1'], 'core': '32.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [2635, -1, 2638, -1], 'generators': [3416619631436329, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.16.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.br1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822011
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.k1', '8.r1', '8.bk1', '8.bp1'], 'contains': ['32.h1', '32.z1', '32.bb1', '32.bd1', '32.be1'], 'core': '32.h1', 'coset_action_label': None, 'count': 24, 'diagramx': [1203, -1, 1204, -1], 'generators': [3823657107099841, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.16.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bs1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822012
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.k1', '8.s1', '8.bk1', '8.bq1', '8.br1'], 'contains': ['32.i1', '32.z1', '32.bb1', '32.be1'], 'core': '32.i1', 'coset_action_label': None, 'count': 24, 'diagramx': [1792, -1, 1794, -1], 'generators': [126940973252046, 3818425453162249, 2917963830, 1558053575931240], 'label': '256.53382.16.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bt1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822013
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.j1', '8.t1', '8.bj1', '8.bp1', '8.br1'], 'contains': ['32.j1', '32.z1', '32.bc1'], 'core': '32.j1', 'coset_action_label': None, 'count': 48, 'diagramx': [2475, -1, 2478, -1], 'generators': [126940973252046, 799458240531169, 2917963830, 1558053575931240], 'label': '256.53382.16.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.bu1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822014
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.n1', '8.u1', '8.bm1', '8.bt1'], 'contains': ['32.h1', '32.ba1', '32.bf1', '32.bi1', '32.bl1'], 'core': '32.h1', 'coset_action_label': None, 'count': 48, 'diagramx': [6414, -1, 6422, -1], 'generators': [3416619631436329, 1179824713041960, 134878510137840, 1558053575931240], 'label': '256.53382.16.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bv1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822015
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.n1', '8.v1', '8.bm1', '8.bs1', '8.bu1'], 'contains': ['32.i1', '32.ba1', '32.bg1', '32.bi1', '32.bl1'], 'core': '32.i1', 'coset_action_label': None, 'count': 48, 'diagramx': [6734, -1, 6743, -1], 'generators': [3416619631436329, 134878510137840, 1327599450054864, 1558053575931240], 'label': '256.53382.16.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bw1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822016
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.o1', '8.w1', '8.bn1', '8.bs1', '8.bt1'], 'contains': ['32.j1', '32.ba1', '32.bh1', '32.bj1', '32.bm1'], 'core': '32.j1', 'coset_action_label': None, 'count': 96, 'diagramx': [8196, -1, 8206, -1], 'generators': [2586153351610447, 126940973252046, 3080248359646008, 1558053575931240], 'label': '256.53382.16.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bx1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822017
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.l1', '8.x1', '8.bl1', '8.bp1', '8.bq1'], 'contains': ['32.g1', '32.bb1', '32.bc1'], 'core': '32.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [3116, -1, 3120, -1], 'generators': [3416619631436329, 126940973252046, 1179826153715760, 1558053575931240], 'label': '256.53382.16.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.by1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822018
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.o1', '8.y1', '8.bn1', '8.bt1', '8.bu1'], 'contains': ['32.g1', '32.ba1', '32.bh1', '32.bj1', '32.bk1'], 'core': '32.g1', 'coset_action_label': None, 'count': 96, 'diagramx': [8049, -1, 8058, -1], 'generators': [2586153351610447, 5276679855650928, 126940973252046, 1558053575931240], 'label': '256.53382.16.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.bz1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822019
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.p1', '8.z1', '8.bo1', '8.bp1'], 'contains': ['32.h1', '32.bc1'], 'core': '32.h1', 'coset_action_label': None, 'count': 24, 'diagramx': [3347, -1, 3351, -1], 'generators': [3823657107099841, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.16.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.ca1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822020
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '1536.408640179', 'aut_weyl_index': 64, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.d1', '2.e1'], 'contains': ['8.e1', '8.o1', '8.w1', '8.y1', '8.bn1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [7134, 6837, 7142, 6788], 'generators': [1558053575931241, 795533299969728, 126940973252046, 2210464151530206, 9250089176568, 1558053575931240], 'label': '256.53382.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.d1', '2.e1'], 'normal_contains': ['8.e1', '8.o1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822021
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.p1', '8.ba1', '8.bo1', '8.bq1', '8.br1'], 'contains': ['32.i1', '32.bc1'], 'core': '32.i1', 'coset_action_label': None, 'count': 24, 'diagramx': [3458, -1, 3463, -1], 'generators': [126940973252046, 3818425453162249, 795535216378854, 1558053575931240], 'label': '256.53382.16.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.cb1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822022
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.l1', '8.bb1', '8.bl1', '8.bp1', '8.br1'], 'contains': ['32.j1', '32.bb1', '32.bc1'], 'core': '32.j1', 'coset_action_label': None, 'count': 48, 'diagramx': [2984, -1, 2988, -1], 'generators': [126940973252046, 1179826153715760, 799458240531169, 1558053575931240], 'label': '256.53382.16.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.cc1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822093
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '64.p2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['32.l2', '32.z1', '32.bn1', '32.bp1'], 'contains': ['128.d1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1938, -1, 1941, -1], 'generators': [126940973252046, 1551515203123567], 'label': '256.53382.64.p2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.p2', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822023
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '32.49', 'aut_weyl_index': 3072, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.bc1', '8.bg1', '8.bh1', '8.bs1', '8.bt1'], 'contains': ['32.bg1', '32.bh1', '32.bl1', '32.bm1'], 'core': '64.e1', 'coset_action_label': None, 'count': 96, 'diagramx': [8932, -1, 8943, -1], 'generators': [795533299969728, 422661114061447, 1327599450054864, 1558053575931240], 'label': '256.53382.16.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.cd1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822024
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['8.bd1', '8.bh1', '8.bt1'], 'contains': ['32.bf1', '32.bh1', '32.bk1'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [9498, -1, 9510, -1], 'generators': [2586153351610447, 795533299969728, 1179824713041960, 1558053575931240], 'label': '256.53382.16.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.ce1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822025
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '16.ce2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 32, 'contained_in': ['8.bd2', '8.bh1', '8.bt1'], 'contains': ['32.bf1', '32.bj1', '32.bm1'], 'core': '64.d1', 'coset_action_label': None, 'count': 64, 'diagramx': [9659, -1, 9671, -1], 'generators': [2579612544196687, 795533299969728, 1179824713041960, 1558053575931240], 'label': '256.53382.16.ce2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.ce2', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822026
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 96, 'contained_in': ['8.be1', '8.bg1', '8.bh1', '8.bi1', '8.bs1', '8.bt1', '8.bu1'], 'contains': ['32.bg1', '32.bh1', '32.bi1', '32.bj1', '32.bl1'], 'core': '64.e1', 'coset_action_label': None, 'count': 192, 'diagramx': [8314, -1, 8324, -1], 'generators': [2579612544196687, 795533299969728, 1327599450054864, 1558053575931240], 'label': '256.53382.16.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.cf1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822027
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '32.49', 'aut_weyl_index': 3072, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['8.bf1', '8.bh1', '8.bi1', '8.bt1', '8.bu1'], 'contains': ['32.bg1', '32.bi1', '32.bj1', '32.bk1'], 'core': '64.e1', 'coset_action_label': None, 'count': 96, 'diagramx': [8757, -1, 8767, -1], 'generators': [2586153351610447, 795533299969728, 1327599450054864, 1558053575931240], 'label': '256.53382.16.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.cg1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822028
    {'ambient': '256.53382', 'aut_centralizer_order': 8192, 'aut_label': '32.a1', 'aut_quo_index': 96, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.r1', '16.s1', '16.t1', '16.u1'], 'contains': ['64.a1', '64.b1', '64.c1', '64.f1'], 'core': '32.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3675, 2219, 3680, 2203], 'generators': [1558053575931241, 126940973252046, 1558053575931240], 'label': '256.53382.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1'], 'normal_contains': ['64.a1', '64.b1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822029
    {'ambient': '256.53382', 'aut_centralizer_order': 12288, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '16.v1', '16.x1'], 'contains': ['64.a1', '64.d1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4200, 228, 4205, 226], 'generators': [1558053575931241, 1179824713041960, 1558053575931240], 'label': '256.53382.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.b1'], 'normal_contains': ['64.a1', '64.d1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.27', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822030
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '32.c1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.b1', '16.c1', '16.w1', '16.y1', '16.ba1', '16.bd1'], 'contains': ['64.a1', '64.e1'], 'core': '32.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5178, 751, 5184, 746], 'generators': [1558053575931241, 1327599450054864, 1558053575931240], 'label': '256.53382.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.b1', '16.c1'], 'normal_contains': ['64.a1', '64.e1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822031
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 96, 'centralizer': '16.b1', 'complements': ['64.t1'], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.f1', '8.h1', '8.p1', '8.z1', '8.ba1', '8.bo1'], 'core': '4.g1', 'coset_action_label': None, 'count': 3, 'diagramx': [4373, 3251, 4379, 3228], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 795535216378854, 9250089176568, 1558053575931240], 'label': '256.53382.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.f1', '8.h1', '8.p1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822032
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '32.d1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.b1', '16.g1', '16.bf1', '16.bh1', '16.bh2'], 'contains': ['64.b1', '64.d1', '64.e1'], 'core': '32.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [4550, 1275, 4555, 1266], 'generators': [1179824713041960, 1453437518158945, 1558053575931240], 'label': '256.53382.32.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.b1', '16.g1'], 'normal_contains': ['64.b1', '64.d1', '64.e1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822033
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '32.e1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.c1', '16.g1', '16.bg1', '16.bi1', '16.bk1', '16.bm1'], 'contains': ['64.b1', '64.e1'], 'core': '32.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [5004, 1799, 5010, 1786], 'generators': [1551513286714441, 1327599450054864, 1558053575931240], 'label': '256.53382.32.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1', 'normal_contained_in': ['16.c1', '16.g1'], 'normal_contains': ['64.b1', '64.e1'], 'normalizer': '1.a1', 'old_label': '32.e1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822034
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '32.f1', 'aut_quo_index': 24, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.e1', '16.f1', '16.g1', '16.bn1', '16.bo1', '16.bp1', '16.bq1'], 'contains': ['64.b1', '64.c1', '64.o1'], 'core': '32.f1', 'coset_action_label': None, 'count': 3, 'diagramx': [3570, 3583, 3575, 3557], 'generators': [1551513286714441, 126940973252046, 1558053575931240], 'label': '256.53382.32.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': ['16.e1', '16.f1', '16.g1'], 'normal_contains': ['64.b1', '64.c1'], 'normalizer': '1.a1', 'old_label': '32.f1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822035
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.g1', 'aut_quo_index': 48, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.a1', '16.f1', '16.h1', '16.i1', '16.l1', '16.br1', '16.by1', '16.bz1'], 'contains': ['64.c1', '64.j1', '64.q1'], 'core': '32.g1', 'coset_action_label': None, 'count': 12, 'diagramx': [4864, 4422, 4870, 4390], 'generators': [3416619631436329, 126940973252046, 1558053575931240], 'label': '256.53382.32.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': ['16.a1', '16.f1', '16.h1', '16.i1', '16.l1'], 'normal_contains': ['64.c1'], 'normalizer': '1.a1', 'old_label': '32.g1', 'projective_image': '128.2163', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822036
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '32.h1', 'aut_quo_index': 24, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.b1', '16.g1', '16.h1', '16.m1', '16.bs1', '16.bv1', '16.ca1'], 'contains': ['64.c1', '64.d1', '64.e1'], 'core': '32.h1', 'coset_action_label': None, 'count': 6, 'diagramx': [4025, 2639, 4031, 2620], 'generators': [3823657107099841, 126940973252046, 1558053575931240], 'label': '256.53382.32.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1', 'normal_contained_in': ['16.b1', '16.g1', '16.h1', '16.m1'], 'normal_contains': ['64.c1', '64.d1', '64.e1'], 'normalizer': '1.a1', 'old_label': '32.h1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822037
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '32.i1', 'aut_quo_index': 48, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.c1', '16.g1', '16.i1', '16.j1', '16.m1', '16.bt1', '16.bw1', '16.cb1'], 'contains': ['64.c1', '64.e1'], 'core': '32.i1', 'coset_action_label': None, 'count': 6, 'diagramx': [4375, 3163, 4380, 3140], 'generators': [126940973252046, 3818425453162249, 1558053575931240], 'label': '256.53382.32.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1', 'normal_contained_in': ['16.c1', '16.g1', '16.i1', '16.j1', '16.m1'], 'normal_contains': ['64.c1', '64.e1'], 'normalizer': '1.a1', 'old_label': '32.i1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822094
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.g1', '32.m1', '32.bo1'], 'contains': ['128.d1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3781, -1, 3785, -1], 'generators': [3416619631436329, 126940973252046], 'label': '256.53382.64.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '64.q1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822038
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.j1', 'aut_quo_index': 48, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.d1', '16.f1', '16.h1', '16.j1', '16.l1', '16.bu1', '16.bx1', '16.cc1'], 'contains': ['64.c1', '64.k1'], 'core': '32.j1', 'coset_action_label': None, 'count': 12, 'diagramx': [4724, 4002, 4730, 3973], 'generators': [126940973252046, 799458240531169, 1558053575931240], 'label': '256.53382.32.j1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1', 'normal_contained_in': ['16.d1', '16.f1', '16.h1', '16.j1', '16.l1'], 'normal_contains': ['64.c1'], 'normalizer': '1.a1', 'old_label': '32.j1', 'projective_image': '128.2163', 'quotient_action_image': '8.3', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822039
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '32.k1', 'aut_quo_index': 26040, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 4096, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '16.k1', '16.l1', '16.m1', '16.n1', '16.o1'], 'contains': ['64.c1', '64.s1'], 'core': '32.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [3885, 6337, 3891, 6291], 'generators': [126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.32.k1', 'mobius_quo': 0, 'mobius_sub': -1024, 'normal_closure': '32.k1', 'normal_contained_in': ['16.e1', '16.k1', '16.l1', '16.m1', '16.n1', '16.o1'], 'normal_contains': ['64.c1'], 'normalizer': '1.a1', 'old_label': '32.k1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822040
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.p1', '16.q1', '16.r1'], 'contains': ['64.f1', '64.g1', '64.m1', '64.p1'], 'core': '128.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1780, -1, 1783, -1], 'generators': [1558053575931241, 126940973252046, 2917963830], 'label': '256.53382.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.l1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822041
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.l2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.q1', '16.r1'], 'contains': ['64.f1', '64.g1', '64.m1', '64.p2'], 'core': '128.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1675, -1, 1677, -1], 'generators': [1558053575931241, 9247650618384, 126940973252046], 'label': '256.53382.32.l2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.l2', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822042
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 24, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 384, 'centralizer': '16.b1', 'complements': ['64.h1', '64.n1', '64.t1'], 'conjugacy_class_count': 24, 'contained_in': ['2.a1', '2.f1'], 'contains': ['8.j1', '8.k1', '8.l1', '8.n1', '8.p1', '8.bp1', '8.bq1', '8.br1'], 'core': '4.h1', 'coset_action_label': None, 'count': 24, 'diagramx': [3931, 7458, 3931, 7404], 'generators': [3416619631436329, 1179824713041960, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.a1', '2.f1'], 'normal_contains': ['8.j1', '8.k1', '8.l1', '8.n1', '8.p1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822043
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.a1', '16.p1'], 'contains': ['64.f1', '64.h1', '64.n1', '64.q1'], 'core': '128.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3781, -1, 3785, -1], 'generators': [1558053575931241, 5276679855650928, 126940973252046], 'label': '256.53382.32.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '32.m1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822044
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.p1', '16.u1'], 'contains': ['64.f1', '64.r1'], 'core': '128.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2351, -1, 2354, -1], 'generators': [1558053575931241, 126940973252046, 795535216378854], 'label': '256.53382.32.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '32.n1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822045
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16384, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '16.q1'], 'contains': ['64.f1', '64.o1', '64.s1'], 'core': '128.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3207, -1, 3211, -1], 'generators': [1558053575931241, 126940973252046, 9250089176568], 'label': '256.53382.32.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.o1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822046
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 4096, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.bc1'], 'contains': ['64.h1', '64.t1'], 'core': '128.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [8785, -1, 8796, -1], 'generators': [1558053575931241, 4703819281996566, 795533299969728], 'label': '256.53382.32.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1', 'old_label': '32.p1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822047
    {'ambient': '256.53382', 'aut_centralizer_order': 3072, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1', '16.v1', '16.w1'], 'contains': ['64.a1', '64.g1', '64.i1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1116, -1, 1117, -1], 'generators': [1558053575931241, 2917963830, 1558053575931240], 'label': '256.53382.32.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.q1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822048
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '16.s1', '16.x1', '16.y1', '16.z1', '16.ba1', '16.bb1', '16.bc1'], 'contains': ['64.a1', '64.h1', '64.j1'], 'core': '64.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7473, -1, 7481, -1], 'generators': [1558053575931241, 5276679855650928, 1558053575931240], 'label': '256.53382.32.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.r1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822049
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.d1', '16.s1', '16.x1', '16.y1', '16.z1', '16.bb1', '16.bd1', '16.be1'], 'contains': ['64.a1', '64.k1'], 'core': '64.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7333, -1, 7341, -1], 'generators': [1558053575931241, 3080248359646008, 1558053575931240], 'label': '256.53382.32.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.s1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822050
    {'ambient': '256.53382', 'aut_centralizer_order': 3072, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1', '16.v1', '16.w1'], 'contains': ['64.a1', '64.l1'], 'core': '64.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [801, -1, 802, -1], 'generators': [1558053575931241, 1179826153715760, 1558053575931240], 'label': '256.53382.32.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.t1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822051
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.r1', '16.bf1', '16.bg1', '16.bn1'], 'contains': ['64.b1', '64.i1', '64.m1'], 'core': '64.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1396, -1, 1397, -1], 'generators': [1453437518158945, 2917963830, 1558053575931240], 'label': '256.53382.32.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.u1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822052
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.f1', '16.s1', '16.bh2', '16.bi1', '16.bj1', '16.bl1', '16.bo1'], 'contains': ['64.b1', '64.j1', '64.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [6850, -1, 6858, -1], 'generators': [1551513286714441, 3080248359646008, 1558053575931240], 'label': '256.53382.32.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.v1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822053
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 32, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.t1', '64.h1', '64.n1'], 'conjugacy_class_count': 32, 'contained_in': ['2.b1', '2.f1'], 'contains': ['8.j1', '8.m1', '8.o1'], 'core': '4.i1', 'coset_action_label': None, 'count': 32, 'diagramx': [5391, 9772, 5396, 9702], 'generators': [2586153351610447, 126940973252046, 3080248359646008, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.b1', '2.f1'], 'normal_contains': ['8.j1', '8.m1', '8.o1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822054
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '16.bh1', '16.bk1', '16.bl1', '16.bo1'], 'contains': ['64.b1', '64.j1', '64.n1'], 'core': '64.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6248, -1, 6256, -1], 'generators': [5276679855650928, 1453437518158945, 1558053575931240], 'label': '256.53382.32.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.w1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822055
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.d1', '16.bh1', '16.bj1', '16.bm1', '16.bo1'], 'contains': ['64.b1', '64.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6090, -1, 6098, -1], 'generators': [3080248359646008, 1453437518158945, 1558053575931240], 'label': '256.53382.32.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.x1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822056
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.t1', '16.bf1', '16.bg1', '16.bp1'], 'contains': ['64.b1', '64.l1'], 'core': '64.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [1535, -1, 1537, -1], 'generators': [1179826153715760, 1453437518158945, 1558053575931240], 'label': '256.53382.32.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.y1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822057
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.k1', '16.r1', '16.bn1', '16.br1', '16.bs1', '16.bt1', '16.bu1'], 'contains': ['64.c1', '64.i1', '64.p1', '64.p2'], 'core': '64.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [1991, -1, 1993, -1], 'generators': [126940973252046, 1558052138927761, 1558053575931240], 'label': '256.53382.32.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.z1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822058
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.l1', '16.s1', '16.bo1', '16.bv1', '16.bw1', '16.bx1', '16.bz1'], 'contains': ['64.c1', '64.j1', '64.k1'], 'core': '64.c1', 'coset_action_label': None, 'count': 48, 'diagramx': [6573, -1, 6581, -1], 'generators': [3416619631436329, 134878510137840, 1558053575931240], 'label': '256.53382.32.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.ba1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822059
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.n1', '16.t1', '16.bp1', '16.bs1', '16.bt1', '16.by1', '16.cc1'], 'contains': ['64.c1', '64.l1'], 'core': '64.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [2668, -1, 2672, -1], 'generators': [3823656628098631, 126940973252046, 1558053575931240], 'label': '256.53382.32.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.bb1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822060
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.o1', '16.u1', '16.bq1', '16.br1', '16.bu1', '16.by1', '16.ca1', '16.cb1', '16.cc1'], 'contains': ['64.c1', '64.r1'], 'core': '64.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [3347, -1, 3351, -1], 'generators': [3416617711802305, 126940973252046, 1558053575931240], 'label': '256.53382.32.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.bc1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822061
    {'ambient': '256.53382', 'aut_centralizer_order': 1536, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.v1', '16.bf1', '16.bs1'], 'contains': ['64.d1', '64.i1', '64.l1'], 'core': '64.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [976, -1, 977, -1], 'generators': [3823657107099841, 2917963830, 1558053575931240], 'label': '256.53382.32.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.bd1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822062
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.w1', '16.bf1', '16.bg1', '16.bs1', '16.bt1'], 'contains': ['64.e1', '64.i1', '64.l1'], 'core': '64.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [1256, -1, 1257, -1], 'generators': [3698119584319327, 2917963830, 1558053575931240], 'label': '256.53382.32.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.be1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822063
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.h1', '16.x1', '16.bh1', '16.bh2', '16.bv1', '16.ce1', '16.ce2'], 'contains': ['64.d1', '64.j1', '64.k1'], 'core': '64.d1', 'coset_action_label': None, 'count': 48, 'diagramx': [6984, -1, 6992, -1], 'generators': [3416619631436329, 1179824713041960, 1558053575931240], 'label': '256.53382.32.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bf1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822064
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 24, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 192, 'centralizer': '32.b1', 'complements': ['64.h1', '64.n1', '64.g1', '64.m1', '64.t1'], 'conjugacy_class_count': 24, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.m1', '8.n1', '8.p1'], 'core': '4.j1', 'coset_action_label': None, 'count': 24, 'diagramx': [5165, 8058, 5170, 8000], 'generators': [2586153351610447, 1179824713041960, 126940973252046, 795535216378854, 9250089176568, 1558053575931240], 'label': '256.53382.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.m1', '8.n1', '8.p1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822065
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.h1', '16.y1', '16.bh1', '16.bi1', '16.bw1', '16.cd1', '16.cf1', '16.cg1'], 'contains': ['64.e1', '64.j1', '64.k1'], 'core': '64.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [7158, -1, 7167, -1], 'generators': [3416619631436329, 1327599450054864, 1558053575931240], 'label': '256.53382.32.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bg1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822066
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['16.z1', '16.bj1', '16.bl1', '16.bx1', '16.bz1', '16.cd1', '16.ce1', '16.cf1'], 'contains': ['64.j1', '64.k1'], 'core': '128.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [8447, -1, 8458, -1], 'generators': [2586153351610447, 3080248359646008, 1558053575931240], 'label': '256.53382.32.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bh1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822067
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.i1', '16.ba1', '16.bh2', '16.bi1', '16.bk1', '16.bv1', '16.bw1', '16.cf1', '16.cg1'], 'contains': ['64.e1', '64.j1'], 'core': '64.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [6758, -1, 6766, -1], 'generators': [3416619631436329, 1187678429726520, 1558053575931240], 'label': '256.53382.32.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bi1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822068
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['16.bb1', '16.bj1', '16.bl1', '16.bx1', '16.bz1', '16.ce2', '16.cf1', '16.cg1'], 'contains': ['64.j1', '64.k1'], 'core': '128.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [8314, -1, 8324, -1], 'generators': [2579612544196687, 3080248359646008, 1558053575931240], 'label': '256.53382.32.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bj1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822069
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 4096, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.bc1', '16.bl1', '16.bz1', '16.ce1', '16.cg1'], 'contains': ['64.j1', '64.t1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [8587, -1, 8598, -1], 'generators': [2586153351610447, 5276679855650928, 1558053575931240], 'label': '256.53382.32.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bk1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822070
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.3', 'aut_weyl_index': 12288, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['16.j1', '16.bd1', '16.bh2', '16.bi1', '16.bm1', '16.bv1', '16.bw1', '16.cd1', '16.cf1'], 'contains': ['64.e1', '64.k1'], 'core': '64.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [6665, -1, 6673, -1], 'generators': [1187678429726520, 799458240531169, 1558053575931240], 'label': '256.53382.32.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bl1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822071
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 4096, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['16.be1', '16.bj1', '16.bx1', '16.cd1', '16.ce2'], 'contains': ['64.k1'], 'core': '128.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [8686, -1, 8697, -1], 'generators': [430599169507801, 3080248359646008, 1558053575931240], 'label': '256.53382.32.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '32.bm1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822072
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.q1', '16.bn1'], 'contains': ['64.m1', '64.o1', '64.p1', '64.p2'], 'core': '256.a1', 'coset_action_label': '32T4709', 'count': 48, 'diagramx': [1885, -1, 1888, -1], 'generators': [1551513286714441, 126940973252046, 2917963830], 'label': '256.53382.32.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.bn1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822073
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 24576, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['16.p1', '16.br1'], 'contains': ['64.p1', '64.q1', '64.r1'], 'core': '256.a1', 'coset_action_label': '32T3926', 'count': 192, 'diagramx': [2534, -1, 2538, -1], 'generators': [3416619631436329, 126940973252046, 2917963830], 'label': '256.53382.32.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '32.bo1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822074
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16384, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.k1', '16.q1'], 'contains': ['64.p1', '64.p2', '64.s1'], 'core': '256.a1', 'coset_action_label': '32T4706', 'count': 16, 'diagramx': [2096, -1, 2099, -1], 'generators': [126940973252046, 1558052138927761, 9250089176568], 'label': '256.53382.32.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '32.bp1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822095
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.n1', '32.bc1', '32.bo1'], 'contains': ['128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2820, -1, 2824, -1], 'generators': [3416617711802305, 126940973252046], 'label': '256.53382.64.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '64.r1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822075
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': 3, 'aut_stab_index': 32, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 256, 'centralizer': '32.b1', 'complements': ['64.g1', '64.m1', '64.h1', '64.n1', '64.t1'], 'conjugacy_class_count': 32, 'contained_in': ['2.d1', '2.f1'], 'contains': ['8.l1', '8.m1', '8.o1'], 'core': '4.k1', 'coset_action_label': None, 'count': 32, 'diagramx': [5602, 9137, 5608, 9071], 'generators': [2586153351610447, 126940973252046, 795535216378854, 3080248359646008, 9250089176568, 1558053575931240], 'label': '256.53382.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.d1', '2.f1'], 'normal_contains': ['8.l1', '8.m1', '8.o1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '128.2163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822076
    {'ambient': '256.53382', 'aut_centralizer_order': 49152, 'aut_label': '64.a1', 'aut_quo_index': 64, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.q1', '32.r1', '32.s1', '32.t1'], 'contains': ['128.a1', '128.b1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4200, 1102, 4205, 1094], 'generators': [1558053575931241, 1558053575931240], 'label': '256.53382.64.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1'], 'normal_contains': ['128.a1', '128.b1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.202', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.202', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822077
    {'ambient': '256.53382', 'aut_centralizer_order': 16384, 'aut_label': '64.b1', 'aut_quo_index': 24, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['32.a1', '32.d1', '32.e1', '32.f1', '32.u1', '32.v1', '32.w1', '32.x1', '32.y1'], 'contains': ['128.b1', '128.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4095, 1972, 4100, 1958], 'generators': [1453437518158945, 1558053575931240], 'label': '256.53382.64.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.a1', '32.d1', '32.e1', '32.f1'], 'normal_contains': ['128.b1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '128.2163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.46', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822078
    {'ambient': '256.53382', 'aut_centralizer_order': 16384, 'aut_label': '64.c1', 'aut_quo_index': 1344, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['32.a1', '32.f1', '32.g1', '32.h1', '32.i1', '32.j1', '32.k1', '32.z1', '32.ba1', '32.bb1', '32.bc1'], 'contains': ['128.b1', '128.d1'], 'core': '64.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [3885, 3370, 3891, 3346], 'generators': [126940973252046, 1558053575931240], 'label': '256.53382.64.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': ['32.a1', '32.f1', '32.g1', '32.h1', '32.i1', '32.j1', '32.k1'], 'normal_contains': ['128.b1'], 'normalizer': '1.a1', 'old_label': '64.c1', 'projective_image': '128.2163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822079
    {'ambient': '256.53382', 'aut_centralizer_order': 24576, 'aut_label': '64.d1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '32.d1', '32.h1', '32.bd1', '32.bf1'], 'contains': ['128.b1'], 'core': '64.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3996, 1398, 4001, 1388], 'generators': [3823657107099841, 1558053575931240], 'label': '256.53382.64.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1', 'normal_contained_in': ['32.b1', '32.d1', '32.h1'], 'normal_contains': ['128.b1'], 'normalizer': '1.a1', 'old_label': '64.d1', 'projective_image': '64.202', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.202', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822080
    {'ambient': '256.53382', 'aut_centralizer_order': 8192, 'aut_label': '64.e1', 'aut_quo_index': 48, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['32.c1', '32.d1', '32.e1', '32.h1', '32.i1', '32.be1', '32.bg1', '32.bi1', '32.bl1'], 'contains': ['128.b1'], 'core': '64.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [4853, 1676, 4782, 1664], 'generators': [3698119584319327, 1558053575931240], 'label': '256.53382.64.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.e1', 'normal_contained_in': ['32.c1', '32.d1', '32.e1', '32.h1', '32.i1'], 'normal_contains': ['128.b1'], 'normalizer': '1.a1', 'old_label': '64.e1', 'projective_image': '128.2163', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.46', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822081
    {'ambient': '256.53382', 'aut_centralizer_order': 8192, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['32.a1', '32.l1', '32.l2', '32.m1', '32.n1', '32.o1'], 'contains': ['128.a1', '128.c1', '128.d1'], 'core': '128.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3312, -1, 3316, -1], 'generators': [1558053575931241, 126940973252046], 'label': '256.53382.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.f1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822082
    {'ambient': '256.53382', 'aut_centralizer_order': 3072, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.l1', '32.l2', '32.q1'], 'contains': ['128.a1', '128.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1727, -1, 1730, -1], 'generators': [1558053575931241, 2917963830], 'label': '256.53382.64.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.g1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822083
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.m1', '32.p1', '32.r1'], 'contains': ['128.a1', '128.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7005, -1, 7012, -1], 'generators': [1558053575931241, 5276679855650928], 'label': '256.53382.64.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '64.h1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822084
    {'ambient': '256.53382', 'aut_centralizer_order': 6144, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.q1', '32.u1', '32.z1', '32.bd1', '32.be1'], 'contains': ['128.b1', '128.e1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1396, -1, 1397, -1], 'generators': [1558052138927761, 1558053575931240], 'label': '256.53382.64.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.i1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822085
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.g1', '32.r1', '32.v1', '32.w1', '32.ba1', '32.bf1', '32.bg1', '32.bh1', '32.bi1', '32.bj1', '32.bk1'], 'contains': ['128.b1', '128.f1'], 'core': '128.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [6900, -1, 6907, -1], 'generators': [3416619631436329, 1558053575931240], 'label': '256.53382.64.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '64.j1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822086
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': 3, 'aut_stab_index': 8, 'aut_weyl_group': '1536.408640541', 'aut_weyl_index': 64, 'centralizer': '32.b1', 'complements': ['64.g1', '64.m1'], 'conjugacy_class_count': 8, 'contained_in': ['2.e1', '2.f1'], 'contains': ['8.n1', '8.o1', '8.bs1', '8.bt1', '8.bu1'], 'core': '4.l1', 'coset_action_label': None, 'count': 8, 'diagramx': [7328, 8621, 7336, 8558], 'generators': [2586153351610447, 795533299969728, 1179824713041960, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.e1', '2.f1'], 'normal_contains': ['8.n1', '8.o1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822087
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.j1', '32.s1', '32.v1', '32.x1', '32.ba1', '32.bf1', '32.bg1', '32.bh1', '32.bj1', '32.bl1', '32.bm1'], 'contains': ['128.b1'], 'core': '128.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [6801, -1, 6808, -1], 'generators': [799458240531169, 1558053575931240], 'label': '256.53382.64.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '64.k1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822088
    {'ambient': '256.53382', 'aut_centralizer_order': 6144, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.t1', '32.y1', '32.bb1', '32.bd1', '32.be1'], 'contains': ['128.b1'], 'core': '128.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1276, -1, 1278, -1], 'generators': [3823656628098631, 1558053575931240], 'label': '256.53382.64.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.l1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822089
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.l1', '32.l2', '32.u1', '32.bn1'], 'contains': ['128.c1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1833, -1, 1835, -1], 'generators': [1453437518158945, 2917963830], 'label': '256.53382.64.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.m1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822090
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['32.m1', '32.w1'], 'contains': ['128.c1', '128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4604, -1, 4383, -1], 'generators': [5276679855650928, 1453437518158945], 'label': '256.53382.64.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '64.n1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822091
    {'ambient': '256.53382', 'aut_centralizer_order': 4096, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['32.f1', '32.o1', '32.bn1'], 'contains': ['128.c1', '128.d1'], 'core': '256.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3207, -1, 3211, -1], 'generators': [1551513286714441, 126940973252046], 'label': '256.53382.64.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.o1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822092
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 49152, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['32.l1', '32.z1', '32.bn1', '32.bo1', '32.bp1'], 'contains': ['128.d1', '128.e1'], 'core': '256.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2044, -1, 2046, -1], 'generators': [126940973252046, 1558052138927761], 'label': '256.53382.64.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.p1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822097
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '16.b1', 'complements': ['128.f1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.e1', '4.g1', '4.h1', '4.m1', '4.n1', '4.o1', '4.s1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3318, 4265, 3323, 4233], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.e1', '4.g1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822098
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '512.7540510', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.q1', '8.r1', '8.t1', '8.x1', '8.z1', '8.bb1', '8.bp1'], 'core': '8.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2174, -1, 2177, -1], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.4.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.m1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822099
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 16384, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['32.p1', '32.bk1'], 'contains': ['128.f1'], 'core': '256.a1', 'coset_action_label': None, 'count': 128, 'diagramx': [8587, -1, 8598, -1], 'generators': [2586153351610447, 5276679855650928], 'label': '256.53382.64.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1', 'old_label': '64.t1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822100
    {'ambient': '256.53382', 'aut_centralizer_order': 49152, 'aut_label': '128.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '1.a1', 'complements': ['2.f1'], 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '64.f1', '64.g1', '64.h1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4088, 1252, 4094, 1243], 'generators': [1558053575931241], 'label': '256.53382.128.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': '128.1757', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.1757', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822101
    {'ambient': '256.53382', 'aut_centralizer_order': 98304, 'aut_label': '128.b1', 'aut_quo_index': 768, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.e1', '64.i1', '64.j1', '64.k1', '64.l1'], 'contains': ['256.a1'], 'core': '128.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3996, 1537, 4001, 1526], 'generators': [1558053575931240], 'label': '256.53382.128.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1', 'normal_contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.e1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.b1', 'projective_image': '128.2163', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2163', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822102
    {'ambient': '256.53382', 'aut_centralizer_order': 16384, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['64.b1', '64.f1', '64.m1', '64.n1', '64.o1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3558, -1, 3562, -1], 'generators': [1453437518158945], 'label': '256.53382.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '128.c1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822103
    {'ambient': '256.53382', 'aut_centralizer_order': 16384, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['64.c1', '64.f1', '64.o1', '64.p1', '64.p2', '64.q1', '64.r1', '64.s1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3312, -1, 3316, -1], 'generators': [126940973252046], 'label': '256.53382.128.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '128.d1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822104
    {'ambient': '256.53382', 'aut_centralizer_order': 6144, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['64.g1', '64.i1', '64.m1', '64.p1', '64.p2'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1885, -1, 1888, -1], 'generators': [1558052138927761], 'label': '256.53382.128.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '128.e1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822105
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 98304, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['64.h1', '64.j1', '64.n1', '64.q1', '64.t1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5737, -1, 5619, -1], 'generators': [3416619631436329], 'label': '256.53382.128.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1', 'old_label': '128.f1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822106
    {'ambient': '256.53382', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '128.b1', '128.c1', '128.d1', '128.e1', '128.f1'], 'contains': [], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3691, 1395, 3868, 1381], 'generators': [], 'label': '256.53382.256.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1', '128.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': '256.53382', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822107
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 48, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.q1', '8.s1', '8.x1', '8.ba1', '8.bq1'], 'core': '8.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2786, -1, 2788, -1], 'generators': [1558053575931241, 795533299969728, 1187678429726520, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.4.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.n1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822108
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 48, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.s1', '8.t1', '8.ba1', '8.bb1', '8.br1'], 'core': '8.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2545, -1, 2547, -1], 'generators': [3411380306487624, 1558053575931241, 1187678429726520, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.4.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.o1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822109
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2048.clr', 'aut_weyl_index': 48, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.e1'], 'contains': ['8.c1', '8.v1', '8.w1', '8.bc1', '8.be1', '8.bg1', '8.bs1'], 'core': '8.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [7908, -1, 7917, -1], 'generators': [3411380306487624, 1558053575931241, 1187678429726520, 359890668724326, 126940973252046, 1558053575931240], 'label': '256.53382.4.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '4.p1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822110
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1024.dlf', 'aut_weyl_index': 96, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.e1'], 'contains': ['8.a1', '8.u1', '8.w1', '8.y1', '8.bc1', '8.bd1', '8.bd2', '8.be1', '8.bf1', '8.bh1', '8.bt1'], 'core': '8.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8567, -1, 8576, -1], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 359890668724326, 126940973252046, 1558053575931240], 'label': '256.53382.4.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '4.q1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822111
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2048.clr', 'aut_weyl_index': 48, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.e1'], 'contains': ['8.b1', '8.v1', '8.y1', '8.be1', '8.bf1', '8.bi1', '8.bu1'], 'core': '8.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7666, -1, 7675, -1], 'generators': [1558053575931241, 795533299969728, 1187678429726520, 359890668724326, 126940973252046, 1558053575931240], 'label': '256.53382.4.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '4.r1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822112
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '512.6344809', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.a1'], 'contains': ['8.i1', '8.bj1', '8.bk1', '8.bl1', '8.bo1', '8.bp1', '8.bq1', '8.br1'], 'core': '8.i1', 'coset_action_label': None, 'count': 24, 'diagramx': [3318, -1, 3323, -1], 'generators': [1551513286714441, 795533299969728, 1179824713041960, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.4.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.s1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822113
    {'ambient': '256.53382', 'aut_centralizer_order': 8, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '512.7530076', 'aut_weyl_index': 192, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.e1'], 'contains': ['8.i1', '8.bg1', '8.bh1', '8.bi1', '8.bm1', '8.bn1', '8.bs1', '8.bt1', '8.bu1'], 'core': '8.i1', 'coset_action_label': None, 'count': 24, 'diagramx': [7473, -1, 7481, -1], 'generators': [1551513286714441, 795533299969728, 1179824713041960, 359890668724326, 126940973252046, 1558053575931240], 'label': '256.53382.4.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '4.t1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822114
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 6, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 768, 'centralizer': '8.a1', 'complements': ['32.bo1'], 'conjugacy_class_count': 6, 'contained_in': ['4.e1', '4.m1', '4.q1'], 'contains': ['16.a1', '16.b1', '16.d1', '16.h1', '16.x1', '16.y1', '16.bh1'], 'core': '8.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6317, 1186, 6325, 1178], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['16.a1', '16.b1', '16.d1', '16.h1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822115
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': ['32.bo1'], 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '4.n1', '4.r1'], 'contains': ['16.a1', '16.c1', '16.i1', '16.ba1', '16.bk1'], 'core': '8.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6115, 1795, 6122, 1782], 'generators': [1558053575931241, 795533299969728, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['16.a1', '16.c1', '16.i1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822116
    {'ambient': '256.53382', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '6144.gk', 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.f1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.f1', '4.i1'], 'core': '2.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5102, 6837, 5107, 6788], 'generators': [1558053575931241, 795533299969728, 126940973252046, 2210464151530206, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.f1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822117
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': ['32.bo1'], 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '4.o1', '4.p1'], 'contains': ['16.c1', '16.d1', '16.j1', '16.bd1', '16.bm1'], 'core': '8.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5482, 577, 5489, 574], 'generators': [3411380306487624, 1558053575931241, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['16.c1', '16.d1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822118
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '8.d1', 'aut_quo_index': 7, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 512, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1'], 'contains': ['16.e1', '16.k1', '16.q1', '16.r1', '16.bn1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [938, 4727, 940, 4692], 'generators': [1558053575931241, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.a1', '4.b1'], 'normal_contains': ['16.e1', '16.k1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822119
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 6, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.c1', '4.d1', '4.e1', '4.f1'], 'contains': ['16.a1', '16.d1', '16.e1', '16.f1', '16.l1', '16.s1', '16.bo1'], 'core': '8.e1', 'coset_action_label': None, 'count': 6, 'diagramx': [5133, 3656, 5139, 3629], 'generators': [1558053575931241, 126940973252046, 3080248359646008, 9250089176568, 1558053575931240], 'label': '256.53382.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.c1', '4.d1', '4.e1', '4.f1'], 'normal_contains': ['16.a1', '16.d1', '16.e1', '16.f1', '16.l1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822120
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '8.f1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 512, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.e1', '4.g1'], 'contains': ['16.b1', '16.c1', '16.e1', '16.g1', '16.m1'], 'core': '8.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [4930, 2404, 4936, 2386], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.b1', '4.e1', '4.g1'], 'normal_contains': ['16.b1', '16.c1', '16.e1', '16.g1', '16.m1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822121
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '8.g1', 'aut_quo_index': 7, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 512, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.c1'], 'contains': ['16.e1', '16.n1', '16.t1', '16.bp1'], 'core': '8.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [1537, 4265, 1538, 4233], 'generators': [1558053575931241, 126940973252046, 1179826153715760, 9250089176568, 1558053575931240], 'label': '256.53382.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.b1', '4.c1'], 'normal_contains': ['16.e1', '16.n1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822122
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 42, 'aut_stab_index': 6, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.c1', '4.d1', '4.g1'], 'contains': ['16.e1', '16.o1', '16.u1', '16.bq1'], 'core': '8.h1', 'coset_action_label': None, 'count': 6, 'diagramx': [3777, 5247, 3782, 5209], 'generators': [1558053575931241, 126940973252046, 795535216378854, 9250089176568, 1558053575931240], 'label': '256.53382.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.a1', '4.c1', '4.d1', '4.g1'], 'normal_contains': ['16.e1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822123
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 2, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': ['32.bo1'], 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '4.s1', '4.t1'], 'contains': ['16.f1', '16.g1', '16.h1', '16.i1', '16.j1', '16.bh2', '16.bi1'], 'core': '8.i1', 'coset_action_label': None, 'count': 12, 'diagramx': [5906, 3028, 5913, 3006], 'generators': [1551513286714441, 795533299969728, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.8.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['16.f1', '16.g1', '16.h1', '16.i1', '16.j1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822124
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': 21, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': ['32.p1'], 'conjugacy_class_count': 24, 'contained_in': ['4.a1', '4.h1', '4.i1'], 'contains': ['16.k1', '16.l1', '16.o1', '16.br1', '16.bu1'], 'core': '8.j1', 'coset_action_label': None, 'count': 24, 'diagramx': [4009, 8640, 4014, 8578], 'generators': [3416619631436329, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.8.j1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1', 'normal_contained_in': ['4.a1', '4.h1', '4.i1'], 'normal_contains': ['16.k1', '16.l1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.j1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822125
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '8.k1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '96.226', 'aut_weyl_index': 1024, 'centralizer': '4.b1', 'complements': ['32.p1'], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.h1'], 'contains': ['16.k1', '16.m1', '16.n1', '16.bs1', '16.bt1'], 'core': '8.k1', 'coset_action_label': None, 'count': 4, 'diagramx': [1738, 6556, 1740, 6509], 'generators': [3823657107099841, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.8.k1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1', 'normal_contained_in': ['4.b1', '4.h1'], 'normal_contains': ['16.k1', '16.m1', '16.n1'], 'normalizer': '1.a1', 'old_label': '8.k1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822126
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.l1', 'aut_quo_index': 21, 'aut_stab_index': 24, 'aut_weyl_group': '64.202', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': ['32.p1'], 'conjugacy_class_count': 24, 'contained_in': ['4.c1', '4.h1', '4.k1'], 'contains': ['16.l1', '16.n1', '16.o1', '16.by1', '16.cc1'], 'core': '8.l1', 'coset_action_label': None, 'count': 24, 'diagramx': [4247, 7924, 4253, 7866], 'generators': [3416619631436329, 126940973252046, 1179826153715760, 9250089176568, 1558053575931240], 'label': '256.53382.8.l1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1', 'normal_contained_in': ['4.c1', '4.h1', '4.k1'], 'normal_contains': ['16.l1', '16.n1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.l1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822127
    {'ambient': '256.53382', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '8192.baa', 'aut_weyl_index': 12, 'centralizer': '32.b1', 'complements': ['128.f1', '128.e1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.g1', '4.j1'], 'core': '2.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4930, 5366, 4935, 5327], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 359892628275870, 9250089176568, 1558053575931240], 'label': '256.53382.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.g1', '4.j1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822128
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': 42, 'aut_stab_index': 48, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '32.b1', 'complements': ['32.p1'], 'conjugacy_class_count': 48, 'contained_in': ['4.d1', '4.i1', '4.j1', '4.k1'], 'contains': ['16.l1', '16.o1'], 'core': '8.m1', 'coset_action_label': None, 'count': 48, 'diagramx': [5307, 9195, 5314, 9128], 'generators': [2586153351610447, 126940973252046, 795535216378854, 9250089176568, 1558053575931240], 'label': '256.53382.8.m1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1', 'normal_contained_in': ['4.d1', '4.i1', '4.j1', '4.k1'], 'normal_contains': ['16.l1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.m1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822129
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.n1', 'aut_quo_index': 42, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '4.h1', '4.j1', '4.l1'], 'contains': ['16.h1', '16.i1', '16.j1', '16.l1', '16.m1', '16.bv1', '16.bw1'], 'core': '8.n1', 'coset_action_label': None, 'count': 12, 'diagramx': [5692, 5932, 5698, 5889], 'generators': [3416619631436329, 1179824713041960, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.8.n1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.n1', 'normal_contained_in': ['4.e1', '4.h1', '4.j1', '4.l1'], 'normal_contains': ['16.h1', '16.i1', '16.j1', '16.l1', '16.m1'], 'normalizer': '1.a1', 'old_label': '8.n1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822130
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': 42, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 512, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 16, 'contained_in': ['4.f1', '4.i1', '4.k1', '4.l1'], 'contains': ['16.l1', '16.bx1', '16.bz1'], 'core': '8.o1', 'coset_action_label': None, 'count': 16, 'diagramx': [7134, 9630, 7142, 9560], 'generators': [2586153351610447, 126940973252046, 3080248359646008, 9250089176568, 1558053575931240], 'label': '256.53382.8.o1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.o1', 'normal_contained_in': ['4.f1', '4.i1', '4.k1', '4.l1'], 'normal_contains': ['16.l1'], 'normalizer': '1.a1', 'old_label': '8.o1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822131
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.p1', 'aut_quo_index': 21, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': ['32.p1'], 'conjugacy_class_count': 12, 'contained_in': ['4.g1', '4.h1', '4.j1'], 'contains': ['16.m1', '16.o1', '16.ca1', '16.cb1'], 'core': '8.p1', 'coset_action_label': None, 'count': 12, 'diagramx': [4716, 7200, 4722, 7147], 'generators': [3823657107099841, 126940973252046, 795535216378854, 9250089176568, 1558053575931240], 'label': '256.53382.8.p1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.p1', 'normal_contained_in': ['4.g1', '4.h1', '4.j1'], 'normal_contains': ['16.m1', '16.o1'], 'normalizer': '1.a1', 'old_label': '8.p1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822132
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.m1', '4.n1'], 'contains': ['16.a1', '16.p1', '16.r1', '16.u1', '16.br1'], 'core': '16.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1334, -1, 1335, -1], 'generators': [1558053575931241, 5276679855650928, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.q1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822133
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 1536, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '4.m1'], 'contains': ['16.b1', '16.r1', '16.t1', '16.v1', '16.w1', '16.bf1', '16.bs1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [381, -1, 382, -1], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.r1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822134
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '4.n1', '4.o1'], 'contains': ['16.c1', '16.r1', '16.t1', '16.w1', '16.bg1', '16.bt1'], 'core': '16.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [583, -1, 584, -1], 'generators': [1558053575931241, 1187678429726520, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.s1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822135
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '4.m1', '4.o1'], 'contains': ['16.d1', '16.r1', '16.u1', '16.bu1'], 'core': '16.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [1112, -1, 1113, -1], 'generators': [1558053575931241, 126940973252046, 3080248359646008, 2917963830, 1558053575931240], 'label': '256.53382.8.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.t1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822136
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.e1', '4.q1'], 'contains': ['16.b1', '16.s1', '16.x1', '16.ba1', '16.bd1', '16.bh2', '16.bv1'], 'core': '16.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6739, -1, 6748, -1], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 134878510137840, 1558053575931240], 'label': '256.53382.8.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.u1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822137
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.e1', '4.p1', '4.r1'], 'contains': ['16.c1', '16.s1', '16.y1', '16.ba1', '16.bd1', '16.bi1', '16.bw1'], 'core': '16.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [6954, -1, 6962, -1], 'generators': [1558053575931241, 795533299969728, 134878510137840, 1327599450054864, 1558053575931240], 'label': '256.53382.8.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.v1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822138
    {'ambient': '256.53382', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '6144.gk', 'aut_weyl_index': 16, 'centralizer': '32.b1', 'complements': ['128.f1', '128.e1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.f1', '4.k1'], 'core': '2.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [5274, 6321, 5279, 6276], 'generators': [1558053575931241, 795533299969728, 126940973252046, 2210464151530206, 359892628275870, 9250089176568, 1558053575931240], 'label': '256.53382.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.f1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '64.202', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822139
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.f1', '4.p1', '4.q1'], 'contains': ['16.d1', '16.s1', '16.z1', '16.bb1', '16.be1', '16.bj1', '16.bx1'], 'core': '16.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [8670, -1, 8681, -1], 'generators': [3411380306487624, 1558053575931241, 126940973252046, 2210464151530206, 1558053575931240], 'label': '256.53382.8.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.w1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822140
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '4.m1', '4.n1'], 'contains': ['16.a1', '16.t1', '16.u1', '16.by1'], 'core': '16.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2174, -1, 2177, -1], 'generators': [1558053575931241, 5276679855650928, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.8.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.x1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822141
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.f1', '4.q1', '4.r1'], 'contains': ['16.a1', '16.s1', '16.z1', '16.bb1', '16.bc1', '16.bl1', '16.bz1'], 'core': '16.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8461, -1, 8472, -1], 'generators': [1558053575931241, 795533299969728, 126940973252046, 2210464151530206, 1558053575931240], 'label': '256.53382.8.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.y1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822142
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.g1', '4.m1'], 'contains': ['16.b1', '16.u1', '16.ca1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2572, -1, 2575, -1], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.8.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.z1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822143
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 384, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.g1', '4.n1', '4.o1'], 'contains': ['16.c1', '16.u1', '16.cb1'], 'core': '16.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2780, -1, 2783, -1], 'generators': [1558053575931241, 1187678429726520, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.8.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.ba1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822144
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '4.m1', '4.o1'], 'contains': ['16.d1', '16.t1', '16.u1', '16.cc1'], 'core': '16.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [1946, -1, 1948, -1], 'generators': [1558053575931241, 126940973252046, 795535216378854, 3080248359646008, 1558053575931240], 'label': '256.53382.8.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bb1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822145
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 192, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.p1', '4.q1'], 'contains': ['16.y1', '16.z1', '16.bd1', '16.be1', '16.cd1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [9297, -1, 9308, -1], 'generators': [3411380306487624, 1558053575931241, 1187678429726520, 359890668724326, 1558053575931240], 'label': '256.53382.8.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bc1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822146
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 128, 'centralizer': '8.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.q1'], 'contains': ['16.x1', '16.z1', '16.bc1', '16.ce1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9500, -1, 9512, -1], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 359890668724326, 1558053575931240], 'label': '256.53382.8.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bd1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822147
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bd2', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 128, 'centralizer': '8.bd2', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.q1'], 'contains': ['16.x1', '16.bb1', '16.be1', '16.ce2'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9708, -1, 9720, -1], 'generators': [1558053575931241, 921165952518414, 1179824713041960, 359890668724326, 1558053575931240], 'label': '256.53382.8.bd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bd2', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822148
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 384, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.p1', '4.q1', '4.r1'], 'contains': ['16.y1', '16.z1', '16.ba1', '16.bb1', '16.bd1', '16.cf1'], 'core': '32.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [8039, -1, 8048, -1], 'generators': [1558053575931241, 921165952518414, 359890668724326, 1327599450054864, 1558053575931240], 'label': '256.53382.8.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.be1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822149
    {'ambient': '256.53382', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '32.b1', 'complements': ['128.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '4.l1', '4.p1', '4.q1', '4.r1', '4.t1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7401, 5844, 7408, 5801], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 126940973252046, 359890668724326, 9250089176568, 1558053575931240], 'label': '256.53382.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822150
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 192, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.q1', '4.r1'], 'contains': ['16.y1', '16.ba1', '16.bb1', '16.bc1', '16.cg1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [9094, -1, 9105, -1], 'generators': [1558053575931241, 795533299969728, 359890668724326, 1327599450054864, 1558053575931240], 'label': '256.53382.8.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bf1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822151
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.928', 'aut_weyl_index': 768, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.p1', '4.t1'], 'contains': ['16.bi1', '16.bj1', '16.bm1', '16.cd1', '16.cf1'], 'core': '32.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [7858, -1, 7868, -1], 'generators': [1445593386585991, 921165952518414, 359890668724326, 1327599450054864, 1558053575931240], 'label': '256.53382.8.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bg1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822152
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '64.264', 'aut_weyl_index': 1536, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['4.q1', '4.t1'], 'contains': ['16.bh1', '16.bh2', '16.bj1', '16.bl1', '16.cd1', '16.ce1', '16.ce2', '16.cf1', '16.cg1'], 'core': '32.d1', 'coset_action_label': None, 'count': 96, 'diagramx': [8885, -1, 8896, -1], 'generators': [795533299969728, 1179824713041960, 359890668724326, 1453437518158945, 1558053575931240], 'label': '256.53382.8.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bh1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822153
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.928', 'aut_weyl_index': 768, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.r1', '4.t1'], 'contains': ['16.bi1', '16.bk1', '16.bl1', '16.cf1', '16.cg1'], 'core': '32.e1', 'coset_action_label': None, 'count': 48, 'diagramx': [7713, -1, 7723, -1], 'generators': [1551513286714441, 795533299969728, 359890668724326, 1327599450054864, 1558053575931240], 'label': '256.53382.8.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bi1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822154
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.a1', '4.s1'], 'contains': ['16.f1', '16.bn1', '16.bq1', '16.br1', '16.bu1'], 'core': '16.f1', 'coset_action_label': None, 'count': 24, 'diagramx': [2999, -1, 3003, -1], 'generators': [1551513286714441, 126940973252046, 3080248359646008, 2917963830, 1558053575931240], 'label': '256.53382.8.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bj1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822155
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 1536, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '4.s1'], 'contains': ['16.g1', '16.bf1', '16.bg1', '16.bn1', '16.bp1', '16.bs1', '16.bt1'], 'core': '16.g1', 'coset_action_label': None, 'count': 12, 'diagramx': [785, -1, 786, -1], 'generators': [1551513286714441, 1179824713041960, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bk1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822156
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.c1', '4.s1'], 'contains': ['16.f1', '16.bp1', '16.bq1', '16.by1', '16.cc1'], 'core': '16.f1', 'coset_action_label': None, 'count': 24, 'diagramx': [3529, -1, 3534, -1], 'generators': [1551513286714441, 126940973252046, 795535216378854, 3080248359646008, 1558053575931240], 'label': '256.53382.8.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bl1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822157
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.264', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '4.t1'], 'contains': ['16.g1', '16.bh1', '16.bh2', '16.bi1', '16.bk1', '16.bm1', '16.bo1', '16.bv1', '16.bw1'], 'core': '16.g1', 'coset_action_label': None, 'count': 24, 'diagramx': [6525, -1, 6533, -1], 'generators': [795533299969728, 1179824713041960, 1453437518158945, 134878510137840, 1558053575931240], 'label': '256.53382.8.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bm1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822158
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.f1', '4.t1'], 'contains': ['16.f1', '16.bj1', '16.bl1', '16.bo1', '16.bx1', '16.bz1'], 'core': '16.f1', 'coset_action_label': None, 'count': 48, 'diagramx': [7279, -1, 7287, -1], 'generators': [1551513286714441, 795533299969728, 126940973252046, 2210464151530206, 1558053575931240], 'label': '256.53382.8.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bn1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822159
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.g1', '4.s1'], 'contains': ['16.g1', '16.bq1', '16.ca1', '16.cb1'], 'core': '16.g1', 'coset_action_label': None, 'count': 12, 'diagramx': [4489, -1, 4494, -1], 'generators': [1551513286714441, 1179824713041960, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.8.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bo1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822160
    {'ambient': '256.53382', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 16, 'aut_weyl_group': '3072.sh', 'aut_weyl_index': 32, 'centralizer': '32.b1', 'complements': ['128.a1', '128.c1', '128.e1', '128.f1'], 'conjugacy_class_count': 16, 'contained_in': ['1.a1'], 'contains': ['4.h1', '4.i1', '4.j1', '4.k1', '4.l1'], 'core': '2.f1', 'coset_action_label': None, 'count': 16, 'diagramx': [5446, 8340, 5452, 8279], 'generators': [2586153351610447, 795533299969728, 1179824713041960, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.h1', '4.i1', '4.j1', '4.k1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '64.202', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 48822161
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '32.51', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['4.h1', '4.m1', '4.s1'], 'contains': ['16.h1', '16.br1', '16.bs1', '16.bu1', '16.by1', '16.ca1', '16.cc1'], 'core': '16.h1', 'coset_action_label': None, 'count': 96, 'diagramx': [2383, -1, 2386, -1], 'generators': [3416619631436329, 1179824713041960, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bp1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822162
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.h1', '4.n1', '4.s1'], 'contains': ['16.i1', '16.br1', '16.bt1', '16.by1', '16.cb1'], 'core': '16.i1', 'coset_action_label': None, 'count': 48, 'diagramx': [3329, -1, 3333, -1], 'generators': [3416619631436329, 1187678429726520, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.8.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.bq1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822163
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 768, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.h1', '4.o1', '4.s1'], 'contains': ['16.j1', '16.bt1', '16.bu1', '16.cb1', '16.cc1'], 'core': '16.j1', 'coset_action_label': None, 'count': 48, 'diagramx': [3184, -1, 3188, -1], 'generators': [1187678429726520, 126940973252046, 799458240531169, 2917963830, 1558053575931240], 'label': '256.53382.8.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.br1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822164
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.928', 'aut_weyl_index': 768, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.l1', '4.p1', '4.t1'], 'contains': ['16.j1', '16.bw1', '16.bx1', '16.cd1', '16.cf1'], 'core': '16.j1', 'coset_action_label': None, 'count': 48, 'diagramx': [7569, -1, 7578, -1], 'generators': [3411380306487624, 2586153351610447, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.8.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bs1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822165
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '64.264', 'aut_weyl_index': 1536, 'centralizer': '16.x1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['4.l1', '4.q1', '4.t1'], 'contains': ['16.h1', '16.bv1', '16.bx1', '16.bz1', '16.cd1', '16.ce1', '16.ce2', '16.cf1', '16.cg1'], 'core': '16.h1', 'coset_action_label': None, 'count': 96, 'diagramx': [8253, -1, 8263, -1], 'generators': [2586153351610447, 795533299969728, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.8.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bt1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 48822166
    {'ambient': '256.53382', 'aut_centralizer_order': 16, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '128.928', 'aut_weyl_index': 768, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.l1', '4.r1', '4.t1'], 'contains': ['16.i1', '16.bw1', '16.bz1', '16.cf1', '16.cg1'], 'core': '16.i1', 'coset_action_label': None, 'count': 48, 'diagramx': [7424, -1, 7433, -1], 'generators': [2586153351610447, 795533299969728, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.8.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '8.bu1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 48822167
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 3072, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.b1', '8.e1', '8.q1', '8.x1', '8.y1'], 'contains': ['32.a1', '32.g1', '32.m1', '32.r1', '32.w1'], 'core': '16.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5045, 2739, 5051, 2719], 'generators': [1558053575931241, 5276679855650928, 126940973252046, 1558053575931240], 'label': '256.53382.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.e1'], 'normal_contains': ['32.a1', '32.g1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '64.202', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822168
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '8.f1', '8.r1', '8.u1', '8.z1'], 'contains': ['32.a1', '32.b1', '32.c1', '32.d1', '32.h1'], 'core': '16.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4312, 462, 4317, 459], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.f1'], 'normal_contains': ['32.a1', '32.b1', '32.c1', '32.d1', '32.h1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822169
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.c1', 'aut_quo_index': 8, 'aut_stab_index': 3, 'aut_weyl_group': '32.49', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.b1', '8.c1', '8.f1', '8.s1', '8.v1', '8.ba1'], 'contains': ['32.a1', '32.c1', '32.e1', '32.i1'], 'core': '16.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4513, 1067, 4519, 1059], 'generators': [1558053575931241, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.c1', '8.f1'], 'normal_contains': ['32.a1', '32.c1', '32.e1', '32.i1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822170
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 8, 'aut_stab_index': 6, 'aut_weyl_group': '32.49', 'aut_weyl_index': 3072, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.c1', '8.e1', '8.t1', '8.w1', '8.bb1'], 'contains': ['32.a1', '32.j1', '32.s1', '32.x1'], 'core': '16.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [4890, 2277, 4897, 2260], 'generators': [1558053575931241, 126940973252046, 3080248359646008, 1558053575931240], 'label': '256.53382.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.a1', '8.c1', '8.e1'], 'normal_contains': ['32.a1', '32.j1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '64.202', 'quotient_action_image': '8.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822171
    {'ambient': '256.53382', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '512.7577399', 'aut_weyl_index': 192, 'centralizer': '16.b1', 'complements': ['64.t1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.d1', '8.e1', '8.h1', '8.j1', '8.q1', '8.t1', '8.bj1'], 'core': '4.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3072, 5270, 3076, 5231], 'generators': [1558053575931241, 126940973252046, 3080248359646008, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.d1', '8.e1', '8.h1', '8.j1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822172
    {'ambient': '256.53382', 'aut_centralizer_order': 2048, 'aut_label': '16.e1', 'aut_quo_index': 840, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'contains': ['32.a1', '32.f1', '32.k1', '32.o1'], 'core': '16.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [3241, 5247, 3246, 5209], 'generators': [1558053575931241, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.16.e1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.e1', 'normal_contained_in': ['8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'normal_contains': ['32.a1', '32.f1', '32.k1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822173
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 4, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['8.e1', '8.i1', '8.bj1', '8.bl1', '8.bn1'], 'contains': ['32.f1', '32.g1', '32.j1', '32.v1'], 'core': '16.f1', 'coset_action_label': None, 'count': 12, 'diagramx': [4702, 4823, 4708, 4788], 'generators': [1551513286714441, 126940973252046, 3080248359646008, 1558053575931240], 'label': '256.53382.16.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': ['8.e1', '8.i1'], 'normal_contains': ['32.f1', '32.g1', '32.j1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822174
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.g1', 'aut_quo_index': 4, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.f1', '8.i1', '8.bk1', '8.bm1', '8.bo1'], 'contains': ['32.d1', '32.e1', '32.f1', '32.h1', '32.i1'], 'core': '16.g1', 'coset_action_label': None, 'count': 6, 'diagramx': [4111, 1672, 4116, 1660], 'generators': [1551513286714441, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.16.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': ['8.f1', '8.i1'], 'normal_contains': ['32.d1', '32.e1', '32.f1', '32.h1', '32.i1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822175
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.h1', 'aut_quo_index': 4, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.a1', 'complements': ['16.p1'], 'conjugacy_class_count': 24, 'contained_in': ['8.a1', '8.i1', '8.n1', '8.bp1', '8.bt1'], 'contains': ['32.g1', '32.h1', '32.j1', '32.bf1', '32.bg1'], 'core': '16.h1', 'coset_action_label': None, 'count': 24, 'diagramx': [5726, 3728, 5733, 3702], 'generators': [3416619631436329, 1179824713041960, 126940973252046, 1558053575931240], 'label': '256.53382.16.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1', 'normal_contained_in': ['8.a1', '8.i1', '8.n1'], 'normal_contains': ['32.g1', '32.h1', '32.j1'], 'normalizer': '1.a1', 'old_label': '16.h1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 48822176
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': 4, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': ['16.p1'], 'conjugacy_class_count': 12, 'contained_in': ['8.b1', '8.i1', '8.n1', '8.bq1', '8.bu1'], 'contains': ['32.g1', '32.i1', '32.bi1'], 'core': '16.i1', 'coset_action_label': None, 'count': 12, 'diagramx': [5538, 4295, 5544, 4264], 'generators': [3416619631436329, 1187678429726520, 126940973252046, 1558053575931240], 'label': '256.53382.16.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1', 'normal_contained_in': ['8.b1', '8.i1', '8.n1'], 'normal_contains': ['32.g1', '32.i1'], 'normalizer': '1.a1', 'old_label': '16.i1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822177
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': 4, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 1536, 'centralizer': '16.b1', 'complements': ['16.p1'], 'conjugacy_class_count': 12, 'contained_in': ['8.c1', '8.i1', '8.n1', '8.br1', '8.bs1'], 'contains': ['32.i1', '32.j1', '32.bl1'], 'core': '16.j1', 'coset_action_label': None, 'count': 12, 'diagramx': [5361, 3163, 5368, 3140], 'generators': [1187678429726520, 126940973252046, 799458240531169, 1558053575931240], 'label': '256.53382.16.j1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1', 'normal_contained_in': ['8.c1', '8.i1', '8.n1'], 'normal_contains': ['32.i1', '32.j1'], 'normalizer': '1.a1', 'old_label': '16.j1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822178
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.k1', 'aut_quo_index': 105, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.j1', '8.k1'], 'contains': ['32.k1', '32.z1', '32.bp1'], 'core': '16.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [2147, 6799, 2150, 6750], 'generators': [126940973252046, 1558052138927761, 9250089176568, 1558053575931240], 'label': '256.53382.16.k1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.k1', 'normal_contained_in': ['8.d1', '8.j1', '8.k1'], 'normal_contains': ['32.k1'], 'normalizer': '1.a1', 'old_label': '16.k1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822179
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.l1', 'aut_quo_index': 1260, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['8.e1', '8.j1', '8.l1', '8.m1', '8.n1', '8.o1'], 'contains': ['32.g1', '32.j1', '32.k1', '32.ba1'], 'core': '16.l1', 'coset_action_label': None, 'count': 12, 'diagramx': [5186, 7681, 5192, 7625], 'generators': [3416619631436329, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.16.l1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.l1', 'normal_contained_in': ['8.e1', '8.j1', '8.l1', '8.m1', '8.n1', '8.o1'], 'normal_contains': ['32.g1', '32.j1', '32.k1'], 'normalizer': '1.a1', 'old_label': '16.l1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822180
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.m1', 'aut_quo_index': 420, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.k1', '8.n1', '8.p1'], 'contains': ['32.h1', '32.i1', '32.k1'], 'core': '16.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [3909, 5732, 3914, 5690], 'generators': [3823657107099841, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.16.m1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.m1', 'normal_contained_in': ['8.f1', '8.k1', '8.n1', '8.p1'], 'normal_contains': ['32.h1', '32.i1', '32.k1'], 'normalizer': '1.a1', 'old_label': '16.m1', 'projective_image': '64.202', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822181
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.n1', 'aut_quo_index': 105, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 2048, 'centralizer': '4.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '8.k1', '8.l1'], 'contains': ['32.k1', '32.bb1'], 'core': '16.n1', 'coset_action_label': None, 'count': 2, 'diagramx': [2824, 6337, 2827, 6291], 'generators': [3823656628098631, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.16.n1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.n1', 'normal_contained_in': ['8.g1', '8.k1', '8.l1'], 'normal_contains': ['32.k1'], 'normalizer': '1.a1', 'old_label': '16.n1', 'projective_image': '128.2163', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822182
    {'ambient': '256.53382', 'aut_centralizer_order': 128, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1088763', 'aut_weyl_index': 128, 'centralizer': '4.b1', 'complements': ['64.t1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.d1', '8.f1', '8.g1', '8.k1', '8.r1', '8.s1', '8.bk1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1237, 2461, 1239, 2444], 'generators': [1558053575931241, 1179824713041960, 126940973252046, 2917963830, 9250089176568, 1558053575931240], 'label': '256.53382.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.d1', '8.f1', '8.g1', '8.k1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822183
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.o1', 'aut_quo_index': 630, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['8.h1', '8.j1', '8.l1', '8.m1', '8.p1'], 'contains': ['32.k1', '32.bc1'], 'core': '16.o1', 'coset_action_label': None, 'count': 12, 'diagramx': [3736, 7200, 3740, 7147], 'generators': [3416617711802305, 126940973252046, 9250089176568, 1558053575931240], 'label': '256.53382.16.o1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.o1', 'normal_contained_in': ['8.h1', '8.j1', '8.l1', '8.m1', '8.p1'], 'normal_contains': ['32.k1'], 'normalizer': '1.a1', 'old_label': '16.o1', 'projective_image': '128.2163', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 48822184
    {'ambient': '256.53382', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '16.14', 'aut_weyl_index': 6144, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.q1'], 'contains': ['32.l1', '32.m1', '32.n1', '32.bo1'], 'core': '128.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1603, -1, 1605, -1], 'generators': [1558053575931241, 5276679855650928, 126940973252046, 2917963830], 'label': '256.53382.16.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '16.p1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822185
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8192, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1'], 'contains': ['32.l1', '32.l2', '32.o1', '32.bn1', '32.bp1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1357, -1, 1359, -1], 'generators': [1558053575931241, 126940973252046, 2917963830, 9250089176568], 'label': '256.53382.16.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.q1', 'projective_image': '128.1757', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822186
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '8.q1', '8.r1', '8.s1', '8.t1'], 'contains': ['32.a1', '32.l1', '32.l2', '32.q1', '32.u1', '32.z1'], 'core': '32.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [848, -1, 849, -1], 'generators': [1558053575931241, 126940973252046, 2917963830, 1558053575931240], 'label': '256.53382.16.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.r1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822187
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.u1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.e1', '8.u1', '8.v1', '8.w1', '8.y1'], 'contains': ['32.a1', '32.r1', '32.s1', '32.v1', '32.ba1'], 'core': '32.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7294, -1, 7303, -1], 'generators': [1558053575931241, 3080248359646008, 134878510137840, 1558053575931240], 'label': '256.53382.16.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.s1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822188
    {'ambient': '256.53382', 'aut_centralizer_order': 1024, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.g1', '8.r1', '8.s1', '8.x1', '8.bb1'], 'contains': ['32.a1', '32.t1', '32.y1', '32.bb1'], 'core': '32.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1001, -1, 1003, -1], 'generators': [1558053575931241, 126940973252046, 1179826153715760, 1558053575931240], 'label': '256.53382.16.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.t1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 48822189
    {'ambient': '256.53382', 'aut_centralizer_order': 512, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 6144, 'centralizer': '8.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.h1', '8.q1', '8.t1', '8.x1', '8.z1', '8.ba1', '8.bb1'], 'contains': ['32.a1', '32.n1', '32.bc1'], 'core': '32.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2301, -1, 2304, -1], 'generators': [1558053575931241, 126940973252046, 795535216378854, 1558053575931240], 'label': '256.53382.16.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.u1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 48822190
    {'ambient': '256.53382', 'aut_centralizer_order': 768, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1'], 'contains': ['32.b1', '32.q1', '32.t1', '32.bd1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [89, -1, 89, -1], 'generators': [1558053575931241, 1179824713041960, 2917963830, 1558053575931240], 'label': '256.53382.16.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.v1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822191
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.r1', '8.s1'], 'contains': ['32.c1', '32.q1', '32.t1', '32.be1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [291, -1, 291, -1], 'generators': [1558053575931241, 2917963830, 1327599450054864, 1558053575931240], 'label': '256.53382.16.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.w1', 'projective_image': '64.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 48822192
    {'ambient': '256.53382', 'aut_centralizer_order': 256, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 3072, 'centralizer': '4.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.u1', '8.bd1', '8.bd2'], 'contains': ['32.b1', '32.r1', '32.s1', '32.bf1'], 'core': '32.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [7860, -1, 7869, -1], 'generators': [1558053575931241, 795533299969728, 1179824713041960, 1558053575931240], 'label': '256.53382.16.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.x1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}