Abstract group data - 256.20278

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 4, 2, 2], 'aut_gens': [[1, 2, 8, 16, 64], [1, 2, 8, 48, 64], [1, 2, 40, 16, 64], [1, 34, 8, 16, 64], [129, 130, 72, 16, 192], [1, 2, 136, 16, 64], [1, 130, 8, 16, 64], [1, 166, 8, 176, 64], [37, 2, 8, 144, 64], [1, 2, 8, 80, 192], [161, 130, 200, 16, 192]], 'aut_group': '49152.bbq', 'aut_hash': 2978329760197401528, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 32, 'aut_perms': [218503724192483464508412443766, 12457408718954246256857766, 107330786090990886387941478929036312, 246986444193470411206045661503582742, 3133821083134703689897446, 246986411507003107923636633836089112, 42158055079956380555174327820238478, 23863687083959581216328092170471083, 247516623228471037418709454770125492, 136495251772013063607327631881907673], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 2, 1], [2, 8, 1, 1], [2, 8, 2, 1], [4, 2, 1, 4], [4, 4, 2, 1], [4, 8, 1, 5], [4, 8, 2, 2], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 16, 1, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{12}.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 2], [2, 8, 3], [4, 2, 4], [4, 4, 2], [4, 8, 9], [4, 16, 2], [8, 4, 4], [8, 8, 6], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.226', 'commutator_count': 1, 'commutator_label': '16.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 20278, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 2], [2, 8, 1, 3], [4, 2, 1, 4], [4, 4, 1, 2], [4, 8, 1, 5], [4, 8, 2, 2], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 322560, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '16.14', 'hash': 20278, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2, 2, 2], 'inner_gens': [[1, 166, 8, 176, 64], [37, 2, 8, 144, 64], [1, 2, 8, 80, 192], [161, 130, 200, 16, 192], [1, 2, 136, 144, 64]], 'inner_hash': 226, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 2], [8, 2]], 'label': '256.20278', 'linC_count': 24, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 14, 'linQ_dim': 12, 'linQ_dim_count': 7, 'linR_count': 7, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2.D4^2', 'ngens': 4, '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': 31, 'number_characteristic_subgroups': 105, 'number_conjugacy_classes': 40, 'number_divisions': 34, 'number_normal_subgroups': 115, 'number_subgroup_autclasses': 370, 'number_subgroup_classes': 437, 'number_subgroups': 1215, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 120], [8, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 8, 48, 64], [1, 2, 40, 16, 64], [1, 34, 8, 16, 64], [129, 130, 72, 16, 192], [1, 2, 136, 16, 64], [1, 130, 8, 16, 64], [1, 2, 8, 16, 64], [1, 2, 8, 16, 64], [1, 2, 8, 16, 64], [1, 2, 8, 16, 64]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320, 0, 0, 0, 0], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 8], [8, 2]], 'representations': {'PC': {'code': 41701904319988413729969385727133142, 'gens': [1, 2, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2657, 41, 3170, 786, 7044, 2892, 428, 116, 1374, 710, 166]}, 'Perm': {'d': 24, 'gens': [25961529430479209822904, 59834960004624371897260, 77871034309918186691778, 112454020772954919900100, 133166139945892945879680, 165639998788419491890129, 139788499212516595357009, 192789399230406543358080]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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_2^2.D_4^2', 'transitive_degree': 64, '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: 101538372
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 20278, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 101538383
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 20278, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 101538394
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 20278, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 101538405
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 20278, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 160, 'size': 1}
  • id: 101538407
    {'aut_label': '2D', 'centralizer': '2.o1.a1', 'counter': 5, 'group_counter': 20278, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 68, 'size': 2}
  • id: 101538408
    {'aut_label': '2E', 'centralizer': '2.o1.a1', 'counter': 6, 'group_counter': 20278, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 100, 'size': 2}
  • id: 101538409
    {'aut_label': '2F', 'centralizer': '4.bj1.a1', 'counter': 7, 'group_counter': 20278, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 8, 'size': 4}
  • id: 101538410
    {'aut_label': '2F', 'centralizer': '4.bj1.a1', 'counter': 8, 'group_counter': 20278, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 40, 'size': 4}
  • id: 101538411
    {'aut_label': '2H', 'centralizer': '8.bj1.a1', 'counter': 9, 'group_counter': 20278, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 1, 'size': 8}
  • id: 101538373
    {'aut_label': '2I', 'centralizer': '8.x1.a1', 'counter': 10, 'group_counter': 20278, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 9, 'size': 8}
  • id: 101538374
    {'aut_label': '2I', 'centralizer': '8.x1.a1', 'counter': 11, 'group_counter': 20278, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 73, 'size': 8}
  • id: 101538375
    {'aut_label': '4A', 'centralizer': '2.e1.a1', 'counter': 12, 'group_counter': 20278, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 4, 'size': 2}
  • id: 101538376
    {'aut_label': '4B', 'centralizer': '2.j1.a1', 'counter': 13, 'group_counter': 20278, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 224, 'size': 2}
  • id: 101538377
    {'aut_label': '4C', 'centralizer': '2.e1.a1', 'counter': 14, 'group_counter': 20278, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 164, 'size': 2}
  • id: 101538378
    {'aut_label': '4D', 'centralizer': '2.j1.a1', 'counter': 15, 'group_counter': 20278, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 64, 'size': 2}
  • id: 101538379
    {'aut_label': '4E', 'centralizer': '4.bm1.a1', 'counter': 16, 'group_counter': 20278, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 12, 'size': 4}
  • id: 101538380
    {'aut_label': '4E', 'centralizer': '4.bm1.a1', 'counter': 17, 'group_counter': 20278, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 44, 'size': 4}
  • id: 101538381
    {'aut_label': '4G', 'centralizer': '8.ch1.a1', 'counter': 18, 'group_counter': 20278, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [3], 'representative': 16, 'size': 8}
  • id: 101538382
    {'aut_label': '4H', 'centralizer': '8.ch1.a1', 'counter': 19, 'group_counter': 20278, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 20, 'size': 8}
  • id: 101538384
    {'aut_label': '4I', 'centralizer': '8.bn1.a1', 'counter': 20, 'group_counter': 20278, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [2], 'representative': 65, 'size': 8}
  • id: 101538385
    {'aut_label': '4J', 'centralizer': '8.bk1.a1', 'counter': 21, 'group_counter': 20278, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 3, 'size': 8}
  • id: 101538386
    {'aut_label': '4K', 'centralizer': '8.co1.a1', 'counter': 22, 'group_counter': 20278, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [4], 'representative': 67, 'size': 8}
  • id: 101538387
    {'aut_label': '4L1', 'centralizer': '8.f1.a1', 'counter': 23, 'group_counter': 20278, 'group_order': 256, 'label': '4L1', 'order': 4, 'powers': [6], 'representative': 26, 'size': 8}
  • id: 101538388
    {'aut_label': '4L1', 'centralizer': '8.f1.a1', 'counter': 24, 'group_counter': 20278, 'group_order': 256, 'label': '4L-1', 'order': 4, 'powers': [6], 'representative': 58, 'size': 8}
  • id: 101538389
    {'aut_label': '4M1', 'centralizer': '8.y1.a1', 'counter': 25, 'group_counter': 20278, 'group_order': 256, 'label': '4M1', 'order': 4, 'powers': [3], 'representative': 11, 'size': 8}
  • id: 101538390
    {'aut_label': '4M1', 'centralizer': '8.y1.a1', 'counter': 26, 'group_counter': 20278, 'group_order': 256, 'label': '4M-1', 'order': 4, 'powers': [3], 'representative': 75, 'size': 8}
  • id: 101538391
    {'aut_label': '4N', 'centralizer': '16.x1.a1', 'counter': 27, 'group_counter': 20278, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [2], 'representative': 17, 'size': 16}
  • id: 101538392
    {'aut_label': '4O', 'centralizer': '16.y1.a1', 'counter': 28, 'group_counter': 20278, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [3], 'representative': 19, 'size': 16}
  • id: 101538393
    {'aut_label': '8A1', 'centralizer': '4.g1.a1', 'counter': 29, 'group_counter': 20278, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [12], 'representative': 2, 'size': 4}
  • id: 101538395
    {'aut_label': '8A1', 'centralizer': '4.g1.a1', 'counter': 30, 'group_counter': 20278, 'group_order': 256, 'label': '8A-1', 'order': 8, 'powers': [12], 'representative': 34, 'size': 4}
  • id: 101538396
    {'aut_label': '8B1', 'centralizer': '4.w1.a1', 'counter': 31, 'group_counter': 20278, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [12], 'representative': 66, 'size': 4}
  • id: 101538397
    {'aut_label': '8B1', 'centralizer': '4.w1.a1', 'counter': 32, 'group_counter': 20278, 'group_order': 256, 'label': '8B-1', 'order': 8, 'powers': [12], 'representative': 98, 'size': 4}
  • id: 101538398
    {'aut_label': '8C', 'centralizer': '8.k1.a1', 'counter': 33, 'group_counter': 20278, 'group_order': 256, 'label': '8C', 'order': 8, 'powers': [13], 'representative': 24, 'size': 8}
  • id: 101538399
    {'aut_label': '8D', 'centralizer': '8.k1.a1', 'counter': 34, 'group_counter': 20278, 'group_order': 256, 'label': '8D', 'order': 8, 'powers': [13], 'representative': 28, 'size': 8}
  • id: 101538400
    {'aut_label': '8E1', 'centralizer': '8.ch1.a1', 'counter': 35, 'group_counter': 20278, 'group_order': 256, 'label': '8E1', 'order': 8, 'powers': [14], 'representative': 18, 'size': 8}
  • id: 101538401
    {'aut_label': '8E1', 'centralizer': '8.ch1.a1', 'counter': 36, 'group_counter': 20278, 'group_order': 256, 'label': '8E-1', 'order': 8, 'powers': [14], 'representative': 50, 'size': 8}
  • id: 101538402
    {'aut_label': '8F1', 'centralizer': '8.bh1.a1', 'counter': 37, 'group_counter': 20278, 'group_order': 256, 'label': '8F1', 'order': 8, 'powers': [12], 'representative': 10, 'size': 8}
  • id: 101538403
    {'aut_label': '8F1', 'centralizer': '8.bh1.a1', 'counter': 38, 'group_counter': 20278, 'group_order': 256, 'label': '8F-1', 'order': 8, 'powers': [12], 'representative': 42, 'size': 8}
  • id: 101538404
    {'aut_label': '8G', 'centralizer': '16.bv1.a1', 'counter': 39, 'group_counter': 20278, 'group_order': 256, 'label': '8G', 'order': 8, 'powers': [15], 'representative': 25, 'size': 16}
  • id: 101538406
    {'aut_label': '8H', 'centralizer': '16.bw1.a1', 'counter': 40, 'group_counter': 20278, 'group_order': 256, 'label': '8H', 'order': 8, 'powers': [13], 'representative': 27, 'size': 16}
• 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: 663170
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1a', '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], 'schur_index': 1}
  • id: 663181
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1b', '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], 'schur_index': 1}
  • id: 663192
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1c', '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], 'schur_index': 1}
  • id: 663198
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1d', '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], 'schur_index': 1}
  • id: 663199
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1e', '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], 'schur_index': 1}
  • id: 663200
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1f', '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], 'schur_index': 1}
  • id: 663201
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1g', '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], 'schur_index': 1}
  • id: 663202
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1h', '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], 'schur_index': 1}
  • id: 663203
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1i', '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], 'schur_index': 1}
  • id: 663171
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1j', '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], 'schur_index': 1}
  • id: 663172
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1k', '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], 'schur_index': 1}
  • id: 663173
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1l', '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], 'schur_index': 1}
  • id: 663174
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1m', '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], 'schur_index': 1}
  • id: 663175
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1n', '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], 'schur_index': 1}
  • id: 663176
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1o', '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], 'schur_index': 1}
  • id: 663177
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.1p', '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], 'schur_index': 1}
  • id: 663178
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663179
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663180
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663182
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663183
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663184
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, 2, 2, -2, -2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663185
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663186
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663187
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -4, 4, 0, 0, 0, -4, 4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663188
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2j', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, -4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663189
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2k', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 0, 0, 0, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663190
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2l', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, -4, 4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663191
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2m', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 4, -4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663193
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.2n', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, 0, 0, 0, 4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663194
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.4a', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663195
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.4b', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663196
    {'cdim': 8, 'counter': 33, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.8a', 'multiplicity': 1, 'nt': [16, 308], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 663197
    {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '256.20278', 'group_order': 256, 'image': None, 'label': '256.20278.8b', 'multiplicity': 1, 'nt': [32, 1426], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• 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: 944470
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.20278.1a', '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]]]}
  • id: 944481
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.m1.a1', 'kernel_order': 128, 'label': '256.20278.1b', '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]]]}
  • id: 944492
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.o1.a1', 'kernel_order': 128, 'label': '256.20278.1c', '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]]]}
  • id: 944503
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.n1.a1', 'kernel_order': 128, 'label': '256.20278.1d', '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]]]}
  • id: 944505
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.l1.a1', 'kernel_order': 128, 'label': '256.20278.1e', '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]]]}
  • id: 944506
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 128, 'label': '256.20278.1f', '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]]]}
  • id: 944507
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 128, 'label': '256.20278.1g', '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]]]}
  • id: 944508
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 128, 'label': '256.20278.1h', '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]]]}
  • id: 944509
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 128, 'label': '256.20278.1i', '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]]]}
  • id: 944471
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.20278.1j', '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]]]}
  • id: 944472
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.20278.1k', '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]]]}
  • id: 944473
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.20278.1l', '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]]]}
  • id: 944474
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.20278.1m', '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]]]}
  • id: 944475
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.20278.1n', '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]]]}
  • id: 944476
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.20278.1o', '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]]]}
  • id: 944477
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.20278.1p', '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]]]}
  • id: 944478
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.v1.a1', 'kernel_order': 32, 'label': '256.20278.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944479
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.w1.a1', 'kernel_order': 32, 'label': '256.20278.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944480
    {'center': '4.i1.a1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.t1.a1', 'kernel_order': 32, 'label': '256.20278.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944482
    {'center': '4.i1.a1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.u1.a1', 'kernel_order': 32, 'label': '256.20278.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944483
    {'center': '4.i1.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.r1.a1', 'kernel_order': 32, 'label': '256.20278.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944484
    {'center': '4.i1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.s1.a1', 'kernel_order': 32, 'label': '256.20278.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944485
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.p1.a1', 'kernel_order': 32, 'label': '256.20278.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944486
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.q1.a1', 'kernel_order': 32, 'label': '256.20278.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944487
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.p1.b1', 'kernel_order': 16, 'label': '256.20278.2i1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[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]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 944488
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.p1.b1', 'kernel_order': 16, 'label': '256.20278.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[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]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 944489
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.p1.a1', 'kernel_order': 16, 'label': '256.20278.2j1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-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]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 944490
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.p1.a1', 'kernel_order': 16, 'label': '256.20278.2j2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-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]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 944491
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.n1.b1', 'kernel_order': 16, 'label': '256.20278.2k1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[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]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944493
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.n1.b1', 'kernel_order': 16, 'label': '256.20278.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-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]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944494
    {'center': '4.q1.a1', 'center_index': 4, 'center_order': 64, 'counter': 31, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.o1.b1', 'kernel_order': 16, 'label': '256.20278.2l1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[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]]]}
  • id: 944495
    {'center': '4.q1.a1', 'center_index': 4, 'center_order': 64, 'counter': 32, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.o1.b1', 'kernel_order': 16, 'label': '256.20278.2l2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[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]]]}
  • id: 944496
    {'center': '4.q1.a1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.o1.a1', 'kernel_order': 16, 'label': '256.20278.2m1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[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]]]}
  • id: 944497
    {'center': '4.q1.a1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.o1.a1', 'kernel_order': 16, 'label': '256.20278.2m2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[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]]]}
  • id: 944498
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 35, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.n1.a1', 'kernel_order': 16, 'label': '256.20278.2n1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[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]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944499
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 36, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.n1.a1', 'kernel_order': 16, 'label': '256.20278.2n2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-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]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944500
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.f1.a1', 'kernel_order': 8, 'label': '256.20278.4a', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944501
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.20278.4b', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 944502
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '128.2020', 'image_order': 128, 'indicator': 1, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.20278.8a', 'nt': [16, 308], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 944504
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '256.20278', 'group_counter': 20278, 'group_order': 256, 'image': None, 'image_isoclass': '128.2021', 'image_order': 128, 'indicator': -1, 'kernel': '128.c1.a1', 'kernel_order': 2, 'label': '256.20278.8b', 'nt': [32, 1426], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 26644620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.20278.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.20278', 'subgroup_hash': 20278, 'subgroup_order': 256, 'subgroup_tex': 'C_2^2.D_4^2', 'supersolvable': True, 'sylow': 2}
  • id: 26644731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1741', 'subgroup_hash': 1741, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times Q_{16}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1629', 'subgroup_hash': 1629, 'subgroup_order': 128, 'subgroup_tex': '(C_2^2\\times C_8):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.524', 'subgroup_hash': 524, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1815', 'subgroup_hash': 1815, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26645013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.497', 'subgroup_hash': 497, 'subgroup_order': 128, 'subgroup_tex': 'D_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.614', 'subgroup_hash': 614, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 26645035
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.640', 'subgroup_hash': 640, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1869', 'subgroup_hash': 1869, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.770', 'subgroup_hash': 770, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.670', 'subgroup_hash': 670, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.810', 'subgroup_hash': 810, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_8).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.l1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.759', 'subgroup_hash': 759, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times D_4):Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.m1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.663', 'subgroup_hash': 663, 'subgroup_order': 128, 'subgroup_tex': 'C_4.(C_4\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 26644676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.n1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.778', 'subgroup_hash': 778, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times C_8).D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.2.o1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.705', 'subgroup_hash': 705, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times \\SD_{16}):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.97', 'subgroup_hash': 97, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.201', 'subgroup_hash': 201, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.98', 'subgroup_hash': 98, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.248', 'subgroup_hash': 248, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.217', 'subgroup_hash': 217, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.97', 'subgroup_hash': 97, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.98', 'subgroup_hash': 98, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.98', 'subgroup_hash': 98, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.89', 'subgroup_hash': 89, 'subgroup_order': 64, 'subgroup_tex': '(C_2^2\\times C_8):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.225', 'subgroup_hash': 225, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.109', 'subgroup_hash': 109, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.86', 'subgroup_hash': 86, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.100', 'subgroup_hash': 100, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.105', 'subgroup_hash': 105, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.72', 'subgroup_hash': 72, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.84', 'subgroup_hash': 84, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.107', 'subgroup_hash': 107, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.24', 'subgroup_hash': 24, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.96', 'subgroup_hash': 96, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.93', 'subgroup_hash': 93, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.24', 'subgroup_hash': 24, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.22', 'subgroup_hash': 22, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.4.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.22', 'subgroup_hash': 22, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.95', 'subgroup_hash': 95, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.98', 'subgroup_hash': 98, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.97', 'subgroup_hash': 97, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.155', 'subgroup_hash': 155, 'subgroup_order': 64, 'subgroup_tex': 'D_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.159', 'subgroup_hash': 159, 'subgroup_order': 64, 'subgroup_tex': 'D_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.170', 'subgroup_hash': 170, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.169', 'subgroup_hash': 169, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.168', 'subgroup_hash': 168, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.172', 'subgroup_hash': 172, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.158', 'subgroup_hash': 158, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.4.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '64.160', 'subgroup_hash': 160, 'subgroup_order': 64, 'subgroup_tex': 'Q_8.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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: 26645023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], '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: 26645025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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: 26645026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26645027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26645028
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645032
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645034
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26645039
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645040
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645041
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26645053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26645055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26645056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.co1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cs1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ct1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cu1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cy1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.cz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.da1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.da1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.da1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.db1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.db1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.db1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.de1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.de1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.de1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.df1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.di1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.di1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.di1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.8.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 169, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', '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': ['D', 'Phi', 'U1', 'L1', 'D1', 'C4'], '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: 26644699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 170, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', '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: 26644700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 171, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', '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: 26644701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 174, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 26644704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 175, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 177, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 178, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644710
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 181, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 185, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 186, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 187, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26644722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644727
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26644729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644736
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644747
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644749
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.co1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cs1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cs1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ct1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.da1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.db1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644799
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.de1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.di1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.di1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.di1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dk1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.do1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.do1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.do1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dq1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.ds1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26644838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.16.dw1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 298, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 26644841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 299, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.46', '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: 26644844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 300, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.46', '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': ['C5'], '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: 26644845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 301, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 26644846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 26644847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 26644848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', '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: 26644849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 307, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 308, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644863
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.be1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.be1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26644884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644899
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644900
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644905
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bo1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bo1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644916
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 366, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644917
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 367, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644918
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 368, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644922
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 371, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644923
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 372, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644924
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 373, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644927
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 376, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644929
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 378, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.32.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26644930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.32.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26644941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 389, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 390, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.232', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 232, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 391, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.20278.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26644945
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 392, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': 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: 26644946
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 393, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': 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: 26644947
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 394, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.206', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 206, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26644948
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 395, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.207', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 207, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 26644949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 26644950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 26644952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 401, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644957
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 402, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644958
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 403, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644959
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 404, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644964
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 409, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 410, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 411, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644968
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 412, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644973
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 417, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 418, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644978
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644979
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.64.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644980
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644981
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644982
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.be1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 26644983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.20278.64.be1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 26644984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 427, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.1204', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1204, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_4^2', '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: 26644985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 428, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2020', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2020, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 429, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.20278.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2021', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2021, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_4^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26644988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.20278.128.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26644995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.20278', 'ambient_counter': 20278, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 437, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.20278.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.20278', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20278, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_4^2', '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: 26644620
    {'ambient': '256.20278', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '2.l1.a1', '2.m1.a1', '2.n1.a1', '2.o1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5131, 4718, 5700, 5531, 5142, 4719, 5694, 5531], 'generators': [1, 2, 8, 16], 'label': '256.20278.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.b1.a1', '2.c1.a1', '2.a1.a1', '2.f1.a1', '2.d1.a1', '2.e1.a1', '2.g1.a1', '2.j1.a1', '2.h1.a1', '2.i1.a1', '2.k1.a1', '2.l1.a1', '2.n1.a1', '2.o1.a1', '2.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644621
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.k1.a1', '4.u1.a1', '4.v1.a1', '4.ba1.a1', '4.bf1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3259, 3791, 7581, 2434, 3266, 3791, 7572, 2433], 'generators': [1, 10, 16], 'label': '256.20278.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.a1', '4.h1.a1', '4.k1.a1', '4.u1.a1', '4.ba1.a1', '4.v1.a1', '4.bf1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644622
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.f1.a1', '16.bb1.a1', '16.bd1.a1', '16.bm1.a1', '16.by1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3404, -1, 4840, -1, 3411, -1, 4834, -1], 'generators': [67, 8, 164], 'label': '256.20278.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bg1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644623
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.g1.a1', '16.bb1.a1', '16.bq1.a1', '16.dm1.a1', '16.dm1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8049, -1, 2469, -1, 8065, -1, 2466, -1], 'generators': [2, 8, 160], 'label': '256.20278.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bh1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644624
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.h1.a1', '16.bb1.a1', '16.bq1.a1', '16.dn1.a1', '16.dn1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 2760, -1, 7846, -1, 2758, -1], 'generators': [66, 8, 160], 'label': '256.20278.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bi1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644625
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.b1.a1', '16.z1.a1', '16.ba1.a1', '16.bf1.a1', '16.bk1.a1', '16.do1.a1', '16.do1.b1', '16.dp1.a1', '16.dp1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8648, -1, 1903, -1, 8666, -1, 1900, -1], 'generators': [1, 8, 160, 64], 'label': '256.20278.8.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bj1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644626
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.b1.a1', '16.bc1.a1', '16.bd1.a1', '16.br1.a1', '16.bs1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [691, -1, 9603, -1, 692, -1, 9593, -1], 'generators': [3, 8, 64], 'label': '256.20278.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bk1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644627
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.b1.a1', '16.bt1.a1', '16.bv1.a1', '16.dq1.a1', '16.dq1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5319, -1, 7846, -1, 5330, -1, 7838, -1], 'generators': [17, 8, 160], 'label': '256.20278.8.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bl1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644628
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.b1.a1', '16.bu1.a1', '16.bw1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1316, -1, 8799, -1, 1319, -1, 8790, -1], 'generators': [19, 8], 'label': '256.20278.8.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bm1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644629
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.br1.a1', '4.bs1.a1'], 'contains': ['16.i1.a1', '16.be1.a1', '16.bf1.a1', '16.bi1.a1', '16.bk1.a1', '16.dr1.a1', '16.dr1.b1', '16.ds1.a1', '16.ds1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8522, -1, 2262, -1, 8539, -1, 2259, -1], 'generators': [1, 172, 160, 64], 'label': '256.20278.8.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bn1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644630
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bn1.a1', '4.br1.a1'], 'contains': ['16.j1.a1', '16.bf1.a1', '16.bg1.a1', '16.bt1.a1', '16.bz1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2809, -1, 8371, -1, 2814, -1, 8362, -1], 'generators': [1, 16, 64], 'label': '256.20278.8.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bo1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644631
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bo1.a1', '4.bs1.a1'], 'contains': ['16.k1.a1', '16.bf1.a1', '16.bh1.a1', '16.bt1.a1', '16.cc1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2896, -1, 8298, -1, 2902, -1, 8289, -1], 'generators': [1, 180, 64], 'label': '256.20278.8.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bp1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644632
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494202', 'aut_weyl_index': 8, 'centralizer': '32.c1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.m1.a1', '4.x1.a1', '4.z1.a1', '4.bb1.a1', '4.bh1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4663, 2799, 5794, 2950, 4672, 2800, 5787, 2950], 'generators': [1, 2, 24], 'label': '256.20278.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.j1.a1', '4.m1.a1', '4.x1.a1', '4.z1.a1', '4.bb1.a1', '4.bh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644633
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bn1.a1', '4.bs1.a1'], 'contains': ['16.l1.a1', '16.bf1.a1', '16.bv1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4687, -1, 6393, -1, 4696, -1, 6386, -1], 'generators': [1, 24], 'label': '256.20278.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bq1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644634
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bo1.a1', '4.br1.a1'], 'contains': ['16.m1.a1', '16.bf1.a1', '16.bv1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4918, -1, 6865, -1, 4928, -1, 6858, -1], 'generators': [1, 188], 'label': '256.20278.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.br1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644635
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bt1.a1', '4.bu1.a1'], 'contains': ['16.c1.a1', '16.bg1.a1', '16.bh1.a1', '16.bl1.a1', '16.bn1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3169, -1, 8053, -1, 3176, -1, 8045, -1], 'generators': [1, 16, 164], 'label': '256.20278.8.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bs1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644636
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.c1.a1', '16.bm1.a1', '16.bq1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7507, -1, 2947, -1, 7522, -1, 2944, -1], 'generators': [1, 10], 'label': '256.20278.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bt1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644637
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bt1.a1', '4.bu1.a1'], 'contains': ['16.c1.a1', '16.bo1.a1', '16.bp1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5899, -1, 4185, -1, 5911, -1, 4180, -1], 'generators': [1, 18], 'label': '256.20278.8.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bu1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644638
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.e1.a1', '16.bj1.a1', '16.bq1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8248, -1, 3185, -1, 8265, -1, 3181, -1], 'generators': [9, 10], 'label': '256.20278.8.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bv1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644639
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.f1.a1', '16.bj1.a1', '16.bq1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8320, -1, 3006, -1, 8337, -1, 3003, -1], 'generators': [73, 10], 'label': '256.20278.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bw1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644640
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.g1.a1', '16.bj1.a1', '16.bm1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7952, -1, 3066, -1, 7968, -1, 3063, -1], 'generators': [9, 2], 'label': '256.20278.8.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bx1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644641
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.h1.a1', '16.bj1.a1', '16.bm1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7364, -1, 3126, -1, 7379, -1, 3122, -1], 'generators': [9, 66], 'label': '256.20278.8.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.by1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.by1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644642
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bn1.a1', '4.br1.a1'], 'contains': ['16.j1.a1', '16.bk1.a1', '16.bv1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4767, -1, 8231, -1, 4776, -1, 8223, -1], 'generators': [9, 16], 'label': '256.20278.8.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bz1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644643
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.djl', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.a1', '4.l1.a1', '4.m1.a1', '4.bc1.a1', '4.bd1.a1', '4.bg1.a1', '4.bi1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6072, 6783, 5598, 7632, 6041, 6786, 5592, 7631], 'generators': [1, 18, 24], 'label': '256.20278.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.a1', '4.l1.a1', '4.m1.a1', '4.bc1.a1', '4.bd1.a1', '4.bg1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644644
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bo1.a1', '4.bs1.a1'], 'contains': ['16.k1.a1', '16.bk1.a1', '16.bv1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4838, -1, 8172, -1, 4848, -1, 8163, -1], 'generators': [9, 180], 'label': '256.20278.8.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ca1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644645
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bn1.a1', '4.bs1.a1'], 'contains': ['16.l1.a1', '16.bk1.a1', '16.bt1.a1', '16.dt1.a1', '16.dt1.b1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4090, -1, 6183, -1, 4098, -1, 6177, -1], 'generators': [17, 24, 64], 'label': '256.20278.8.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cb1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644646
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bo1.a1', '4.br1.a1'], 'contains': ['16.m1.a1', '16.bk1.a1', '16.bt1.a1', '16.du1.a1', '16.du1.b1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4433, -1, 6757, -1, 4443, -1, 6751, -1], 'generators': [17, 188, 64], 'label': '256.20278.8.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cc1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644647
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bv1.a1', '4.bw1.a1'], 'contains': ['16.d1.a1', '16.bl1.a1', '16.bn1.a1', '16.bz1.a1', '16.cc1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3098, -1, 8112, -1, 3104, -1, 8104, -1], 'generators': [65, 16, 164], 'label': '256.20278.8.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cd1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644648
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.ce1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bt1.a1', '4.bv1.a1'], 'contains': ['16.e1.a1', '16.bl1.a1', '16.bo1.a1', '16.ca1.a1', '16.cd1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2096, -1, 9529, -1, 2100, -1, 9518, -1], 'generators': [3, 16, 164], 'label': '256.20278.8.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.ce1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644649
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bu1.a1', '4.bw1.a1'], 'contains': ['16.f1.a1', '16.bl1.a1', '16.bo1.a1', '16.cb1.a1', '16.ce1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2168, -1, 9469, -1, 2172, -1, 9459, -1], 'generators': [67, 16, 164], 'label': '256.20278.8.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cf1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644650
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.bt1.a1', '4.bw1.a1'], 'contains': ['16.g1.a1', '16.bl1.a1', '16.bp1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5723, -1, 4272, -1, 5735, -1, 4267, -1], 'generators': [2, 16], 'label': '256.20278.8.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cg1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644651
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.bu1.a1', '4.bv1.a1'], 'contains': ['16.h1.a1', '16.bl1.a1', '16.bp1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5601, -1, 4432, -1, 5613, -1, 4428, -1], 'generators': [66, 16], 'label': '256.20278.8.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.ch1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644652
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.ci1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.d1.a1', '16.bm1.a1', '16.bq1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7435, -1, 3245, -1, 7450, -1, 3241, -1], 'generators': [65, 10], 'label': '256.20278.8.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.ci1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644653
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bv1.a1', '4.bw1.a1'], 'contains': ['16.d1.a1', '16.bo1.a1', '16.bp1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5828, -1, 4358, -1, 5840, -1, 4354, -1], 'generators': [65, 18], 'label': '256.20278.8.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cj1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644654
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.l1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.o1.a1', '4.p1.a1', '4.t1.a1', '4.u1.a1', '4.x1.a1', '4.bg1.a1'], 'core': '2.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 4926, 7221, 3158, 4141, 4926, 7213, 3157], 'generators': [9, 10, 16], 'label': '256.20278.2.l1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.l1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.o1.a1', '4.p1.a1', '4.n1.a1', '4.x1.a1', '4.t1.a1', '4.u1.a1', '4.bg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.l1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.l1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644655
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.ck1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.bt1.a1', '4.bv1.a1'], 'contains': ['16.e1.a1', '16.bn1.a1', '16.bp1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5441, -1, 5094, -1, 5452, -1, 5088, -1], 'generators': [17, 18], 'label': '256.20278.8.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.ck1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644656
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.bu1.a1', '4.bw1.a1'], 'contains': ['16.f1.a1', '16.bn1.a1', '16.bp1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5512, -1, 5034, -1, 5524, -1, 5029, -1], 'generators': [81, 18], 'label': '256.20278.8.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cl1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644657
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.bt1.a1', '4.bw1.a1'], 'contains': ['16.g1.a1', '16.bn1.a1', '16.bo1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5070, -1, 5153, -1, 5080, -1, 5147, -1], 'generators': [17, 2], 'label': '256.20278.8.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cm1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644658
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.bu1.a1', '4.bv1.a1'], 'contains': ['16.h1.a1', '16.bn1.a1', '16.bo1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4998, -1, 5213, -1, 5008, -1, 5207, -1], 'generators': [17, 66], 'label': '256.20278.8.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cn1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644659
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.co1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bx1.a1', '4.by1.a1'], 'contains': ['16.i1.a1', '16.br1.a1', '16.bs1.a1', '16.bx1.a1', '16.by1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [869, -1, 9691, -1, 871, -1, 9681, -1], 'generators': [3, 172, 64], 'label': '256.20278.8.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.co1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.co1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644660
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.br1.a1', '4.bs1.a1'], 'contains': ['16.i1.a1', '16.bt1.a1', '16.bv1.a1', '16.dv1.a1', '16.dv1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5169, -1, 7970, -1, 5180, -1, 7962, -1], 'generators': [17, 172, 160], 'label': '256.20278.8.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cp1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644661
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.bx1.a1', '4.by1.a1'], 'contains': ['16.i1.a1', '16.bu1.a1', '16.bw1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1031, -1, 8859, -1, 1032, -1, 8849, -1], 'generators': [19, 172], 'label': '256.20278.8.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cq1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644662
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bp1.a1', '4.bx1.a1'], 'contains': ['16.j1.a1', '16.br1.a1', '16.bu1.a1', '16.ca1.a1', '16.cb1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [263, -1, 9913, -1, 264, -1, 9903, -1], 'generators': [3, 16, 64], 'label': '256.20278.8.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cr1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644663
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.bp1.a1', '4.bx1.a1'], 'contains': ['16.j1.a1', '16.bs1.a1', '16.bw1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [959, -1, 9215, -1, 961, -1, 9205, -1], 'generators': [11, 16], 'label': '256.20278.8.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cs1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644664
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.ct1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bq1.a1', '4.by1.a1'], 'contains': ['16.k1.a1', '16.br1.a1', '16.bu1.a1', '16.cd1.a1', '16.ce1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [334, -1, 9854, -1, 336, -1, 9843, -1], 'generators': [3, 180, 64], 'label': '256.20278.8.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.ct1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644665
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.m1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.brr', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.a1', '4.bd1.a1', '4.bh1.a1'], 'core': '2.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5868, 7012, 5380, 7058, 5858, 7015, 5371, 6983], 'generators': [9, 2, 16], 'label': '256.20278.2.m1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.m1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.q1.a1', '4.s1.a1', '4.v1.a1', '4.w1.a1', '4.bd1.a1', '4.bh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.m1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.m1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644666
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.bq1.a1', '4.by1.a1'], 'contains': ['16.k1.a1', '16.bs1.a1', '16.bw1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1173, -1, 9037, -1, 1175, -1, 9027, -1], 'generators': [11, 180], 'label': '256.20278.8.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cu1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644667
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.cv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.bp1.a1', '4.by1.a1'], 'contains': ['16.l1.a1', '16.br1.a1', '16.bw1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [780, -1, 8918, -1, 782, -1, 8909, -1], 'generators': [3, 24], 'label': '256.20278.8.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cv1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644668
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.bq1.a1', '4.bx1.a1'], 'contains': ['16.m1.a1', '16.br1.a1', '16.bw1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1244, -1, 9096, -1, 1247, -1, 9086, -1], 'generators': [3, 188], 'label': '256.20278.8.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cw1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644669
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.bp1.a1', '4.by1.a1'], 'contains': ['16.l1.a1', '16.bs1.a1', '16.bu1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [601, -1, 8977, -1, 603, -1, 8968, -1], 'generators': [19, 24], 'label': '256.20278.8.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cx1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644670
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.bq1.a1', '4.bx1.a1'], 'contains': ['16.m1.a1', '16.bs1.a1', '16.bu1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1102, -1, 9156, -1, 1104, -1, 9146, -1], 'generators': [19, 188], 'label': '256.20278.8.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.cy1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644671
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.cz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.n1.a1', '16.cf1.a1', '16.cf1.b1', '16.ch1.a1', '16.cj1.a1', '16.di1.a1', '16.dk1.a1', '16.dp1.a1', '16.ds1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9516, -1, 1815, -1, 9536, -1, 1813, -1], 'generators': [1, 8, 4, 64], 'label': '256.20278.8.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.cz1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 26644672
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.cz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.n1.b1', '16.cf1.c1', '16.cf1.d1', '16.ch1.a1', '16.cj1.a1', '16.di1.b1', '16.dk1.b1', '16.dp1.b1', '16.ds1.b1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9516, -1, 1991, -1, 9536, -1, 1988, -1], 'generators': [1, 168, 4, 64], 'label': '256.20278.8.cz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.cz1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 26644673
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.da1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.o1.a1', '16.cf1.a1', '16.cf1.c1', '16.cg1.a1', '16.ci1.a1', '16.dj1.a1', '16.dj1.c1', '16.dl1.a1', '16.dl1.c1', '16.do1.a1', '16.dr1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9341, -1, 2063, -1, 9360, -1, 2061, -1], 'generators': [1, 8, 164, 224], 'label': '256.20278.8.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.da1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.da1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644674
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.da1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.o1.b1', '16.cf1.b1', '16.cf1.d1', '16.cg1.a1', '16.ci1.a1', '16.dj1.b1', '16.dj1.d1', '16.dl1.b1', '16.dl1.d1', '16.do1.b1', '16.dr1.b1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9341, -1, 1493, -1, 9360, -1, 1491, -1], 'generators': [65, 8, 164, 224], 'label': '256.20278.8.da1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.da1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.da1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644675
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.n1.a1', '16.ck1.a1', '16.cn1.a1', '16.dq1.a1', '16.dv1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7693, -1, 7063, -1, 7709, -1, 7056, -1], 'generators': [17, 8, 4], 'label': '256.20278.8.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.db1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.db1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 26644676
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.n1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16384.km', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.g1.a1', '128.f1.a1', '128.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.r1.a1', '4.s1.a1', '4.y1.a1', '4.z1.a1', '4.bf1.a1', '4.bi1.a1'], 'core': '2.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5511, 3562, 4779, 5247, 5522, 3562, 4769, 5247], 'generators': [17, 18, 24], 'label': '256.20278.2.n1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.n1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.o1.a1', '4.r1.a1', '4.s1.a1', '4.y1.a1', '4.z1.a1', '4.bf1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.n1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.n1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644677
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.n1.b1', '16.ck1.a1', '16.cn1.a1', '16.dq1.b1', '16.dv1.b1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7693, -1, 7147, -1, 7709, -1, 7139, -1], 'generators': [17, 168, 4], 'label': '256.20278.8.db1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.db1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.db1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 26644678
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.n1.a1', '16.cl1.a1', '16.cm1.a1', '16.dm1.a1', '16.dn1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8406, -1, 2646, -1, 8423, -1, 2643, -1], 'generators': [2, 8, 64], 'label': '256.20278.8.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.dc1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644679
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.n1.b1', '16.cl1.a1', '16.cm1.a1', '16.dm1.b1', '16.dn1.b1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8406, -1, 2875, -1, 8423, -1, 2872, -1], 'generators': [2, 168, 64], 'label': '256.20278.8.dc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.dc1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644680
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.o1.a1', '16.co1.a1', '16.cp1.a1', '16.dt1.a1', '16.du1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4262, -1, 5898, -1, 4270, -1, 5892, -1], 'generators': [17, 24, 164], 'label': '256.20278.8.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '8.dd1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644681
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.o1.b1', '16.co1.a1', '16.cp1.a1', '16.dt1.b1', '16.du1.b1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4262, -1, 5612, -1, 4270, -1, 5607, -1], 'generators': [81, 24, 164], 'label': '256.20278.8.dd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '8.dd1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644682
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.de1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1'], 'contains': ['16.o1.a1', '16.cq1.a1', '16.cr1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6444, -1, 3492, -1, 6457, -1, 3488, -1], 'generators': [9, 18], 'label': '256.20278.8.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '8.de1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.de1.a1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 26644683
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.de1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1'], 'contains': ['16.o1.b1', '16.cq1.a1', '16.cr1.a1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6444, -1, 3419, -1, 6457, -1, 3415, -1], 'generators': [73, 18], 'label': '256.20278.8.de1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '8.de1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.de1.b1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 26644684
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.df1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.cs1.a1', '16.cs1.a2', '16.cs1.b1', '16.cs1.b2', '16.ct1.a1', '16.cu1.a1', '16.cw1.a1', '16.di1.a1', '16.di1.b1', '16.dk1.a1', '16.dk1.b1', '16.do1.a1', '16.do1.b1', '16.dr1.a1', '16.dr1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9253, -1, 1566, -1, 9272, -1, 1564, -1], 'generators': [1, 8, 228, 224], 'label': '256.20278.8.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.df1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.df1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644685
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.p1.a1', '16.cs1.a1', '16.cs1.a2', '16.cv1.a1', '16.cx1.a1', '16.dj1.a1', '16.dj1.b1', '16.dl1.a1', '16.dl1.b1', '16.dp1.a1', '16.ds1.b1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9429, -1, 1421, -1, 9448, -1, 1419, -1], 'generators': [1, 8, 164, 64], 'label': '256.20278.8.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.dg1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644686
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.p1.b1', '16.cs1.b1', '16.cs1.b2', '16.cv1.a1', '16.cx1.a1', '16.dj1.c1', '16.dj1.d1', '16.dl1.c1', '16.dl1.d1', '16.dp1.b1', '16.ds1.a1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9429, -1, 1638, -1, 9448, -1, 1637, -1], 'generators': [1, 168, 164, 64], 'label': '256.20278.8.dg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.dg1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.b1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644687
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.o1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': ['128.g1.a1', '128.f1.a1', '128.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.p1.a1', '4.q1.a1', '4.r1.a1', '4.ba1.a1', '4.bb1.a1', '4.bc1.a1', '4.be1.a1'], 'core': '2.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3723, 4718, 5917, 3365, 3731, 4719, 5911, 3364], 'generators': [17, 2, 24], 'label': '256.20278.2.o1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.o1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.p1.a1', '4.q1.a1', '4.r1.a1', '4.ba1.a1', '4.bb1.a1', '4.bc1.a1', '4.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.o1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644688
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.dh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.ct1.a1', '16.da1.a1', '16.dc1.a1', '16.dm1.a1', '16.dm1.b1', '16.dn1.a1', '16.dn1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8161, -1, 2562, -1, 8177, -1, 2559, -1], 'generators': [2, 8, 224], 'label': '256.20278.8.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '8.dh1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644689
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.di1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.p1.a1', '16.de1.a1', '16.dg1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6167, -1, 4634, -1, 6180, -1, 4629, -1], 'generators': [18, 8], 'label': '256.20278.8.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.di1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644690
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.di1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.p1.b1', '16.de1.a1', '16.dg1.a1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6167, -1, 4733, -1, 6180, -1, 4728, -1], 'generators': [18, 168], 'label': '256.20278.8.di1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.di1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644691
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.p1.a1', '16.df1.a1', '16.dh1.a1', '16.dq1.a1', '16.dv1.b1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7592, -1, 7333, -1, 7608, -1, 7325, -1], 'generators': [17, 8, 164], 'label': '256.20278.8.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.dj1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 26644692
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.p1.b1', '16.df1.a1', '16.dh1.a1', '16.dq1.b1', '16.dv1.a1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7592, -1, 7416, -1, 7608, -1, 7408, -1], 'generators': [17, 168, 164], 'label': '256.20278.8.dj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.dj1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.b1', 'subgroup_fusion': None, 'weyl_group': '32.28'}
  • id: 26644693
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.dk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.cu1.a1', '16.cy1.a1', '16.dd1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3533, -1, 5292, -1, 3540, -1, 5286, -1], 'generators': [1, 26], 'label': '256.20278.8.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.dk1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644694
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.cw1.a1', '16.cz1.a1', '16.db1.a1', '16.dt1.a1', '16.dt1.b1', '16.du1.a1', '16.du1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3919, -1, 5756, -1, 3926, -1, 5749, -1], 'generators': [17, 24, 228], 'label': '256.20278.8.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '8.dl1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644695
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.dm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1'], 'contains': ['16.cy1.a1', '16.da1.a1', '16.db1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3662, -1, 5483, -1, 3669, -1, 5478, -1], 'generators': [2, 24], 'label': '256.20278.8.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '8.dm1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644696
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.dn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.226', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1'], 'contains': ['16.cz1.a1', '16.dc1.a1', '16.dd1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3782, -1, 5383, -1, 3789, -1, 5378, -1], 'generators': [17, 10], 'label': '256.20278.8.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf1.a1', 'old_label': '8.dn1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 26644697
    {'ambient': '256.20278', 'aut_centralizer_order': 1024, 'aut_label': '16.a1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4476, 5348, 6368, 5829, 4485, 5336, 6362, 5828], 'generators': [164, 160, 64], 'label': '256.20278.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.f1.a1', '8.d1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.m1.a1', '8.l1.a1', '8.k1.a1', '8.n1.a1', '8.o1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644698
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.x1.a1', '8.bd1.a1', '8.be1.a1', '8.bj1.a1', '8.bn1.a1', '8.cz1.a1', '8.cz1.b1', '8.da1.a1', '8.da1.b1', '8.df1.a1', '8.dg1.a1', '8.dg1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8771, 8611, 2027, 3931, 8789, 8611, 2024, 3931], 'generators': [1, 8, 164, 64, 160], 'label': '256.20278.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644699
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.bj1.a1', '8.bk1.a1', '8.bl1.a1', '8.bm1.a1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.h1.b1', '32.j1.a1', '32.bi1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5124, 6836, 6463, 7390, 5135, 6826, 6456, 7390], 'generators': [8, 160, 64], 'label': '256.20278.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1'], 'normal_contains': ['32.c1.a1', '32.h1.a1', '32.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644700
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.r1.a1', '8.s1.a1', '8.bd1.a1', '8.bs1.a1', '8.bt1.a1', '8.bu1.a1'], 'contains': ['32.b1.a1', '32.k1.a1', '32.bm1.a1', '32.bn1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6436, 1834, 3181, 2503, 6449, 1833, 3178, 2503], 'generators': [1, 164, 160], 'label': '256.20278.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.s1.a1', '8.r1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644701
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.t1.a1', '8.u1.a1', '8.be1.a1', '8.cd1.a1', '8.ci1.a1', '8.cj1.a1'], 'contains': ['32.b1.a1', '32.p1.a1', '32.bt1.a1', '32.cd1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6329, 2610, 4326, 2715, 6342, 2609, 4321, 2715], 'generators': [65, 164, 160], 'label': '256.20278.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.u1.a1', '8.t1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644702
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.r1.a1', '8.t1.a1', '8.bf1.a1', '8.bv1.a1', '8.ce1.a1', '8.ck1.a1'], 'contains': ['32.b1.a1', '32.q1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4572, 2222, 5646, 2115, 4582, 2221, 5640, 2115], 'generators': [3, 164], 'label': '256.20278.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.e1.a1', '8.r1.a1', '8.t1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644703
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.s1.a1', '8.u1.a1', '8.bg1.a1', '8.bw1.a1', '8.cf1.a1', '8.cl1.a1'], 'contains': ['32.b1.a1', '32.r1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4644, 1655, 5586, 3103, 4654, 1655, 5580, 3103], 'generators': [67, 164], 'label': '256.20278.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.e1.a1', '8.s1.a1', '8.u1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644704
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.r1.a1', '8.u1.a1', '8.bh1.a1', '8.bx1.a1', '8.cg1.a1', '8.cm1.a1'], 'contains': ['32.b1.a1', '32.bv1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6145, 2398, 4415, 2927, 6157, 2398, 4410, 2927], 'generators': [2, 160], 'label': '256.20278.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.j1.a1', '8.r1.a1', '8.u1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644705
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '16.h1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '4.w1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.s1.a1', '8.t1.a1', '8.bi1.a1', '8.by1.a1', '8.ch1.a1', '8.cn1.a1'], 'contains': ['32.b1.a1', '32.bw1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5827, 2045, 4503, 2291, 5838, 2045, 4497, 2291], 'generators': [66, 160], 'label': '256.20278.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.j1.a1', '8.s1.a1', '8.t1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644706
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.i1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '8.u1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.v1.a1', '8.w1.a1', '8.bn1.a1', '8.co1.a1', '8.cp1.a1', '8.cq1.a1'], 'contains': ['32.c1.a1', '32.i1.a1', '32.i1.b1', '32.m1.a1', '32.by1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5018, 7048, 6552, 7035, 5028, 7038, 6545, 7034], 'generators': [172, 160, 64], 'label': '256.20278.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.a1.a1', '8.v1.a1', '8.w1.a1'], 'normal_contains': ['32.c1.a1', '32.i1.a1', '32.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644707
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.j1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.p1.a1', '8.v1.a1', '8.bo1.a1', '8.bz1.a1', '8.cr1.a1', '8.cs1.a1'], 'contains': ['32.c1.a1', '32.n1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2568, 7225, 8136, 7213, 2573, 7216, 8127, 7212], 'generators': [16, 64], 'label': '256.20278.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.d1.a1', '8.p1.a1', '8.v1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644708
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.k1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.q1.a1', '8.w1.a1', '8.bp1.a1', '8.ca1.a1', '8.ct1.a1', '8.cu1.a1'], 'contains': ['32.c1.a1', '32.o1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2639, 6658, 8076, 8029, 2644, 6648, 8068, 8034], 'generators': [180, 64], 'label': '256.20278.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.d1.a1', '8.q1.a1', '8.w1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644709
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.k1.a1', '8.p1.a1', '8.q1.a1', '8.v1.a1', '8.w1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2497, 9919, 6630, 9919, 2502, 9919, 6623, 9919], 'generators': [8, 16, 164], 'label': '256.20278.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.k1.a1', '8.p1.a1', '8.q1.a1', '8.v1.a1', '8.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644710
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '16.l1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.p1.a1', '8.w1.a1', '8.bq1.a1', '8.cb1.a1', '8.cv1.a1', '8.cx1.a1'], 'contains': ['32.c1.a1', '32.ca1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3047, 7401, 6924, 7602, 3053, 7392, 6917, 7602], 'generators': [24, 64], 'label': '256.20278.16.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': ['8.k1.a1', '8.p1.a1', '8.w1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.l1.a1', 'projective_image': '64.226', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644711
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '16.m1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.q1.a1', '8.v1.a1', '8.br1.a1', '8.cc1.a1', '8.cw1.a1', '8.cy1.a1'], 'contains': ['32.c1.a1', '32.cb1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3152, 6482, 7737, 7813, 3159, 6472, 7729, 7812], 'generators': [188, 64], 'label': '256.20278.16.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': ['8.k1.a1', '8.q1.a1', '8.v1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.m1.a1', 'projective_image': '64.226', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644712
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.cz1.a1', '8.db1.a1', '8.dc1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.i1.a1', '32.v1.a1', '32.bg1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8706, 6163, 4753, 6715, 8723, 6154, 4748, 6714], 'generators': [8, 4, 64], 'label': '256.20278.16.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.d1.a1', '32.h1.a1', '32.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.n1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644713
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.cz1.b1', '8.db1.b1', '8.dc1.b1'], 'contains': ['32.d1.a1', '32.h1.b1', '32.i1.b1', '32.v1.b1', '32.bg1.b1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8706, 6163, 5220, 6430, 8723, 6154, 5214, 6430], 'generators': [168, 4, 64], 'label': '256.20278.16.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.d1.a1', '32.h1.b1', '32.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.n1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644714
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.da1.a1', '8.dd1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.x1.a1', '32.bq1.a1', '32.br1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8473, 5864, 3442, 4673, 8491, 5843, 3438, 4531], 'generators': [9, 164, 224], 'label': '256.20278.16.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.o1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644715
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.da1.b1', '8.dd1.b1', '8.de1.b1'], 'contains': ['32.e1.a1', '32.x1.b1', '32.bq1.b1', '32.br1.b1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8473, 5864, 3004, 5029, 8491, 5843, 3001, 5315], 'generators': [73, 164, 224], 'label': '256.20278.16.o1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.o1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644716
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.p1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.dg1.a1', '8.di1.a1', '8.dj1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.i1.b1', '32.z1.a1', '32.bh1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8634, 6305, 5278, 6856, 8651, 6296, 5273, 6857], 'generators': [8, 164, 64], 'label': '256.20278.16.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.g1.a1', '32.h1.a1', '32.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.p1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644717
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.p1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.dg1.b1', '8.di1.b1', '8.dj1.b1'], 'contains': ['32.g1.a1', '32.h1.b1', '32.i1.a1', '32.z1.b1', '32.bh1.b1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8634, 6305, 5338, 6572, 8651, 6296, 5333, 6572], 'generators': [168, 164, 64], 'label': '256.20278.16.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.g1.a1', '32.h1.b1', '32.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.p1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644718
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.x1.a1', '8.y1.a1'], 'contains': ['32.a1.a1', '32.j1.a1', '32.m1.a1', '32.v1.a1', '32.v1.b1', '32.z1.a1', '32.z1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5933, -1, 5145, -1, 5945, -1, 5140, -1], 'generators': [8, 228, 160], 'label': '256.20278.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.q1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644719
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.x1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.k1.a1', '32.p1.a1', '32.w1.a1', '32.ba1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5337, -1, 4237, -1, 5348, -1, 4233, -1], 'generators': [1, 228, 160], 'label': '256.20278.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.r1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644720
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1', '8.y1.a1', '8.bf1.a1', '8.bg1.a1', '8.bk1.a1', '8.co1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2614, 9428, 6971, 7062, 2619, 9427, 6963, 7062], 'generators': [3, 8, 164, 64], 'label': '256.20278.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.f1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644721
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.x1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.l1.a1', '32.x1.a1', '32.x1.b1', '32.bb1.a1', '32.ci1.a1', '32.cp1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7417, -1, 3311, -1, 7432, -1, 3308, -1], 'generators': [9, 228, 160, 128], 'label': '256.20278.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.s1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644722
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.z1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.n1.a1', '32.o1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2259, -1, 9201, -1, 2264, -1, 9191, -1], 'generators': [16, 228], 'label': '256.20278.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.t1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644723
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.y1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.q1.a1', '32.r1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1618, -1, 9430, -1, 1622, -1, 9419, -1], 'generators': [3, 228], 'label': '256.20278.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.u1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644724
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.ba1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.bc1.a1', '32.cj1.a1', '32.cq1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1391, -1, 8525, -1, 1394, -1, 8516, -1], 'generators': [26, 160, 128], 'label': '256.20278.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.v1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644725
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.y1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.s1.a1', '32.ck1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1513, -1, 8953, -1, 1516, -1, 8943, -1], 'generators': [11, 228, 128], 'label': '256.20278.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.w1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644726
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.z1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.t1.a1', '32.y1.a1', '32.bd1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2364, -1, 8304, -1, 2370, -1, 8295, -1], 'generators': [17, 228, 160], 'label': '256.20278.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.x1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644727
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.u1.a1', '32.cl1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [948, -1, 9342, -1, 950, -1, 9332, -1], 'generators': [19, 228, 128], 'label': '256.20278.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.y1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644728
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.bd1.a1', '8.bj1.a1'], 'contains': ['32.j1.a1', '32.k1.a1', '32.l1.a1', '32.be1.a1', '32.be1.b1', '32.be1.c1', '32.be1.d1', '32.cm1.a1', '32.cr1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7923, -1, 20, -1, 7939, -1, 21, -1], 'generators': [1, 8, 160, 128], 'label': '256.20278.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.z1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644729
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.be1.a1', '8.bj1.a1'], 'contains': ['32.j1.a1', '32.l1.a1', '32.p1.a1', '32.bf1.a1', '32.bf1.b1', '32.bf1.c1', '32.bf1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7610, -1, 2131, -1, 7625, -1, 2128, -1], 'generators': [65, 8, 160], 'label': '256.20278.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ba1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644730
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bd1.a1', '8.be1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1', '8.bi1.a1'], 'contains': ['32.b1.a1', '32.j1.a1', '32.m1.a1', '32.bg1.a1', '32.bg1.b1', '32.bh1.a1', '32.bh1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6852, -1, 3597, -1, 6866, -1, 3593, -1], 'generators': [8, 164, 160], 'label': '256.20278.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bb1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644731
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.h1.a1', '4.m1.a1', '4.n1.a1', '4.r1.a1', '4.bn1.a1', '4.bo1.a1', '4.br1.a1', '4.bs1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4775, 7234, 6579, 7352, 4784, 7238, 6571, 7352], 'generators': [1, 8, 16, 164], 'label': '256.20278.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.h1.a1', '4.m1.a1', '4.n1.a1', '4.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644732
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.l1.a1', '8.di1.a1', '8.di1.b1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6081, 3959, 4618, 6748, 6093, 3959, 4613, 6748], 'generators': [18, 8, 160], 'label': '256.20278.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.f1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.f1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644733
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.bf1.a1', '8.bk1.a1'], 'contains': ['32.j1.a1', '32.q1.a1', '32.s1.a1', '32.cn1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1859, -1, 9055, -1, 1863, -1, 9045, -1], 'generators': [3, 8, 128], 'label': '256.20278.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.bc1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644734
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.bg1.a1', '8.bk1.a1'], 'contains': ['32.j1.a1', '32.r1.a1', '32.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2036, -1, 8813, -1, 2040, -1, 8803, -1], 'generators': [67, 8], 'label': '256.20278.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.bd1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644735
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.bd1.a1', '8.bn1.a1'], 'contains': ['32.k1.a1', '32.l1.a1', '32.m1.a1', '32.bj1.a1', '32.bj1.b1', '32.bj1.c1', '32.bj1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7837, -1, 1418, -1, 7853, -1, 1417, -1], 'generators': [1, 172, 160], 'label': '256.20278.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.be1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644736
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.bj1.a1', '8.bn1.a1', '8.bo1.a1', '8.bp1.a1', '8.bq1.a1', '8.br1.a1'], 'contains': ['32.c1.a1', '32.k1.a1', '32.p1.a1', '32.bk1.a1', '32.bl1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5451, -1, 5050, -1, 5462, -1, 5045, -1], 'generators': [1, 160, 64], 'label': '256.20278.16.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bf1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644737
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bo1.a1', '8.bs1.a1'], 'contains': ['32.k1.a1', '32.n1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2862, -1, 7891, -1, 2868, -1, 7883, -1], 'generators': [1, 16], 'label': '256.20278.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bg1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644738
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bp1.a1', '8.bs1.a1'], 'contains': ['32.k1.a1', '32.o1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2950, -1, 7818, -1, 2956, -1, 7810, -1], 'generators': [1, 180], 'label': '256.20278.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bh1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644739
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.be1.a1', '8.bn1.a1'], 'contains': ['32.l1.a1', '32.m1.a1', '32.p1.a1', '32.bo1.a1', '32.bo1.b1', '32.bo1.c1', '32.bo1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7723, -1, 2790, -1, 7739, -1, 2787, -1], 'generators': [65, 172, 160], 'label': '256.20278.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bi1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644740
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.bd1.a1', '8.be1.a1', '8.bv1.a1', '8.bw1.a1', '8.bx1.a1', '8.by1.a1'], 'contains': ['32.b1.a1', '32.l1.a1', '32.bp1.a1', '32.br1.a1', '32.br1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8795, -1, 2635, -1, 8813, -1, 2632, -1], 'generators': [9, 164, 160], 'label': '256.20278.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bj1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644741
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.bj1.a1', '8.bn1.a1', '8.bz1.a1', '8.ca1.a1', '8.cb1.a1', '8.cc1.a1'], 'contains': ['32.c1.a1', '32.l1.a1', '32.bq1.a1', '32.bq1.b1', '32.bs1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7503, -1, 4590, -1, 7518, -1, 4586, -1], 'generators': [9, 160, 64], 'label': '256.20278.16.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bk1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644742
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.bs1.a1', '8.cd1.a1', '8.ce1.a1', '8.cf1.a1', '8.cg1.a1', '8.ch1.a1'], 'contains': ['32.b1.a1', '32.n1.a1', '32.o1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3237, -1, 8603, -1, 3244, -1, 8594, -1], 'generators': [16, 164], 'label': '256.20278.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bl1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644743
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '8.n1.a1', '8.bl1.a1', '8.cp1.a1', '8.db1.a1', '8.db1.b1', '8.dj1.a1', '8.dj1.b1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6822, 6308, 7225, 8861, 6836, 6308, 7217, 8861], 'generators': [17, 8, 164, 160], 'label': '256.20278.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.h1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644744
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.bf1.a1', '8.bg1.a1', '8.bt1.a1', '8.bx1.a1', '8.by1.a1', '8.ci1.a1'], 'contains': ['32.b1.a1', '32.s1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4715, -1, 5397, -1, 4725, -1, 5392, -1], 'generators': [11, 164], 'label': '256.20278.16.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bm1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644745
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.bs1.a1', '8.cd1.a1', '8.ck1.a1', '8.cl1.a1', '8.cm1.a1', '8.cn1.a1'], 'contains': ['32.b1.a1', '32.t1.a1', '32.bu1.a1', '32.ce1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4361, -1, 5720, -1, 4370, -1, 5714, -1], 'generators': [17, 164, 160], 'label': '256.20278.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bn1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644746
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bu1.a1', '8.ce1.a1', '8.cf1.a1', '8.cj1.a1', '8.cm1.a1', '8.cn1.a1'], 'contains': ['32.b1.a1', '32.u1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3764, -1, 5794, -1, 3772, -1, 5788, -1], 'generators': [19, 164], 'label': '256.20278.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bo1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644747
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.bu1.a1', '8.cg1.a1', '8.ch1.a1', '8.cj1.a1', '8.ck1.a1', '8.cl1.a1'], 'contains': ['32.b1.a1', '32.cf1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5566, -1, 4956, -1, 5577, -1, 4950, -1], 'generators': [18, 160], 'label': '256.20278.16.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bp1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644748
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.bh1.a1', '8.bi1.a1', '8.bt1.a1', '8.bv1.a1', '8.bw1.a1', '8.ci1.a1'], 'contains': ['32.b1.a1', '32.bx1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6966, -1, 4149, -1, 6980, -1, 4145, -1], 'generators': [10, 160], 'label': '256.20278.16.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bq1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644749
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.bk1.a1', '8.co1.a1', '8.cr1.a1', '8.ct1.a1', '8.cv1.a1', '8.cw1.a1'], 'contains': ['32.c1.a1', '32.q1.a1', '32.r1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1694, -1, 9265, -1, 1698, -1, 9255, -1], 'generators': [3, 64], 'label': '256.20278.16.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.br1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644750
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.bk1.a1', '8.co1.a1', '8.cs1.a1', '8.cu1.a1', '8.cx1.a1', '8.cy1.a1'], 'contains': ['32.c1.a1', '32.s1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2180, -1, 8444, -1, 2184, -1, 8435, -1], 'generators': [11, 64], 'label': '256.20278.16.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bs1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644751
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.bl1.a1', '8.bo1.a1', '8.bp1.a1', '8.cb1.a1', '8.cc1.a1', '8.cp1.a1'], 'contains': ['32.c1.a1', '32.t1.a1', '32.bz1.a1', '32.cg1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4070, -1, 7648, -1, 4078, -1, 7641, -1], 'generators': [17, 160, 64], 'label': '256.20278.16.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bt1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644752
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bm1.a1', '8.cq1.a1', '8.cr1.a1', '8.ct1.a1', '8.cx1.a1', '8.cy1.a1'], 'contains': ['32.c1.a1', '32.u1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1762, -1, 8385, -1, 1765, -1, 8376, -1], 'generators': [19, 64], 'label': '256.20278.16.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bu1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644753
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.bv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.bl1.a1', '8.bq1.a1', '8.br1.a1', '8.bz1.a1', '8.ca1.a1', '8.cp1.a1'], 'contains': ['32.c1.a1', '32.ch1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5230, -1, 7561, -1, 5241, -1, 7552, -1], 'generators': [25, 160], 'label': '256.20278.16.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bv1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644754
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.o1.a1', '8.bm1.a1', '8.cq1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2752, 6641, 6728, 8255, 2758, 6641, 6721, 8255], 'generators': [19, 8, 164], 'label': '256.20278.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.i1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644755
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.bm1.a1', '8.cq1.a1', '8.cs1.a1', '8.cu1.a1', '8.cv1.a1', '8.cw1.a1'], 'contains': ['32.c1.a1', '32.cc1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2479, -1, 8209, -1, 2484, -1, 8201, -1], 'generators': [27, 64], 'label': '256.20278.16.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bw1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644756
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.bf1.a1', '8.co1.a1'], 'contains': ['32.m1.a1', '32.q1.a1', '32.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1956, -1, 9134, -1, 1960, -1, 9125, -1], 'generators': [3, 172], 'label': '256.20278.16.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.bx1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644757
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '16.by1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.bg1.a1', '8.co1.a1'], 'contains': ['32.m1.a1', '32.r1.a1', '32.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2112, -1, 8875, -1, 2117, -1, 8866, -1], 'generators': [67, 172], 'label': '256.20278.16.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.by1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644758
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bo1.a1', '8.cd1.a1'], 'contains': ['32.n1.a1', '32.p1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2711, -1, 8017, -1, 2716, -1, 8008, -1], 'generators': [65, 16], 'label': '256.20278.16.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.bz1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644759
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.ce1.a1', '8.cr1.a1'], 'contains': ['32.n1.a1', '32.q1.a1', '32.u1.a1', '32.co1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1062, -1, 9689, -1, 1064, -1, 9679, -1], 'generators': [3, 16, 128], 'label': '256.20278.16.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.ca1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644760
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.cf1.a1', '8.cr1.a1'], 'contains': ['32.n1.a1', '32.r1.a1', '32.u1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1151, -1, 9615, -1, 1154, -1, 9604, -1], 'generators': [67, 16], 'label': '256.20278.16.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.cb1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644761
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bp1.a1', '8.cd1.a1'], 'contains': ['32.o1.a1', '32.p1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2782, -1, 7957, -1, 2788, -1, 7949, -1], 'generators': [65, 180], 'label': '256.20278.16.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.cc1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644762
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.ce1.a1', '8.ct1.a1'], 'contains': ['32.o1.a1', '32.q1.a1', '32.u1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1223, -1, 9555, -1, 1225, -1, 9545, -1], 'generators': [3, 180], 'label': '256.20278.16.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.cd1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644763
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.cf1.a1', '8.ct1.a1'], 'contains': ['32.o1.a1', '32.r1.a1', '32.u1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1294, -1, 9496, -1, 1297, -1, 9486, -1], 'generators': [67, 180], 'label': '256.20278.16.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.ce1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644764
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.cz1.a1', '8.da1.a1'], 'contains': ['32.v1.a1', '32.w1.a1', '32.x1.a1', '32.be1.a1', '32.bf1.a1', '32.bj1.a1', '32.bo1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9934, -1, 2042, -1, 9954, -1, 2040, -1], 'generators': [1, 8, 68], 'label': '256.20278.16.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644765
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.m1.a1', '8.bh1.a1', '8.bi1.a1', '8.dc1.a1', '8.dc1.b1', '8.dh1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7382, 7760, 2861, 4823, 7397, 7760, 2858, 4823], 'generators': [2, 8, 160, 64], 'label': '256.20278.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.j1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644766
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.cz1.a1', '8.da1.b1'], 'contains': ['32.v1.a1', '32.w1.a1', '32.x1.b1', '32.be1.b1', '32.bf1.b1', '32.bj1.c1', '32.bo1.c1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9934, -1, 1153, -1, 9954, -1, 1152, -1], 'generators': [65, 8, 68], 'label': '256.20278.16.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644767
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.cz1.b1', '8.da1.a1'], 'contains': ['32.v1.b1', '32.w1.a1', '32.x1.a1', '32.be1.c1', '32.bf1.c1', '32.bj1.b1', '32.bo1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9934, -1, 2279, -1, 9954, -1, 2276, -1], 'generators': [1, 232, 68], 'label': '256.20278.16.cf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644768
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.cz1.b1', '8.da1.b1'], 'contains': ['32.v1.b1', '32.w1.a1', '32.x1.b1', '32.be1.d1', '32.bf1.d1', '32.bj1.d1', '32.bo1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9934, -1, 1331, -1, 9954, -1, 1329, -1], 'generators': [65, 232, 68], 'label': '256.20278.16.cf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644769
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.da1.a1', '8.da1.b1'], 'contains': ['32.e1.a1', '32.v1.a1', '32.v1.b1', '32.bh1.a1', '32.bh1.b1', '32.bi1.a1', '32.by1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8563, -1, 3368, -1, 8580, -1, 3364, -1], 'generators': [8, 164, 224], 'label': '256.20278.16.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.cg1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644770
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.cz1.a1', '8.cz1.b1'], 'contains': ['32.d1.a1', '32.w1.a1', '32.bl1.a1', '32.bm1.a1', '32.bt1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8313, -1, 2870, -1, 8329, -1, 2867, -1], 'generators': [1, 4, 64], 'label': '256.20278.16.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.ch1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644771
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.ci1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.da1.a1', '8.da1.b1'], 'contains': ['32.e1.a1', '32.w1.a1', '32.bk1.a1', '32.bn1.a1', '32.cd1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8170, -1, 2930, -1, 8186, -1, 2927, -1], 'generators': [1, 164, 224], 'label': '256.20278.16.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ci1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644772
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.cz1.a1', '8.cz1.b1'], 'contains': ['32.d1.a1', '32.x1.a1', '32.x1.b1', '32.bp1.a1', '32.bs1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9079, -1, 2546, -1, 9098, -1, 2543, -1], 'generators': [9, 4, 64], 'label': '256.20278.16.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.cj1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644773
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.ck1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.db1.a1', '8.db1.b1'], 'contains': ['32.d1.a1', '32.y1.a1', '32.bu1.a1', '32.cg1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4911, -1, 7077, -1, 4921, -1, 7069, -1], 'generators': [17, 4, 64], 'label': '256.20278.16.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ck1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644774
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.cl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.dc1.a1', '8.dc1.b1'], 'contains': ['32.d1.a1', '32.bv1.a1', '32.bw1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7072, -1, 3996, -1, 7086, -1, 3992, -1], 'generators': [2, 64], 'label': '256.20278.16.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.cl1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644775
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.dc1.a1', '8.dc1.b1'], 'contains': ['32.d1.a1', '32.bx1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7163, -1, 4073, -1, 7178, -1, 4068, -1], 'generators': [10, 64], 'label': '256.20278.16.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.cm1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644776
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1', '8.z1.a1', '8.bo1.a1', '8.bp1.a1', '8.bs1.a1', '8.cd1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3176, 607, 8198, 2981, 3182, 607, 8190, 2981], 'generators': [1, 16, 164, 64], 'label': '256.20278.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644777
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.db1.a1', '8.db1.b1'], 'contains': ['32.d1.a1', '32.ch1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6751, -1, 7001, -1, 6765, -1, 6993, -1], 'generators': [25, 4], 'label': '256.20278.16.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.cn1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644778
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.dd1.a1', '8.dd1.b1'], 'contains': ['32.e1.a1', '32.y1.a1', '32.bz1.a1', '32.ce1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4255, -1, 6835, -1, 4263, -1, 6828, -1], 'generators': [17, 164, 224], 'label': '256.20278.16.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.co1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644779
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.dd1.a1', '8.dd1.b1'], 'contains': ['32.e1.a1', '32.ca1.a1', '32.cb1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3569, -1, 6084, -1, 3576, -1, 6077, -1], 'generators': [24, 164], 'label': '256.20278.16.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.cp1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644780
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.de1.a1', '8.de1.b1'], 'contains': ['32.e1.a1', '32.cf1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5657, -1, 4815, -1, 5669, -1, 4810, -1], 'generators': [18, 224], 'label': '256.20278.16.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.cq1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644781
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.de1.a1', '8.de1.b1'], 'contains': ['32.e1.a1', '32.cc1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4162, -1, 5460, -1, 4171, -1, 5454, -1], 'generators': [27, 164], 'label': '256.20278.16.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.cr1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644782
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.df1.a1', '8.dg1.a1'], 'contains': ['32.z1.a1', '32.ba1.a1', '32.bb1.a1', '32.be1.a1', '32.bf1.b1', '32.bj1.d1', '32.bo1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9508, -1, 799, -1, 9528, -1, 799, -1], 'generators': [1, 8, 228], 'label': '256.20278.16.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cs1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644783
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.df1.a1', '8.dg1.a1'], 'contains': ['32.z1.a1', '32.ba1.a1', '32.bb1.a1', '32.be1.b1', '32.bf1.a1', '32.bj1.b1', '32.bo1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9508, -1, 622, -1, 9528, -1, 622, -1], 'generators': [161, 8, 228], 'label': '256.20278.16.cs1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cs1.a2', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.a2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644784
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.df1.a1', '8.dg1.b1'], 'contains': ['32.z1.b1', '32.ba1.a1', '32.bb1.a1', '32.be1.d1', '32.bf1.c1', '32.bj1.a1', '32.bo1.c1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9508, -1, 977, -1, 9528, -1, 975, -1], 'generators': [1, 168, 228], 'label': '256.20278.16.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cs1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644785
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.df1.a1', '8.dg1.b1'], 'contains': ['32.z1.b1', '32.ba1.a1', '32.bb1.a1', '32.be1.c1', '32.bf1.d1', '32.bj1.c1', '32.bo1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9508, -1, 888, -1, 9528, -1, 887, -1], 'generators': [161, 168, 228], 'label': '256.20278.16.cs1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cs1.b2', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.b2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644786
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.df1.a1', '8.dh1.a1'], 'contains': ['32.f1.a1', '32.z1.a1', '32.z1.b1', '32.bg1.a1', '32.bg1.b1', '32.bi1.a1', '32.by1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8384, -1, 3516, -1, 8401, -1, 3512, -1], 'generators': [8, 228, 224], 'label': '256.20278.16.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ct1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644787
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.j1.a1', '8.r1.a1', '8.s1.a1', '8.t1.a1', '8.u1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6967, 81, 3886, 81, 6981, 81, 3882, 81], 'generators': [1, 2, 64], 'label': '256.20278.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.j1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.j1.a1', '8.s1.a1', '8.r1.a1', '8.u1.a1', '8.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644788
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.df1.a1', '8.dk1.a1'], 'contains': ['32.f1.a1', '32.ba1.a1', '32.bk1.a1', '32.bm1.a1', '32.bt1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7990, -1, 3256, -1, 8007, -1, 3252, -1], 'generators': [1, 228, 224], 'label': '256.20278.16.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.cu1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644789
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.cv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.dg1.a1', '8.dg1.b1'], 'contains': ['32.g1.a1', '32.ba1.a1', '32.bl1.a1', '32.bn1.a1', '32.cd1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8240, -1, 2709, -1, 8257, -1, 2706, -1], 'generators': [1, 164, 64], 'label': '256.20278.16.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.cv1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644790
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.df1.a1', '8.dl1.a1'], 'contains': ['32.f1.a1', '32.bb1.a1', '32.bp1.a1', '32.bq1.a1', '32.bq1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8080, -1, 3092, -1, 8097, -1, 3089, -1], 'generators': [9, 228, 224], 'label': '256.20278.16.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cw1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644791
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.dg1.a1', '8.dg1.b1'], 'contains': ['32.g1.a1', '32.bb1.a1', '32.br1.a1', '32.br1.b1', '32.bs1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8901, -1, 1775, -1, 8919, -1, 1773, -1], 'generators': [9, 164, 64], 'label': '256.20278.16.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.cx1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644792
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.dk1.a1', '8.dm1.a1'], 'contains': ['32.f1.a1', '32.bc1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3301, -1, 6676, -1, 3308, -1, 6669, -1], 'generators': [26, 224], 'label': '256.20278.16.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '16.cy1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644793
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.dl1.a1', '8.dn1.a1'], 'contains': ['32.f1.a1', '32.bd1.a1', '32.bu1.a1', '32.bz1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3675, -1, 6746, -1, 3683, -1, 6740, -1], 'generators': [17, 228, 224], 'label': '256.20278.16.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.cz1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 26644794
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.da1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.dh1.a1', '8.dm1.a1'], 'contains': ['32.f1.a1', '32.bv1.a1', '32.bw1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6039, -1, 4679, -1, 6051, -1, 4674, -1], 'generators': [2, 224], 'label': '256.20278.16.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.da1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.da1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644795
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.db1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.dl1.a1', '8.dm1.a1'], 'contains': ['32.f1.a1', '32.ca1.a1', '32.cb1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3463, -1, 5932, -1, 3470, -1, 5926, -1], 'generators': [24, 228], 'label': '256.20278.16.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.db1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.db1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644796
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.dc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.dh1.a1', '8.dn1.a1'], 'contains': ['32.f1.a1', '32.bx1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6237, -1, 4879, -1, 6249, -1, 4874, -1], 'generators': [10, 224], 'label': '256.20278.16.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.dc1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644797
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.dd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.dk1.a1', '8.dn1.a1'], 'contains': ['32.f1.a1', '32.cc1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3372, -1, 5857, -1, 3378, -1, 5850, -1], 'generators': [27, 228], 'label': '256.20278.16.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.dd1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644798
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.o1.a1', '8.dk1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3342, 938, 5638, 353, 3349, 938, 5632, 353], 'generators': [1, 26, 64], 'label': '256.20278.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.c1.a1', '2.j1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644799
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '16.de1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.di1.a1', '8.di1.b1'], 'contains': ['32.g1.a1', '32.bc1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3832, -1, 6622, -1, 3840, -1, 6616, -1], 'generators': [26, 64], 'label': '256.20278.16.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.de1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.de1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644800
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.df1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.dj1.a1', '8.dj1.b1'], 'contains': ['32.g1.a1', '32.bd1.a1', '32.ce1.a1', '32.cg1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4805, -1, 7472, -1, 4815, -1, 7464, -1], 'generators': [17, 164, 64], 'label': '256.20278.16.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.df1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 26644801
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.dg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.di1.a1', '8.di1.b1'], 'contains': ['32.g1.a1', '32.cf1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5735, -1, 5525, -1, 5747, -1, 5519, -1], 'generators': [18, 64], 'label': '256.20278.16.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.dg1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644802
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '16.dh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.dj1.a1', '8.dj1.b1'], 'contains': ['32.g1.a1', '32.ch1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6528, -1, 7154, -1, 6541, -1, 7146, -1], 'generators': [25, 164], 'label': '256.20278.16.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.dh1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644803
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.di1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.cz1.a1', '8.df1.a1'], 'contains': ['32.be1.a1', '32.be1.b1', '32.bg1.a1', '32.bj1.a1', '32.bj1.c1', '32.bm1.a1', '32.bp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9721, -1, 268, -1, 9740, -1, 268, -1], 'generators': [1, 8, 4], 'label': '256.20278.16.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.di1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.di1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644804
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.di1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.cz1.b1', '8.df1.a1'], 'contains': ['32.be1.c1', '32.be1.d1', '32.bg1.b1', '32.bj1.b1', '32.bj1.d1', '32.bm1.a1', '32.bp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9721, -1, 357, -1, 9740, -1, 357, -1], 'generators': [1, 168, 4], 'label': '256.20278.16.di1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.di1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.di1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644805
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.da1.a1', '8.dg1.a1'], 'contains': ['32.be1.a1', '32.bh1.a1', '32.bj1.b1', '32.bn1.a1', '32.br1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9614, -1, 446, -1, 9634, -1, 445, -1], 'generators': [1, 8, 164], 'label': '256.20278.16.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dj1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644806
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.da1.b1', '8.dg1.a1'], 'contains': ['32.be1.b1', '32.bh1.a1', '32.bj1.d1', '32.bn1.a1', '32.br1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9614, -1, 92, -1, 9634, -1, 92, -1], 'generators': [161, 8, 164], 'label': '256.20278.16.dj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dj1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644807
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.da1.a1', '8.dg1.b1'], 'contains': ['32.be1.c1', '32.bh1.b1', '32.bj1.a1', '32.bn1.a1', '32.br1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9614, -1, 534, -1, 9634, -1, 533, -1], 'generators': [161, 168, 164], 'label': '256.20278.16.dj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dj1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644808
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.da1.b1', '8.dg1.b1'], 'contains': ['32.be1.d1', '32.bh1.b1', '32.bj1.c1', '32.bn1.a1', '32.br1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9614, -1, 181, -1, 9634, -1, 180, -1], 'generators': [1, 168, 164], 'label': '256.20278.16.dj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dj1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644809
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.m1.a1', '8.bt1.a1', '8.ci1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7084, 7426, 3788, 667, 7098, 7426, 3785, 667], 'generators': [1, 10, 64], 'label': '256.20278.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644810
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cz1.a1', '8.df1.a1'], 'contains': ['32.bf1.a1', '32.bf1.b1', '32.bg1.a1', '32.bo1.a1', '32.bo1.c1', '32.bp1.a1', '32.bt1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9347, -1, 1967, -1, 9366, -1, 1965, -1], 'generators': [65, 8, 4], 'label': '256.20278.16.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dk1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644811
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cz1.b1', '8.df1.a1'], 'contains': ['32.bf1.c1', '32.bf1.d1', '32.bg1.b1', '32.bo1.b1', '32.bo1.d1', '32.bp1.a1', '32.bt1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9347, -1, 2204, -1, 9366, -1, 2202, -1], 'generators': [65, 168, 4], 'label': '256.20278.16.dk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dk1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dk1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644812
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.da1.a1', '8.dg1.a1'], 'contains': ['32.bf1.a1', '32.bh1.a1', '32.bo1.b1', '32.br1.a1', '32.cd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9276, -1, 2353, -1, 9294, -1, 2351, -1], 'generators': [225, 8, 164], 'label': '256.20278.16.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dl1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644813
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.da1.b1', '8.dg1.a1'], 'contains': ['32.bf1.b1', '32.bh1.a1', '32.bo1.d1', '32.br1.b1', '32.cd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9276, -1, 1493, -1, 9294, -1, 1491, -1], 'generators': [65, 8, 164], 'label': '256.20278.16.dl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dl1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644814
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.da1.a1', '8.dg1.b1'], 'contains': ['32.bf1.c1', '32.bh1.b1', '32.bo1.a1', '32.br1.a1', '32.cd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9276, -1, 2412, -1, 9294, -1, 2410, -1], 'generators': [65, 168, 164], 'label': '256.20278.16.dl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dl1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644815
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.da1.b1', '8.dg1.b1'], 'contains': ['32.bf1.d1', '32.bh1.b1', '32.bo1.c1', '32.br1.b1', '32.cd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9276, -1, 1553, -1, 9294, -1, 1551, -1], 'generators': [225, 168, 164], 'label': '256.20278.16.dl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.dl1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644816
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.dm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.dc1.a1', '8.dh1.a1'], 'contains': ['32.bg1.a1', '32.bv1.a1', '32.bx1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7333, -1, 3691, -1, 7348, -1, 3688, -1], 'generators': [2, 8], 'label': '256.20278.16.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.dm1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644817
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.dm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.dc1.b1', '8.dh1.a1'], 'contains': ['32.bg1.b1', '32.bv1.a1', '32.bx1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7333, -1, 3779, -1, 7348, -1, 3776, -1], 'generators': [2, 168], 'label': '256.20278.16.dm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.dm1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dm1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644818
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.dn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '8.dc1.a1', '8.dh1.a1'], 'contains': ['32.bg1.a1', '32.bw1.a1', '32.bx1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7241, -1, 3856, -1, 7256, -1, 3852, -1], 'generators': [66, 8], 'label': '256.20278.16.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.dn1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644819
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '16.dn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 512, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '8.dc1.b1', '8.dh1.a1'], 'contains': ['32.bg1.b1', '32.bw1.a1', '32.bx1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7241, -1, 3921, -1, 7256, -1, 3916, -1], 'generators': [66, 168], 'label': '256.20278.16.dn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '16.dn1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644820
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.l1.a1', '8.bu1.a1', '8.cj1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5923, 2759, 4358, 5531, 5935, 2759, 4354, 5531], 'generators': [1, 18, 64], 'label': '256.20278.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644821
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.do1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.da1.a1', '8.df1.a1'], 'contains': ['32.be1.a1', '32.be1.c1', '32.bf1.a1', '32.bf1.c1', '32.bi1.a1', '32.bk1.a1', '32.bq1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1686, -1, 9205, -1, 1684, -1], 'generators': [1, 8, 224], 'label': '256.20278.16.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.do1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.do1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644822
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.do1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.da1.b1', '8.df1.a1'], 'contains': ['32.be1.b1', '32.be1.d1', '32.bf1.b1', '32.bf1.d1', '32.bi1.a1', '32.bk1.a1', '32.bq1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 711, -1, 9205, -1, 710, -1], 'generators': [65, 8, 224], 'label': '256.20278.16.do1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.do1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.do1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644823
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.cz1.a1', '8.dg1.a1'], 'contains': ['32.h1.a1', '32.be1.a1', '32.be1.b1', '32.bf1.a1', '32.bf1.b1', '32.bl1.a1', '32.bs1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9827, -1, 1064, -1, 9847, -1, 1064, -1], 'generators': [1, 8, 64], 'label': '256.20278.16.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dp1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644824
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.cz1.b1', '8.dg1.b1'], 'contains': ['32.h1.b1', '32.be1.c1', '32.be1.d1', '32.bf1.c1', '32.bf1.d1', '32.bl1.a1', '32.bs1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9827, -1, 1242, -1, 9847, -1, 1240, -1], 'generators': [1, 168, 64], 'label': '256.20278.16.dp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dp1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644825
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.db1.a1', '8.dj1.a1'], 'contains': ['32.h1.a1', '32.cg1.a1', '32.ch1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6675, -1, 7218, -1, 6688, -1, 7210, -1], 'generators': [17, 8], 'label': '256.20278.16.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '16.dq1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644826
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.db1.b1', '8.dj1.b1'], 'contains': ['32.h1.b1', '32.cg1.a1', '32.ch1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6675, -1, 7281, -1, 6688, -1, 7273, -1], 'generators': [17, 168], 'label': '256.20278.16.dq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '16.dq1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dq1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644827
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.da1.a1', '8.df1.a1'], 'contains': ['32.bj1.a1', '32.bj1.b1', '32.bk1.a1', '32.bo1.a1', '32.bo1.b1', '32.bq1.a1', '32.by1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8991, -1, 2472, -1, 9009, -1, 2469, -1], 'generators': [1, 172, 224], 'label': '256.20278.16.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dr1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644828
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.da1.b1', '8.df1.a1'], 'contains': ['32.bj1.c1', '32.bj1.d1', '32.bk1.a1', '32.bo1.c1', '32.bo1.d1', '32.bq1.b1', '32.by1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8991, -1, 1612, -1, 9009, -1, 1610, -1], 'generators': [65, 172, 224], 'label': '256.20278.16.dr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dr1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644829
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.cz1.a1', '8.dg1.b1'], 'contains': ['32.i1.a1', '32.bj1.a1', '32.bj1.c1', '32.bl1.a1', '32.bo1.a1', '32.bo1.c1', '32.bs1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9419, -1, 1849, -1, 9438, -1, 1847, -1], 'generators': [1, 12, 64], 'label': '256.20278.16.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ds1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644830
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.cz1.b1', '8.dg1.a1'], 'contains': ['32.i1.b1', '32.bj1.b1', '32.bj1.d1', '32.bl1.a1', '32.bo1.b1', '32.bo1.d1', '32.bs1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9419, -1, 1908, -1, 9438, -1, 1906, -1], 'generators': [1, 172, 64], 'label': '256.20278.16.ds1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ds1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26644831
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.n1.a1', '8.bq1.a1', '8.br1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5623, 7136, 6181, 9411, 5635, 7135, 6174, 9412], 'generators': [1, 24, 164], 'label': '256.20278.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.k1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644832
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cb1.a1', '8.dd1.a1', '8.dl1.a1'], 'contains': ['32.bq1.a1', '32.bz1.a1', '32.ca1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3902, -1, 6223, -1, 3910, -1, 6216, -1], 'generators': [17, 24], 'label': '256.20278.16.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.dt1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644833
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cb1.a1', '8.dd1.b1', '8.dl1.a1'], 'contains': ['32.bq1.b1', '32.bz1.a1', '32.ca1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3902, -1, 6008, -1, 3910, -1, 6002, -1], 'generators': [81, 24], 'label': '256.20278.16.dt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.dt1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644834
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cc1.a1', '8.dd1.a1', '8.dl1.a1'], 'contains': ['32.bq1.a1', '32.bz1.a1', '32.cb1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3978, -1, 6285, -1, 3986, -1, 6279, -1], 'generators': [17, 188], 'label': '256.20278.16.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.du1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644835
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cc1.a1', '8.dd1.b1', '8.dl1.a1'], 'contains': ['32.bq1.b1', '32.bz1.a1', '32.cb1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3978, -1, 6159, -1, 3986, -1, 6153, -1], 'generators': [81, 188], 'label': '256.20278.16.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.du1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644836
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.db1.a1', '8.dj1.b1'], 'contains': ['32.i1.a1', '32.cg1.a1', '32.ch1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6602, -1, 7342, -1, 6615, -1, 7334, -1], 'generators': [17, 12], 'label': '256.20278.16.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '16.dv1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644837
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.db1.b1', '8.dj1.a1'], 'contains': ['32.i1.b1', '32.cg1.a1', '32.ch1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6602, -1, 7399, -1, 6615, -1, 7391, -1], 'generators': [17, 172], 'label': '256.20278.16.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '16.dv1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644838
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1'], 'contains': ['32.ci1.a1', '32.cj1.a1', '32.cl1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [843, -1, 8739, -1, 845, -1, 8730, -1], 'generators': [9, 26], 'label': '256.20278.16.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '16.dw1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644839
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1'], 'contains': ['32.ci1.a1', '32.cj1.a1', '32.cl1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [843, -1, 8666, -1, 845, -1, 8657, -1], 'generators': [9, 154], 'label': '256.20278.16.dw1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '16.dw1.a2', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644840
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 72, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.o1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.q1.a1', '16.r1.a1', '16.s1.a1', '16.t1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.n1.a1', '64.v1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3530, 5263, 7648, 5829, 3537, 5246, 7640, 5828], 'generators': [228, 160, 128], 'label': '256.20278.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644841
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '32.b1', 'aut_quo_index': 768, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.bb1.a1', '16.bj1.a1', '16.bl1.a1', '16.bm1.a1', '16.bn1.a1', '16.bo1.a1', '16.bp1.a1', '16.bq1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.f1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6145, 2504, 4814, 3015, 6157, 2504, 4832, 3015], 'generators': [164, 160], 'label': '256.20278.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.f1.a1', '16.d1.a1', '16.e1.a1', '16.g1.a1', '16.h1.a1'], 'normal_contains': ['64.a1.a1', '64.d1.a1', '64.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644842
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1', '4.i1.a1', '4.k1.a1', '4.o1.a1', '4.q1.a1', '4.bj1.a1', '4.bk1.a1', '4.bl1.a1', '4.bm1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7465, 7683, 3377, 2693, 7481, 7519, 3373, 2693], 'generators': [1, 2, 8, 64], 'label': '256.20278.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1', '4.i1.a1', '4.k1.a1', '4.o1.a1', '4.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644843
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.l1.a1', '2.m1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.n1.a1', '8.bz1.a1', '8.ca1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4985, 8312, 7599, 7760, 4996, 8312, 7590, 7760], 'generators': [9, 16, 164], 'label': '256.20278.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.a1.a1', '2.l1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644844
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '32.c1', 'aut_quo_index': 768, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1', '16.bf1.a1', '16.bk1.a1', '16.br1.a1', '16.bs1.a1', '16.bt1.a1', '16.bu1.a1', '16.bv1.a1', '16.bw1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.g1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4476, 6578, 7314, 7146, 4485, 6486, 7306, 7140], 'generators': [160, 64], 'label': '256.20278.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1'], 'normal_contains': ['64.a1.a1', '64.e1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644845
    {'ambient': '256.20278', 'aut_centralizer_order': 1024, 'aut_label': '32.d1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.n1.a1', '16.n1.b1', '16.ch1.a1', '16.cj1.a1', '16.ck1.a1', '16.cl1.a1', '16.cm1.a1', '16.cn1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.g1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7060, 5642, 4171, 5997, 7074, 5625, 4166, 5997], 'generators': [4, 64], 'label': '256.20278.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.a1.a1', '16.n1.a1', '16.n1.b1'], 'normal_contains': ['64.b1.a1', '64.d1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '128.1204', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644846
    {'ambient': '256.20278', 'aut_centralizer_order': 1024, 'aut_label': '32.e1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.o1.a1', '16.o1.b1', '16.cg1.a1', '16.ci1.a1', '16.co1.a1', '16.cp1.a1', '16.cq1.a1', '16.cr1.a1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.f1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6039, 5852, 4016, 5660, 6051, 5835, 4012, 5660], 'generators': [164, 224], 'label': '256.20278.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.a1.a1', '16.o1.b1', '16.o1.a1'], 'normal_contains': ['64.b1.a1', '64.f1.a1', '64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '128.1204', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644847
    {'ambient': '256.20278', 'aut_centralizer_order': 1024, 'aut_label': '32.f1', 'aut_quo_index': 72, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.ct1.a1', '16.cu1.a1', '16.cw1.a1', '16.cy1.a1', '16.cz1.a1', '16.da1.a1', '16.db1.a1', '16.dc1.a1', '16.dd1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.e1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5933, 5431, 4902, 6208, 5946, 5414, 4919, 6207], 'generators': [228, 224], 'label': '256.20278.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.c1.a1', '64.d1.a1', '64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '128.1204', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644848
    {'ambient': '256.20278', 'aut_centralizer_order': 1024, 'aut_label': '32.g1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.p1.a1', '16.p1.b1', '16.cv1.a1', '16.cx1.a1', '16.de1.a1', '16.df1.a1', '16.dg1.a1', '16.dh1.a1'], 'contains': ['64.c1.a1', '64.f1.a1', '64.g1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6528, 6062, 5326, 6417, 6541, 6045, 5309, 6417], 'generators': [164, 64], 'label': '256.20278.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.a1.a1', '16.p1.a1', '16.p1.b1'], 'normal_contains': ['64.c1.a1', '64.f1.a1', '64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '128.1204', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644849
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.h1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.a1', '16.p1.a1', '16.dp1.a1', '16.dq1.a1'], 'contains': ['64.g1.a1', '64.h1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8432, 6223, 5005, 6912, 8449, 6206, 5011, 6912], 'generators': [8, 64], 'label': '256.20278.32.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': ['16.b1.a1', '16.n1.a1', '16.p1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644850
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.h1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.n1.b1', '16.p1.b1', '16.dp1.b1', '16.dq1.b1'], 'contains': ['64.g1.a1', '64.h1.b1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8432, 6223, 5051, 6578, 8449, 6206, 5058, 6578], 'generators': [168, 64], 'label': '256.20278.32.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': ['16.b1.a1', '16.n1.b1', '16.p1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644851
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.i1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.n1.a1', '16.p1.b1', '16.ds1.a1', '16.dv1.a1'], 'contains': ['64.g1.a1', '64.k1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8086, 6335, 5098, 6689, 8103, 6317, 5104, 6690], 'generators': [12, 64], 'label': '256.20278.32.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': ['16.i1.a1', '16.n1.a1', '16.p1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.i1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644852
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.i1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.n1.b1', '16.p1.a1', '16.ds1.b1', '16.dv1.b1'], 'contains': ['64.g1.a1', '64.k1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8086, 6335, 5232, 6801, 8103, 6317, 5238, 6801], 'generators': [172, 64], 'label': '256.20278.32.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': ['16.i1.a1', '16.n1.b1', '16.p1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.i1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644853
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.q1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1', '16.bd1.a1'], 'contains': ['64.a1.a1', '64.h1.a1', '64.h1.b1', '64.o1.a1', '64.w1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5510, -1, 3752, -1, 5521, -1, 3748, -1], 'generators': [8, 160, 128], 'label': '256.20278.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644854
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.m1.a1', '8.bv1.a1', '8.bw1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8076, 4802, 3437, 1234, 8092, 4802, 3434, 1233], 'generators': [9, 10, 64], 'label': '256.20278.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644855
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.r1.a1', '16.z1.a1', '16.be1.a1', '16.bf1.a1', '16.bg1.a1', '16.bh1.a1'], 'contains': ['64.a1.a1', '64.i1.a1', '64.p1.a1', '64.x1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5785, -1, 3420, -1, 5797, -1, 3417, -1], 'generators': [1, 160, 128], 'label': '256.20278.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644856
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.z1.a1', '16.ba1.a1', '16.be1.a1', '16.bi1.a1', '16.bj1.a1', '16.bk1.a1'], 'contains': ['64.a1.a1', '64.j1.a1', '64.j1.b1', '64.q1.a1', '64.y1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7417, -1, 2690, -1, 7432, -1, 2687, -1], 'generators': [9, 160, 128], 'label': '256.20278.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.l1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644857
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.q1.a1', '16.bb1.a1', '16.be1.a1', '16.bi1.a1', '16.bx1.a1', '16.by1.a1'], 'contains': ['64.a1.a1', '64.k1.a1', '64.k1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5701, -1, 5165, -1, 5712, -1, 5172, -1], 'generators': [172, 160], 'label': '256.20278.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.m1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644858
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.t1.a1', '16.bg1.a1', '16.bl1.a1', '16.bz1.a1', '16.ca1.a1', '16.cb1.a1'], 'contains': ['64.a1.a1', '64.r1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2568, -1, 8661, -1, 2573, -1, 8645, -1], 'generators': [16, 128], 'label': '256.20278.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.n1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644859
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.t1.a1', '16.bh1.a1', '16.bl1.a1', '16.cc1.a1', '16.cd1.a1', '16.ce1.a1'], 'contains': ['64.a1.a1', '64.z1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2782, -1, 8573, -1, 2788, -1, 8557, -1], 'generators': [180, 128], 'label': '256.20278.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.o1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644860
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.r1.a1', '16.ba1.a1', '16.bf1.a1', '16.bi1.a1', '16.bz1.a1', '16.cc1.a1'], 'contains': ['64.a1.a1', '64.l1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5595, -1, 4326, -1, 5606, -1, 4321, -1], 'generators': [65, 160], 'label': '256.20278.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.p1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644861
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.u1.a1', '16.bc1.a1', '16.br1.a1', '16.bx1.a1', '16.ca1.a1', '16.cd1.a1'], 'contains': ['64.a1.a1', '64.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1956, -1, 9122, -1, 1960, -1, 9122, -1], 'generators': [3, 128], 'label': '256.20278.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.q1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644862
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.u1.a1', '16.bd1.a1', '16.br1.a1', '16.by1.a1', '16.cb1.a1', '16.ce1.a1'], 'contains': ['64.a1.a1', '64.ba1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2062, -1, 8846, -1, 2066, -1, 8839, -1], 'generators': [67, 128], 'label': '256.20278.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.r1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644863
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.bc1.a1', '16.bd1.a1', '16.bm1.a1', '16.bs1.a1', '16.bx1.a1', '16.by1.a1'], 'contains': ['64.a1.a1', '64.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2168, -1, 8486, -1, 2172, -1, 8470, -1], 'generators': [11, 128], 'label': '256.20278.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.s1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644864
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.bg1.a1', '16.bh1.a1', '16.bn1.a1', '16.bt1.a1', '16.bz1.a1', '16.cc1.a1'], 'contains': ['64.a1.a1', '64.m1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3614, -1, 7577, -1, 3622, -1, 7569, -1], 'generators': [17, 160], 'label': '256.20278.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.t1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644865
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.p1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.l1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.i1.a1', '8.ba1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2235, 4255, 7356, 1781, 2240, 4255, 7348, 1781], 'generators': [9, 26, 64], 'label': '256.20278.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.c1.a1', '2.l1.a1', '2.o1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644866
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.bo1.a1', '16.bu1.a1', '16.ca1.a1', '16.cb1.a1', '16.cd1.a1', '16.ce1.a1'], 'contains': ['64.a1.a1', '64.u1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1639, -1, 9210, -1, 1643, -1, 9210, -1], 'generators': [19, 128], 'label': '256.20278.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.u1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644867
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.q1.a1', '16.cf1.a1', '16.cf1.b1', '16.cg1.a1'], 'contains': ['64.b1.a1', '64.h1.a1', '64.k1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8593, -1, 3471, -1, 8610, -1, 3467, -1], 'generators': [8, 68], 'label': '256.20278.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.v1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644868
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '16.q1.a1', '16.cf1.c1', '16.cf1.d1', '16.cg1.a1'], 'contains': ['64.b1.a1', '64.h1.b1', '64.k1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8593, -1, 3610, -1, 8610, -1, 3606, -1], 'generators': [232, 68], 'label': '256.20278.32.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.v1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644869
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.cf1.a1', '16.cf1.b1', '16.cf1.c1', '16.cf1.d1', '16.ch1.a1', '16.ci1.a1'], 'contains': ['64.b1.a1', '64.i1.a1', '64.l1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7919, -1, 2587, -1, 7935, -1, 2584, -1], 'generators': [1, 68], 'label': '256.20278.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.w1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644870
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.s1.a1', '16.cf1.a1', '16.cf1.c1', '16.cj1.a1'], 'contains': ['64.b1.a1', '64.j1.a1', '64.bb1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8652, -1, 3099, -1, 8670, -1, 3096, -1], 'generators': [9, 68, 128], 'label': '256.20278.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.x1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644871
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.s1.a1', '16.cf1.b1', '16.cf1.d1', '16.cj1.a1'], 'contains': ['64.b1.a1', '64.j1.b1', '64.bb1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8652, -1, 2636, -1, 8670, -1, 2634, -1], 'generators': [73, 68, 128], 'label': '256.20278.32.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.x1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644872
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.ck1.a1', '16.co1.a1'], 'contains': ['64.b1.a1', '64.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4306, -1, 6835, -1, 4315, -1, 6828, -1], 'generators': [17, 68], 'label': '256.20278.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '32.y1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644873
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.q1.a1', '16.cs1.a1', '16.cs1.a2', '16.ct1.a1'], 'contains': ['64.c1.a1', '64.h1.a1', '64.k1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8375, -1, 3517, -1, 8393, -1, 3513, -1], 'generators': [8, 228], 'label': '256.20278.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.z1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644874
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bx1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.q1.a1', '16.cs1.b1', '16.cs1.b2', '16.ct1.a1'], 'contains': ['64.c1.a1', '64.h1.b1', '64.k1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8375, -1, 3563, -1, 8393, -1, 3559, -1], 'generators': [168, 228], 'label': '256.20278.32.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.z1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644875
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.cs1.a1', '16.cs1.a2', '16.cs1.b1', '16.cs1.b2', '16.cu1.a1', '16.cv1.a1'], 'contains': ['64.c1.a1', '64.i1.a1', '64.l1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7533, -1, 2231, -1, 7548, -1, 2228, -1], 'generators': [1, 228], 'label': '256.20278.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ba1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644876
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.m1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.j1.a1', '8.bx1.a1', '8.by1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7219, 8886, 3555, 2698, 7233, 8886, 3552, 2698], 'generators': [9, 2, 64], 'label': '256.20278.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.b1.a1', '2.o1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644877
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.cs1.a1', '16.cs1.a2', '16.cs1.b1', '16.cs1.b2', '16.cw1.a1', '16.cx1.a1'], 'contains': ['64.c1.a1', '64.j1.a1', '64.j1.b1', '64.bc1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8146, -1, 1773, -1, 8163, -1, 1771, -1], 'generators': [9, 228, 128], 'label': '256.20278.32.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bb1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644878
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.cy1.a1', '16.de1.a1'], 'contains': ['64.c1.a1', '64.bd1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3445, -1, 7401, -1, 3452, -1, 7394, -1], 'generators': [26, 128], 'label': '256.20278.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '32.bc1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644879
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.cz1.a1', '16.df1.a1'], 'contains': ['64.c1.a1', '64.m1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3720, -1, 7489, -1, 3728, -1, 7481, -1], 'generators': [17, 228], 'label': '256.20278.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf1.a1', 'old_label': '32.bd1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 26644880
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.cf1.a1', '16.cs1.a1', '16.di1.a1', '16.dj1.a1', '16.do1.a1', '16.dp1.a1'], 'contains': ['64.h1.a1', '64.i1.a1', '64.j1.a1', '64.be1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9302, -1, 1294, -1, 9321, -1, 1293, -1], 'generators': [1, 8, 128], 'label': '256.20278.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.be1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644881
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.cf1.b1', '16.cs1.a2', '16.di1.a1', '16.dj1.b1', '16.do1.b1', '16.dp1.a1'], 'contains': ['64.h1.a1', '64.i1.a1', '64.j1.b1', '64.be1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9302, -1, 1188, -1, 9321, -1, 1188, -1], 'generators': [161, 8, 128], 'label': '256.20278.32.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.be1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644882
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.cf1.c1', '16.cs1.b2', '16.di1.b1', '16.dj1.c1', '16.do1.a1', '16.dp1.b1'], 'contains': ['64.h1.b1', '64.i1.a1', '64.j1.a1', '64.be1.c1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9302, -1, 1348, -1, 9321, -1, 1346, -1], 'generators': [161, 168, 128], 'label': '256.20278.32.be1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.be1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644883
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.cf1.d1', '16.cs1.b1', '16.di1.b1', '16.dj1.d1', '16.do1.b1', '16.dp1.b1'], 'contains': ['64.h1.b1', '64.i1.a1', '64.j1.b1', '64.be1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9302, -1, 1242, -1, 9321, -1, 1240, -1], 'generators': [1, 168, 128], 'label': '256.20278.32.be1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.be1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644884
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.cf1.a1', '16.cs1.a2', '16.dk1.a1', '16.dl1.a1', '16.do1.a1', '16.dp1.a1'], 'contains': ['64.h1.a1', '64.j1.a1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1998, -1, 9205, -1, 1996, -1], 'generators': [225, 8], 'label': '256.20278.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bf1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644885
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.cf1.b1', '16.cs1.a1', '16.dk1.a1', '16.dl1.b1', '16.do1.b1', '16.dp1.a1'], 'contains': ['64.h1.a1', '64.j1.b1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1630, -1, 9205, -1, 1628, -1], 'generators': [65, 8], 'label': '256.20278.32.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bf1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644886
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.cf1.c1', '16.cs1.b1', '16.dk1.b1', '16.dl1.c1', '16.do1.a1', '16.dp1.b1'], 'contains': ['64.h1.b1', '64.j1.a1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 2044, -1, 9205, -1, 2042, -1], 'generators': [65, 168], 'label': '256.20278.32.bf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bf1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644887
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.r1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.n1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.k1.a1', '8.cb1.a1', '8.cc1.a1', '8.dd1.a1', '8.dd1.b1', '8.dl1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3919, 5724, 5954, 5206, 3926, 5724, 5948, 5206], 'generators': [17, 24, 164, 64], 'label': '256.20278.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.a1.a1', '2.n1.a1', '2.o1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644888
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.cf1.d1', '16.cs1.b2', '16.dk1.b1', '16.dl1.d1', '16.do1.b1', '16.dp1.b1'], 'contains': ['64.h1.b1', '64.j1.b1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1677, -1, 9205, -1, 1675, -1], 'generators': [225, 168], 'label': '256.20278.32.bf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bf1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644889
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bb1.a1', '16.ct1.a1', '16.di1.a1', '16.dk1.a1', '16.dm1.a1', '16.dn1.a1'], 'contains': ['64.d1.a1', '64.h1.a1', '64.k1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8512, -1, 3216, -1, 8529, -1, 3212, -1], 'generators': [8, 4], 'label': '256.20278.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bg1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644890
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '16.bb1.a1', '16.ct1.a1', '16.di1.b1', '16.dk1.b1', '16.dm1.b1', '16.dn1.b1'], 'contains': ['64.d1.a1', '64.h1.b1', '64.k1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8512, -1, 3304, -1, 8529, -1, 3300, -1], 'generators': [168, 4], 'label': '256.20278.32.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bg1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644891
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bb1.a1', '16.cg1.a1', '16.dj1.a1', '16.dj1.b1', '16.dl1.a1', '16.dl1.b1'], 'contains': ['64.f1.a1', '64.h1.a1', '64.k1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8738, -1, 2760, -1, 8755, -1, 2757, -1], 'generators': [8, 164], 'label': '256.20278.32.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bh1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644892
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.bb1.a1', '16.cg1.a1', '16.dj1.c1', '16.dj1.d1', '16.dl1.c1', '16.dl1.d1'], 'contains': ['64.f1.a1', '64.h1.b1', '64.k1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8738, -1, 2894, -1, 8755, -1, 2891, -1], 'generators': [168, 164], 'label': '256.20278.32.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bh1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644893
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.cg1.a1', '16.ct1.a1', '16.do1.a1', '16.do1.b1'], 'contains': ['64.e1.a1', '64.h1.a1', '64.h1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8031, -1, 3149, -1, 8047, -1, 3145, -1], 'generators': [8, 224], 'label': '256.20278.32.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bi1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644894
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cf1.a1', '16.cs1.b1', '16.di1.a1', '16.dj1.c1', '16.dr1.a1', '16.ds1.a1'], 'contains': ['64.i1.a1', '64.j1.a1', '64.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9242, -1, 1537, -1, 9261, -1, 1535, -1], 'generators': [161, 12], 'label': '256.20278.32.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bj1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644895
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cf1.c1', '16.cs1.a2', '16.di1.b1', '16.dj1.a1', '16.dr1.a1', '16.ds1.b1'], 'contains': ['64.i1.a1', '64.j1.a1', '64.k1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9242, -1, 1583, -1, 9261, -1, 1582, -1], 'generators': [1, 172], 'label': '256.20278.32.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bj1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644896
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cf1.b1', '16.cs1.b2', '16.di1.a1', '16.dj1.d1', '16.dr1.b1', '16.ds1.a1'], 'contains': ['64.i1.a1', '64.j1.b1', '64.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9242, -1, 1397, -1, 9261, -1, 1396, -1], 'generators': [1, 12], 'label': '256.20278.32.bj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bj1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644897
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cf1.d1', '16.cs1.a1', '16.di1.b1', '16.dj1.b1', '16.dr1.b1', '16.ds1.b1'], 'contains': ['64.i1.a1', '64.j1.b1', '64.k1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9242, -1, 1444, -1, 9261, -1, 1442, -1], 'generators': [161, 172], 'label': '256.20278.32.bj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bj1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644898
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.m1.a1', '2.n1.a1'], 'contains': ['8.c1.a1', '8.l1.a1', '8.o1.a1', '8.de1.a1', '8.de1.b1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6345, 3638, 3670, 6121, 6358, 3638, 3667, 6120], 'generators': [9, 18, 64], 'label': '256.20278.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.c1.a1', '2.n1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.l1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644899
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.ci1.a1', '16.cu1.a1', '16.do1.a1', '16.do1.b1', '16.dr1.a1', '16.dr1.b1'], 'contains': ['64.e1.a1', '64.i1.a1', '64.l1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7614, -1, 2982, -1, 7629, -1, 2979, -1], 'generators': [1, 224], 'label': '256.20278.32.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bk1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644900
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.ch1.a1', '16.cv1.a1', '16.dp1.a1', '16.dp1.b1', '16.ds1.a1', '16.ds1.b1'], 'contains': ['64.g1.a1', '64.i1.a1', '64.l1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8295, -1, 2432, -1, 8311, -1, 2429, -1], 'generators': [1, 64], 'label': '256.20278.32.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bl1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644901
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.ch1.a1', '16.cu1.a1', '16.di1.a1', '16.di1.b1'], 'contains': ['64.d1.a1', '64.i1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7862, -1, 2184, -1, 7879, -1, 2182, -1], 'generators': [1, 4], 'label': '256.20278.32.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bm1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644902
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.ci1.a1', '16.cv1.a1', '16.dj1.a1', '16.dj1.b1', '16.dj1.c1', '16.dj1.d1'], 'contains': ['64.f1.a1', '64.i1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7807, -1, 1490, -1, 7823, -1, 1489, -1], 'generators': [1, 164], 'label': '256.20278.32.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bn1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644903
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cf1.a1', '16.cs1.b2', '16.dk1.a1', '16.dl1.c1', '16.dr1.a1', '16.ds1.a1'], 'contains': ['64.j1.a1', '64.k1.a1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9058, -1, 2344, -1, 9076, -1, 2342, -1], 'generators': [65, 12], 'label': '256.20278.32.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bo1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644904
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cf1.c1', '16.cs1.a1', '16.dk1.b1', '16.dl1.a1', '16.dr1.a1', '16.ds1.b1'], 'contains': ['64.j1.a1', '64.k1.b1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9058, -1, 2520, -1, 9076, -1, 2517, -1], 'generators': [225, 172], 'label': '256.20278.32.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bo1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644905
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cf1.b1', '16.cs1.b1', '16.dk1.a1', '16.dl1.d1', '16.dr1.b1', '16.ds1.a1'], 'contains': ['64.j1.b1', '64.k1.a1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9058, -1, 1843, -1, 9076, -1, 1841, -1], 'generators': [225, 12], 'label': '256.20278.32.bo1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bo1.c1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644906
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cf1.d1', '16.cs1.a2', '16.dk1.b1', '16.dl1.b1', '16.dr1.b1', '16.ds1.b1'], 'contains': ['64.j1.b1', '64.k1.b1', '64.l1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9058, -1, 1931, -1, 9076, -1, 1929, -1], 'generators': [65, 172], 'label': '256.20278.32.bo1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bo1.d1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644907
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cj1.a1', '16.cw1.a1', '16.di1.a1', '16.di1.b1', '16.dk1.a1', '16.dk1.b1'], 'contains': ['64.d1.a1', '64.j1.a1', '64.j1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8874, -1, 2091, -1, 8892, -1, 2089, -1], 'generators': [9, 4], 'label': '256.20278.32.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bp1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644908
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.bk1.a1', '16.cw1.a1', '16.do1.a1', '16.dr1.a1', '16.dt1.a1', '16.du1.a1'], 'contains': ['64.e1.a1', '64.j1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7478, -1, 3703, -1, 7492, -1, 3699, -1], 'generators': [9, 224], 'label': '256.20278.32.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bq1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644909
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.t1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.l1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.i1.a1', '8.bb1.a1', '8.ce1.a1', '8.cf1.a1', '8.cr1.a1', '8.ct1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1699, 4512, 9257, 4214, 1703, 4511, 9248, 4214], 'generators': [3, 16, 164, 64], 'label': '256.20278.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.d1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644910
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.bk1.a1', '16.cw1.a1', '16.do1.b1', '16.dr1.b1', '16.dt1.b1', '16.du1.b1'], 'contains': ['64.e1.a1', '64.j1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7478, -1, 3371, -1, 7492, -1, 3367, -1], 'generators': [73, 224], 'label': '256.20278.32.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bq1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644911
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.bj1.a1', '16.cx1.a1', '16.dj1.a1', '16.dj1.c1', '16.dl1.a1', '16.dl1.c1'], 'contains': ['64.f1.a1', '64.j1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8817, -1, 2138, -1, 8836, -1, 2135, -1], 'generators': [9, 164], 'label': '256.20278.32.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.br1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644912
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.bj1.a1', '16.cx1.a1', '16.dj1.b1', '16.dj1.d1', '16.dl1.b1', '16.dl1.d1'], 'contains': ['64.f1.a1', '64.j1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8817, -1, 1723, -1, 8836, -1, 1721, -1], 'generators': [169, 164], 'label': '256.20278.32.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.br1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644913
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.cj1.a1', '16.cx1.a1', '16.dp1.a1', '16.dp1.b1', '16.ds1.a1', '16.ds1.b1'], 'contains': ['64.g1.a1', '64.j1.a1', '64.j1.b1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8930, -1, 2277, -1, 8948, -1, 2274, -1], 'generators': [9, 64], 'label': '256.20278.32.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bs1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644914
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.ch1.a1', '16.cu1.a1', '16.dk1.a1', '16.dk1.b1'], 'contains': ['64.d1.a1', '64.l1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7751, -1, 3049, -1, 7767, -1, 3046, -1], 'generators': [65, 4], 'label': '256.20278.32.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bt1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644915
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.ck1.a1', '16.cz1.a1'], 'contains': ['64.d1.a1', '64.m1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4612, -1, 6175, -1, 4622, -1, 6169, -1], 'generators': [17, 4], 'label': '256.20278.32.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '32.bu1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644916
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.cl1.a1', '16.da1.a1', '16.dm1.a1', '16.dm1.b1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6923, -1, 3902, -1, 6936, -1, 3898, -1], 'generators': [2], 'label': '256.20278.32.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.bv1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644917
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '4.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.cl1.a1', '16.da1.a1', '16.dn1.a1', '16.dn1.b1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6866, -1, 3949, -1, 6880, -1, 3945, -1], 'generators': [66], 'label': '256.20278.32.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.bw1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644918
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.cm1.a1', '16.dc1.a1', '16.dm1.a1', '16.dm1.b1', '16.dn1.a1', '16.dn1.b1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6978, -1, 3856, -1, 6992, -1, 3852, -1], 'generators': [10], 'label': '256.20278.32.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '32.bx1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644919
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.cg1.a1', '16.ct1.a1', '16.dr1.a1', '16.dr1.b1'], 'contains': ['64.e1.a1', '64.k1.a1', '64.k1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7974, -1, 3656, -1, 7991, -1, 3652, -1], 'generators': [172, 224], 'label': '256.20278.32.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.by1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644920
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.b1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'contains': ['8.d1.a1', '8.f1.a1', '8.m1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2891, 5093, 7853, 942, 2897, 5093, 7845, 943], 'generators': [10, 16], 'label': '256.20278.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'normal_contains': ['8.f1.a1', '8.d1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644921
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bt1.a1', '16.co1.a1', '16.cz1.a1', '16.dt1.a1', '16.dt1.b1', '16.du1.a1', '16.du1.b1'], 'contains': ['64.e1.a1', '64.m1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4070, -1, 6223, -1, 4078, -1, 6216, -1], 'generators': [17, 224], 'label': '256.20278.32.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '32.bz1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644922
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.cp1.a1', '16.db1.a1', '16.dt1.a1', '16.dt1.b1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3857, -1, 6022, -1, 3865, -1, 6028, -1], 'generators': [24], 'label': '256.20278.32.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '32.ca1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644923
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.cp1.a1', '16.db1.a1', '16.du1.a1', '16.du1.b1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3913, -1, 6106, -1, 3921, -1, 6101, -1], 'generators': [188], 'label': '256.20278.32.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '32.cb1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644924
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bw1.a1', '16.cr1.a1', '16.dd1.a1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3801, -1, 5658, -1, 3809, -1, 5652, -1], 'generators': [27], 'label': '256.20278.32.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '32.cc1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644925
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.ci1.a1', '16.cv1.a1', '16.dl1.a1', '16.dl1.b1', '16.dl1.c1', '16.dl1.d1'], 'contains': ['64.f1.a1', '64.l1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7695, -1, 2827, -1, 7710, -1, 2824, -1], 'generators': [65, 164], 'label': '256.20278.32.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.cd1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644926
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.co1.a1', '16.df1.a1'], 'contains': ['64.f1.a1', '64.m1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4556, -1, 6269, -1, 4566, -1, 6262, -1], 'generators': [17, 164], 'label': '256.20278.32.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.ce1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644927
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bp1.a1', '16.cq1.a1', '16.dg1.a1'], 'contains': ['64.f1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6225, -1, 4747, -1, 6239, -1, 4764, -1], 'generators': [18], 'label': '256.20278.32.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '32.cf1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644928
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bt1.a1', '16.ck1.a1', '16.df1.a1', '16.dq1.a1', '16.dq1.b1', '16.dv1.a1', '16.dv1.b1'], 'contains': ['64.g1.a1', '64.m1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4911, -1, 7247, -1, 4921, -1, 7239, -1], 'generators': [17, 64], 'label': '256.20278.32.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '32.cg1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 26644929
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bv1.a1', '16.cn1.a1', '16.dh1.a1', '16.dq1.a1', '16.dq1.b1', '16.dv1.a1', '16.dv1.b1'], 'contains': ['64.g1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6642, -1, 7200, -1, 6655, -1, 7192, -1], 'generators': [25], 'label': '256.20278.32.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '32.ch1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644930
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.dw1.a1', '16.dw1.a2'], 'contains': ['64.n1.a1', '64.q1.a1', '64.bb1.a1', '64.bb1.b1', '64.bc1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4391, -1, 6319, -1, 4400, -1, 6312, -1], 'generators': [9, 228, 32], 'label': '256.20278.32.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '32.ci1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644931
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.v1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.o1.a1', '8.cs1.a1', '8.cu1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1838, 9152, 8319, 8530, 1842, 9152, 8311, 8530], 'generators': [11, 16, 164], 'label': '256.20278.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644932
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.dw1.a1', '16.dw1.a2'], 'contains': ['64.n1.a1', '64.bd1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1533, -1, 8397, -1, 1537, -1, 8382, -1], 'generators': [26, 32], 'label': '256.20278.32.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '32.cj1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644933
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1'], 'contains': ['64.n1.a1', '64.t1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1427, -1, 8934, -1, 1431, -1, 8927, -1], 'generators': [11, 228], 'label': '256.20278.32.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.ck1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644934
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.dw1.a1', '16.dw1.a2'], 'contains': ['64.n1.a1', '64.u1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1107, -1, 8749, -1, 1109, -1, 8733, -1], 'generators': [19, 228], 'label': '256.20278.32.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '32.cl1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644935
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1'], 'contains': ['64.o1.a1', '64.p1.a1', '64.q1.a1', '64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5849, -1, 1136, -1, 5861, -1, 1135, -1], 'generators': [1, 8, 32], 'label': '256.20278.32.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '32.cm1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644936
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1'], 'contains': ['64.o1.a1', '64.s1.a1', '64.t1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1745, -1, 9028, -1, 1748, -1, 9028, -1], 'generators': [3, 8], 'label': '256.20278.32.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.bc1.a1', 'old_label': '32.cn1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644937
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ca1.a1'], 'contains': ['64.r1.a1', '64.s1.a1', '64.u1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1347, -1, 9278, -1, 1350, -1, 9277, -1], 'generators': [3, 16], 'label': '256.20278.32.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.ca1.a1', 'old_label': '32.co1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 26644938
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1'], 'contains': ['64.v1.a1', '64.y1.a1', '64.bb1.a1', '64.bb1.b1', '64.bc1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7144, -1, 3805, -1, 7158, -1, 3801, -1], 'generators': [9, 228, 160], 'label': '256.20278.32.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '32.cp1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644939
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1'], 'contains': ['64.v1.a1', '64.bd1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1851, -1, 7718, -1, 1854, -1, 7710, -1], 'generators': [26, 160], 'label': '256.20278.32.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '32.cq1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644940
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1024, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1'], 'contains': ['64.w1.a1', '64.x1.a1', '64.y1.a1', '64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8210, -1, 1083, -1, 8227, -1, 1082, -1], 'generators': [1, 8, 160], 'label': '256.20278.32.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '32.cr1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644941
    {'ambient': '256.20278', 'aut_centralizer_order': 4096, 'aut_label': '64.a1', 'aut_quo_index': 128, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.j1.a1', '32.k1.a1', '32.l1.a1', '32.m1.a1', '32.n1.a1', '32.o1.a1', '32.p1.a1', '32.q1.a1', '32.r1.a1', '32.s1.a1', '32.t1.a1', '32.u1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4486, 5312, 7333, 5779, 4490, 5295, 7325, 5779], 'generators': [160, 128], 'label': '256.20278.64.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.226', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.226', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644942
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '16.h1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1', '8.cg1.a1', '8.ch1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5777, 5384, 4480, 6419, 5789, 5383, 4475, 6419], 'generators': [2, 16, 64], 'label': '256.20278.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'normal_contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26644943
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.o1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '32.v1.a1', '32.v1.b1', '32.w1.a1', '32.x1.a1', '32.x1.b1', '32.y1.a1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6632, 5551, 3692, 5906, 6646, 5533, 3688, 5906], 'generators': [68, 128], 'label': '256.20278.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.25', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644944
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.o1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '32.z1.a1', '32.z1.b1', '32.ba1.a1', '32.bb1.a1', '32.bc1.a1', '32.bd1.a1'], 'contains': ['128.a1.a1', '128.e1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5945, 5677, 4902, 6255, 5957, 5660, 4919, 6255], 'generators': [228, 128], 'label': '256.20278.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.28', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644945
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '32.bg1.a1', '32.bg1.b1', '32.bm1.a1', '32.bp1.a1', '32.bt1.a1', '32.bu1.a1', '32.bv1.a1', '32.bw1.a1', '32.bx1.a1'], 'contains': ['128.a1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6940, 5431, 3590, 6024, 6954, 5414, 3586, 6025], 'generators': [4], 'label': '256.20278.64.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1.a1', 'normal_contained_in': ['32.b1.a1', '32.d1.a1', '32.f1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644946
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.e1.a1', '32.f1.a1', '32.bi1.a1', '32.bk1.a1', '32.bq1.a1', '32.bq1.b1', '32.by1.a1', '32.bz1.a1', '32.ca1.a1', '32.cb1.a1', '32.cc1.a1'], 'contains': ['128.a1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6017, 5908, 4016, 6136, 6029, 5891, 4012, 6136], 'generators': [224], 'label': '256.20278.64.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.e1.a1', 'normal_contained_in': ['32.c1.a1', '32.e1.a1', '32.f1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.28', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644947
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.f1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '32.bh1.a1', '32.bh1.b1', '32.bn1.a1', '32.br1.a1', '32.br1.b1', '32.cd1.a1', '32.ce1.a1', '32.cf1.a1'], 'contains': ['128.a1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6883, 5796, 3309, 5660, 6898, 5779, 3305, 5660], 'generators': [164], 'label': '256.20278.64.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.f1.a1', 'normal_contained_in': ['32.b1.a1', '32.e1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.25', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644948
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.g1', 'aut_quo_index': 128, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '2.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '32.h1.a1', '32.h1.b1', '32.i1.a1', '32.i1.b1', '32.bl1.a1', '32.bs1.a1', '32.cg1.a1', '32.ch1.a1'], 'contains': ['128.a1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7060, 6142, 5075, 6634, 7074, 6126, 5081, 6634], 'generators': [64], 'label': '256.20278.64.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.g1.a1', 'normal_contained_in': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '32.h1.a1', '32.h1.b1', '32.i1.a1', '32.i1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.1204', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.31', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644949
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.j1.a1', '32.v1.a1', '32.z1.a1', '32.be1.a1', '32.be1.b1', '32.bf1.a1', '32.bf1.b1', '32.bg1.a1', '32.bh1.a1', '32.bi1.a1'], 'contains': ['128.a1.a1', '128.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8375, -1, 2998, -1, 8393, -1, 2995, -1], 'generators': [8, 128], 'label': '256.20278.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644950
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.j1.a1', '32.v1.b1', '32.z1.b1', '32.be1.c1', '32.be1.d1', '32.bf1.c1', '32.bf1.d1', '32.bg1.b1', '32.bh1.b1', '32.bi1.a1'], 'contains': ['128.a1.a1', '128.f1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8375, -1, 3158, -1, 8393, -1, 3154, -1], 'generators': [168, 128], 'label': '256.20278.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.h1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644951
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.w1.a1', '32.ba1.a1', '32.be1.a1', '32.be1.b1', '32.be1.c1', '32.be1.d1', '32.bj1.a1', '32.bj1.b1', '32.bj1.c1', '32.bj1.d1', '32.bk1.a1', '32.bl1.a1', '32.bm1.a1', '32.bn1.a1'], 'contains': ['128.a1.a1', '128.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7807, -1, 1537, -1, 7823, -1, 1535, -1], 'generators': [1, 128], 'label': '256.20278.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.i1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644952
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.x1.a1', '32.bb1.a1', '32.be1.a1', '32.be1.c1', '32.bf1.a1', '32.bf1.c1', '32.bj1.a1', '32.bj1.b1', '32.bo1.a1', '32.bo1.b1', '32.bp1.a1', '32.bq1.a1', '32.br1.a1', '32.bs1.a1'], 'contains': ['128.a1.a1', '128.h1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8817, -1, 2138, -1, 8836, -1, 2135, -1], 'generators': [9, 128], 'label': '256.20278.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.j1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644953
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.s1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5268, 4255, 4881, 5531, 5279, 4255, 4872, 5531], 'generators': [1, 18, 8], 'label': '256.20278.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644954
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.x1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'contains': ['8.e1.a1', '8.f1.a1', '8.n1.a1'], 'core': '4.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3029, 2208, 7085, 1524, 3035, 2209, 7078, 1524], 'generators': [25, 26], 'label': '256.20278.4.x1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.x1.a1', 'normal_contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.f1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644955
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.x1.b1', '32.bb1.a1', '32.be1.b1', '32.be1.d1', '32.bf1.b1', '32.bf1.d1', '32.bj1.c1', '32.bj1.d1', '32.bo1.c1', '32.bo1.d1', '32.bp1.a1', '32.bq1.b1', '32.br1.b1', '32.bs1.a1'], 'contains': ['128.a1.a1', '128.h1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8817, -1, 2008, -1, 8836, -1, 2006, -1], 'generators': [169, 128], 'label': '256.20278.64.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.j1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644956
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.m1.a1', '32.v1.a1', '32.z1.b1', '32.bg1.a1', '32.bh1.b1', '32.bj1.a1', '32.bj1.c1', '32.bo1.a1', '32.bo1.c1', '32.by1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8316, -1, 3216, -1, 8333, -1, 3212, -1], 'generators': [12], 'label': '256.20278.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.k1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644957
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.m1.a1', '32.v1.b1', '32.z1.a1', '32.bg1.b1', '32.bh1.a1', '32.bj1.b1', '32.bj1.d1', '32.bo1.b1', '32.bo1.d1', '32.by1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8316, -1, 3263, -1, 8333, -1, 3259, -1], 'generators': [172], 'label': '256.20278.64.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.k1.b1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644958
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bn1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.w1.a1', '32.ba1.a1', '32.bf1.a1', '32.bf1.b1', '32.bf1.c1', '32.bf1.d1', '32.bk1.a1', '32.bl1.a1', '32.bo1.a1', '32.bo1.b1', '32.bo1.c1', '32.bo1.d1', '32.bt1.a1', '32.cd1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7720, -1, 2388, -1, 7736, -1, 2385, -1], 'generators': [65], 'label': '256.20278.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.l1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644959
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.t1.a1', '32.y1.a1', '32.bd1.a1', '32.bu1.a1', '32.bz1.a1', '32.ce1.a1', '32.cg1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4551, -1, 6246, -1, 4560, -1, 6239, -1], 'generators': [17], 'label': '256.20278.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '64.m1.a1', 'projective_image': '128.1204', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644960
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.ci1.a1', '32.cj1.a1', '32.ck1.a1', '32.cl1.a1'], 'contains': ['128.b1.a1', '128.d1.a1', '128.e1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3457, -1, 7596, -1, 3465, -1, 7588, -1], 'generators': [228, 32], 'label': '256.20278.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '64.n1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644961
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.cm1.a1', '32.cn1.a1'], 'contains': ['128.b1.a1', '128.f1.a1', '128.f1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5510, -1, 3052, -1, 5521, -1, 3048, -1], 'generators': [8, 32], 'label': '256.20278.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '64.o1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644962
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.cm1.a1'], 'contains': ['128.b1.a1', '128.g1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5785, -1, 1955, -1, 5797, -1, 1953, -1], 'generators': [1, 32], 'label': '256.20278.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bo1.a1', 'old_label': '64.p1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644963
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.ci1.a1', '32.cm1.a1'], 'contains': ['128.b1.a1', '128.h1.a1', '128.h1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5849, -1, 3104, -1, 5861, -1, 3101, -1], 'generators': [9, 32], 'label': '256.20278.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '64.q1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644964
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '32.co1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2111, -1, 8661, -1, 2116, -1, 8645, -1], 'generators': [16], 'label': '256.20278.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bv1.a1', 'old_label': '64.r1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644965
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.y1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.l1.a1', '8.ck1.a1', '8.cl1.a1'], 'core': '4.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4839, 315, 5036, 4489, 4850, 315, 5031, 4489], 'generators': [17, 18, 64], 'label': '256.20278.4.y1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.y1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.y1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644966
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1.a1', '32.cn1.a1', '32.co1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1851, -1, 9075, -1, 1854, -1, 9075, -1], 'generators': [3], 'label': '256.20278.64.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bp1.a1', 'old_label': '64.s1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644967
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.ck1.a1', '32.cn1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2168, -1, 8550, -1, 2172, -1, 8534, -1], 'generators': [11], 'label': '256.20278.64.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.y1.a1', 'old_label': '64.t1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644968
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.a1', '32.cl1.a1', '32.co1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1493, -1, 8870, -1, 1496, -1, 8920, -1], 'generators': [19], 'label': '256.20278.64.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '64.u1.a1', 'projective_image': '128.2020', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644969
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.cp1.a1', '32.cq1.a1'], 'contains': ['128.c1.a1', '128.d1.a1', '128.e1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4310, -1, 6295, -1, 4314, -1, 6289, -1], 'generators': [228, 160], 'label': '256.20278.64.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '64.v1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644970
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.cr1.a1'], 'contains': ['128.c1.a1', '128.f1.a1', '128.f1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6760, -1, 1902, -1, 6774, -1, 1900, -1], 'generators': [8, 160], 'label': '256.20278.64.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '64.w1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644971
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.cr1.a1'], 'contains': ['128.c1.a1', '128.g1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6824, -1, 1463, -1, 6838, -1, 1441, -1], 'generators': [1, 160], 'label': '256.20278.64.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bn1.a1', 'old_label': '64.x1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644972
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.cp1.a1', '32.cr1.a1'], 'contains': ['128.c1.a1', '128.h1.a1', '128.h1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7144, -1, 2946, -1, 7158, -1, 2942, -1], 'generators': [9, 160], 'label': '256.20278.64.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '64.y1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644973
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.ch1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4425, -1, 7461, -1, 4430, -1, 7453, -1], 'generators': [180], 'label': '256.20278.64.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bv1.a1', 'old_label': '64.z1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644974
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.co1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.a1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4370, -1, 7533, -1, 4374, -1, 7525, -1], 'generators': [67], 'label': '256.20278.64.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bx1.a1', 'old_label': '64.ba1.a1', 'projective_image': '128.2021', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644975
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.a1', '32.ci1.a1', '32.cp1.a1'], 'contains': ['128.d1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6999, -1, 3745, -1, 7014, -1, 3741, -1], 'generators': [9, 68], 'label': '256.20278.64.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '64.bb1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644976
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.z1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.k1.a1', '8.o1.a1', '8.cv1.a1', '8.cw1.a1'], 'core': '4.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2371, 1267, 6849, 5823, 2377, 1267, 6842, 5822], 'generators': [3, 24, 164], 'label': '256.20278.4.z1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.z1.a1', 'normal_contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'normal_contains': ['8.e1.a1', '8.k1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.z1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644977
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.b1', '32.ci1.a1', '32.cp1.a1'], 'contains': ['128.d1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6999, -1, 3639, -1, 7014, -1, 3636, -1], 'generators': [73, 68], 'label': '256.20278.64.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '64.bb1.b1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 26644978
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '16.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bb1.a1', '32.ci1.a1', '32.cp1.a1'], 'contains': ['128.e1.a1', '128.h1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6696, -1, 3419, -1, 6710, -1, 3416, -1], 'generators': [9, 228], 'label': '256.20278.64.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.s1.a1', 'old_label': '64.bc1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644979
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2048, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bc1.a1', '32.cj1.a1', '32.cq1.a1'], 'contains': ['128.e1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3518, -1, 7408, -1, 3525, -1, 7400, -1], 'generators': [26], 'label': '256.20278.64.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '64.bd1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644980
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.be1.a1', '32.cm1.a1', '32.cr1.a1'], 'contains': ['128.f1.a1', '128.g1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8440, -1, 1305, -1, 8456, -1, 1309, -1], 'generators': [1, 8], 'label': '256.20278.64.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '64.be1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644981
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.be1.b1', '32.cm1.a1', '32.cr1.a1'], 'contains': ['128.f1.a1', '128.g1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8440, -1, 1200, -1, 8456, -1, 1198, -1], 'generators': [161, 8], 'label': '256.20278.64.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '64.be1.b1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644982
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.be1.c1', '32.cm1.a1', '32.cr1.a1'], 'contains': ['128.f1.b1', '128.g1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8440, -1, 1369, -1, 8456, -1, 1383, -1], 'generators': [161, 168], 'label': '256.20278.64.be1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '64.be1.c1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644983
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '16.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.be1.d1', '32.cm1.a1', '32.cr1.a1'], 'contains': ['128.f1.b1', '128.g1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8440, -1, 1252, -1, 8456, -1, 1251, -1], 'generators': [1, 168], 'label': '256.20278.64.be1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.z1.a1', 'old_label': '64.be1.d1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644984
    {'ambient': '256.20278', 'aut_centralizer_order': 4096, 'aut_label': '128.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.h1.a1', '64.h1.b1', '64.i1.a1', '64.j1.a1', '64.j1.b1', '64.k1.a1', '64.k1.b1', '64.l1.a1', '64.m1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6824, 5614, 3263, 6014, 6824, 5597, 3259, 6012], 'generators': [128], 'label': '256.20278.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.f1.a1', '64.e1.a1', '64.g1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.1204', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.1204', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644985
    {'ambient': '256.20278', 'aut_centralizer_order': 4096, 'aut_label': '128.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.n1.a1', '64.o1.a1', '64.p1.a1', '64.q1.a1', '64.r1.a1', '64.s1.a1', '64.t1.a1', '64.u1.a1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3964, 5424, 7474, 5779, 3967, 5407, 7466, 5779], 'generators': [32], 'label': '256.20278.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': '128.2020', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2020', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644986
    {'ambient': '256.20278', 'aut_centralizer_order': 4096, 'aut_label': '128.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.v1.a1', '64.w1.a1', '64.x1.a1', '64.y1.a1', '64.z1.a1', '64.ba1.a1'], 'contains': ['256.a1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6724, 5312, 3521, 5890, 6724, 5295, 3470, 5890], 'generators': [160], 'label': '256.20278.128.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.c1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.c1.a1', 'projective_image': '128.2021', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2021', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26645019
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1'], 'contains': ['8.u1.a1', '8.cd1.a1', '8.cf1.a1', '8.cg1.a1', '8.cj1.a1', '8.cl1.a1', '8.cm1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5373, -1, 4915, -1, 5384, -1, 4910, -1], 'generators': [65, 2, 16], 'label': '256.20278.4.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bw1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26644987
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.ba1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'contains': ['8.f1.a1', '8.g1.a1', '8.h1.a1', '8.bc1.a1'], 'core': '4.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2106, 2484, 8076, 2430, 2110, 2484, 8068, 2430], 'generators': [17, 26, 64], 'label': '256.20278.4.ba1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ba1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'normal_contains': ['8.f1.a1', '8.g1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ba1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644988
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.n1.a1', '64.v1.a1', '64.bb1.a1', '64.bb1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6632, -1, 3719, -1, 6646, -1, 3715, -1], 'generators': [68], 'label': '256.20278.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '128.d1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644989
    {'ambient': '256.20278', 'aut_centralizer_order': 2048, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '2.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.n1.a1', '64.v1.a1', '64.bc1.a1', '64.bd1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5244, -1, 5599, -1, 5255, -1, 5604, -1], 'generators': [228], 'label': '256.20278.128.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '128.e1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644990
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.o1.a1', '64.w1.a1', '64.be1.a1', '64.be1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6880, -1, 2161, -1, 6880, -1, 2154, -1], 'generators': [8], 'label': '256.20278.128.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '128.f1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644991
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '4.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.o1.a1', '64.w1.a1', '64.be1.c1', '64.be1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6880, -1, 2725, -1, 6880, -1, 2414, -1], 'generators': [168], 'label': '256.20278.128.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '128.f1.b1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644992
    {'ambient': '256.20278', 'aut_centralizer_order': 512, 'aut_label': '128.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.p1.a1', '64.x1.a1', '64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6936, -1, 1416, -1, 6936, -1, 1409, -1], 'generators': [1], 'label': '256.20278.128.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bj1.a1', 'old_label': '128.g1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644993
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.j1.a1', '64.q1.a1', '64.y1.a1', '64.bb1.a1', '64.bc1.a1', '64.be1.a1', '64.be1.c1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6999, -1, 3076, -1, 7014, -1, 3072, -1], 'generators': [9], 'label': '256.20278.128.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '128.h1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644994
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4096, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.j1.b1', '64.q1.a1', '64.y1.a1', '64.bb1.b1', '64.bc1.a1', '64.be1.b1', '64.be1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6999, -1, 2974, -1, 7014, -1, 2970, -1], 'generators': [169], 'label': '256.20278.128.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '128.h1.b1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644995
    {'ambient': '256.20278', '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.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.c1.a1', '128.d1.a1', '128.e1.a1', '128.f1.a1', '128.f1.b1', '128.g1.a1', '128.h1.a1', '128.h1.b1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6788, 5424, 3132, 5890, 6752, 5407, 3212, 5890], 'generators': [], 'label': '256.20278.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.20278', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 26644996
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '4.bb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.j1.a1', '2.o1.a1'], 'contains': ['8.f1.a1', '8.j1.a1', '8.k1.a1', '8.dm1.a1'], 'core': '4.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3529, 3296, 5794, 2096, 3536, 3296, 5787, 2096], 'generators': [2, 24, 64], 'label': '256.20278.4.bb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bb1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.a1', '2.o1.a1'], 'normal_contains': ['8.f1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bb1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26644997
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.bc1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'contains': ['8.g1.a1', '8.i1.a1', '8.k1.a1', '8.cx1.a1', '8.cy1.a1'], 'core': '4.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1971, 9694, 7965, 9694, 1976, 9695, 7956, 9694], 'generators': [19, 24, 164], 'label': '256.20278.4.bc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bc1.a1', 'normal_contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'normal_contains': ['8.g1.a1', '8.i1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bc1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26644998
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.bd1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'contains': ['8.g1.a1', '8.l1.a1', '8.n1.a1'], 'core': '4.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6220, 8057, 6074, 9157, 6234, 8057, 6068, 9156], 'generators': [25, 18], 'label': '256.20278.4.bd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bd1.a1', 'normal_contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'normal_contains': ['8.g1.a1', '8.l1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bd1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26644999
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.be1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.56086', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.j1.a1', '8.cm1.a1', '8.cn1.a1'], 'core': '4.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4705, 1942, 5347, 3264, 4715, 1941, 5341, 3264], 'generators': [17, 2, 64], 'label': '256.20278.4.be1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.be1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'normal_contains': ['8.h1.a1', '8.i1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.be1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26645000
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.bf1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'contains': ['8.h1.a1', '8.m1.a1', '8.o1.a1', '8.dn1.a1'], 'core': '4.bf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3726, 1617, 5482, 3589, 3733, 1617, 5477, 3589], 'generators': [17, 10, 64], 'label': '256.20278.4.bf1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bf1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'normal_contains': ['8.h1.a1', '8.m1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bf1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645001
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '4.bg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.d1', '64.be1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'contains': ['8.i1.a1', '8.m1.a1', '8.n1.a1'], 'core': '4.bg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6674, 6881, 6288, 7504, 6687, 6880, 6281, 7505], 'generators': [25, 10], 'label': '256.20278.4.bg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bg1.a1', 'normal_contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'normal_contains': ['8.i1.a1', '8.m1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bg1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645020
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.v1.a1', '8.co1.a1', '8.cq1.a1', '8.cr1.a1', '8.cs1.a1', '8.cw1.a1', '8.cy1.a1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1061, -1, 9133, -1, 1063, -1, 9124, -1], 'generators': [3, 172, 16], 'label': '256.20278.4.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.bx1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645002
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.g1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.t1.a1', '4.v1.a1', '4.z1.a1', '4.bc1.a1', '4.bp1.a1', '4.bq1.a1', '4.bx1.a1', '4.by1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1905, 8554, 8142, 8002, 1909, 8518, 8133, 8128], 'generators': [3, 8, 16, 164], 'label': '256.20278.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.b1.a1', '4.f1.a1', '4.t1.a1', '4.z1.a1', '4.v1.a1', '4.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645003
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.bh1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.c1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'contains': ['8.j1.a1', '8.n1.a1', '8.o1.a1'], 'core': '4.bh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6470, 2999, 5250, 7302, 6483, 2999, 5245, 7302], 'generators': [25, 2], 'label': '256.20278.4.bh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bh1.a1', 'normal_contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'normal_contains': ['8.j1.a1', '8.n1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bh1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645004
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '4.bi1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 32, 'centralizer': '32.b1.a1', 'complements': ['64.be1.a1', '64.be1.b1', '64.be1.c1', '64.be1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'contains': ['8.k1.a1', '8.l1.a1', '8.m1.a1'], 'core': '4.bi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6572, 6013, 4258, 8015, 6585, 6013, 4254, 8015], 'generators': [18, 24], 'label': '256.20278.4.bi1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bi1.a1', 'normal_contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'normal_contains': ['8.m1.a1', '8.l1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bi1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645005
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.r1.a1', '8.bd1.a1', '8.bf1.a1', '8.bh1.a1', '8.bt1.a1', '8.bv1.a1', '8.bx1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7933, -1, 3124, -1, 7949, -1, 3121, -1], 'generators': [1, 2, 8], 'label': '256.20278.4.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bj1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645006
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.s1.a1', '8.bd1.a1', '8.bg1.a1', '8.bi1.a1', '8.bt1.a1', '8.bw1.a1', '8.by1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7695, -1, 3006, -1, 7711, -1, 3003, -1], 'generators': [1, 66, 8], 'label': '256.20278.4.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bk1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645007
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.t1.a1', '8.be1.a1', '8.bf1.a1', '8.bi1.a1', '8.bv1.a1', '8.by1.a1', '8.ci1.a1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7549, -1, 3316, -1, 7565, -1, 3312, -1], 'generators': [65, 66, 8], 'label': '256.20278.4.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bl1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645008
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.u1.a1', '8.be1.a1', '8.bg1.a1', '8.bh1.a1', '8.bw1.a1', '8.bx1.a1', '8.ci1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7820, -1, 3218, -1, 7837, -1, 3215, -1], 'generators': [65, 2, 8], 'label': '256.20278.4.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bm1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645009
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.p1.a1', '8.bj1.a1', '8.bl1.a1', '8.bo1.a1', '8.bq1.a1', '8.bz1.a1', '8.cb1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4090, -1, 6526, -1, 4098, -1, 6520, -1], 'generators': [1, 8, 16], 'label': '256.20278.4.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bn1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645010
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.q1.a1', '8.bj1.a1', '8.bl1.a1', '8.bp1.a1', '8.br1.a1', '8.ca1.a1', '8.cc1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4563, -1, 7470, -1, 4573, -1, 7462, -1], 'generators': [1, 8, 180], 'label': '256.20278.4.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bo1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645011
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.p1.a1', '8.bk1.a1', '8.bm1.a1', '8.cr1.a1', '8.cs1.a1', '8.cv1.a1', '8.cx1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [827, -1, 8977, -1, 828, -1, 8968, -1], 'generators': [3, 8, 16], 'label': '256.20278.4.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.bp1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645012
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.q1.a1', '8.bk1.a1', '8.bm1.a1', '8.ct1.a1', '8.cu1.a1', '8.cw1.a1', '8.cy1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1209, -1, 9038, -1, 1211, -1, 9028, -1], 'generators': [3, 8, 180], 'label': '256.20278.4.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.bq1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645013
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494202', 'aut_weyl_index': 8, 'centralizer': '32.b1.a1', 'complements': ['128.g1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.g1.a1', '4.u1.a1', '4.w1.a1', '4.bb1.a1', '4.bi1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5388, 5266, 4980, 5787, 5399, 5266, 4971, 5910], 'generators': [2, 8, 16], 'label': '256.20278.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.b1.a1', '4.g1.a1', '4.u1.a1', '4.bb1.a1', '4.w1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645014
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.v1.a1', '8.bn1.a1', '8.bo1.a1', '8.br1.a1', '8.bz1.a1', '8.cc1.a1', '8.cp1.a1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4406, -1, 7729, -1, 4415, -1, 7721, -1], 'generators': [1, 172, 16], 'label': '256.20278.4.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.br1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.br1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645015
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.w1.a1', '8.bn1.a1', '8.bp1.a1', '8.bq1.a1', '8.ca1.a1', '8.cb1.a1', '8.cp1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4247, -1, 6396, -1, 4256, -1, 6389, -1], 'generators': [1, 172, 180], 'label': '256.20278.4.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bs1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645016
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1'], 'contains': ['8.r1.a1', '8.bs1.a1', '8.bu1.a1', '8.ce1.a1', '8.cg1.a1', '8.ck1.a1', '8.cm1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5498, -1, 4810, -1, 5510, -1, 4806, -1], 'generators': [1, 2, 16], 'label': '256.20278.4.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bt1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645017
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1'], 'contains': ['8.s1.a1', '8.bs1.a1', '8.bu1.a1', '8.cf1.a1', '8.ch1.a1', '8.cl1.a1', '8.cn1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5248, -1, 4732, -1, 5259, -1, 4726, -1], 'generators': [1, 66, 16], 'label': '256.20278.4.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bu1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645018
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1'], 'contains': ['8.t1.a1', '8.cd1.a1', '8.ce1.a1', '8.ch1.a1', '8.cj1.a1', '8.ck1.a1', '8.cn1.a1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5131, -1, 5151, -1, 5142, -1, 5146, -1], 'generators': [65, 66, 16], 'label': '256.20278.4.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bv1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645021
    {'ambient': '256.20278', 'aut_centralizer_order': 8, 'aut_label': '4.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.56083', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.w1.a1', '8.co1.a1', '8.cq1.a1', '8.ct1.a1', '8.cu1.a1', '8.cv1.a1', '8.cx1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [908, -1, 8917, -1, 932, -1, 8908, -1], 'generators': [3, 172, 180], 'label': '256.20278.4.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.by1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.by1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645022
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.n1.a1', '16.n1.b1', '16.p1.a1', '16.p1.b1', '16.q1.a1', '16.bb1.a1', '16.cg1.a1', '16.ct1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6962, 6641, 4531, 7002, 6976, 6641, 4526, 7002], 'generators': [8, 164, 160, 64], 'label': '256.20278.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.b1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.n1.a1', '16.n1.b1', '16.p1.a1', '16.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645023
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.r1.a1', '16.bf1.a1', '16.ch1.a1', '16.ci1.a1', '16.cu1.a1', '16.cv1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7263, 2748, 3328, 2860, 7278, 2749, 3325, 2860], 'generators': [1, 164, 160, 64], 'label': '256.20278.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.i1.a1', '4.j1.a1', '4.h1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645024
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.djl', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.g1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.x1.a1', '4.y1.a1', '4.ba1.a1', '4.bd1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4550, 4015, 6302, 6172, 4559, 4015, 6244, 6221], 'generators': [17, 18, 8], 'label': '256.20278.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.x1.a1', '4.y1.a1', '4.ba1.a1', '4.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645025
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.a1.a1', '16.o1.a1', '16.o1.b1', '16.s1.a1', '16.bj1.a1', '16.bk1.a1', '16.cj1.a1', '16.cw1.a1', '16.cx1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8894, 5872, 2367, 4387, 8912, 5872, 2364, 4387], 'generators': [9, 164, 160, 64], 'label': '256.20278.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.o1.a1', '4.p1.a1', '4.n1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'normal_contains': ['16.a1.a1', '16.o1.b1', '16.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26645026
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.k1.a1', '16.t1.a1', '16.bl1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1420, 6132, 8712, 6394, 1424, 6132, 8703, 6394], 'generators': [16, 164, 64], 'label': '256.20278.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.a1.a1', '16.j1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645027
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.o1.a1', '4.t1.a1', '4.x1.a1', '4.y1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.f1.a1', '16.u1.a1', '16.br1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2696, 2237, 6486, 3126, 2701, 2237, 6479, 3126], 'generators': [3, 164, 64], 'label': '256.20278.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.o1.a1', '4.x1.a1', '4.t1.a1', '4.y1.a1', '4.z1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645028
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.a1', '4.u1.a1', '4.x1.a1', '4.ba1.a1', '4.bb1.a1'], 'contains': ['16.a1.a1', '16.v1.a1', '16.cy1.a1', '16.de1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2265, 3342, 7724, 2610, 2269, 3342, 7715, 2610], 'generators': [26, 160, 64], 'label': '256.20278.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.a1', '4.x1.a1', '4.u1.a1', '4.ba1.a1', '4.bb1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '64.226', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645029
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.g1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.k1.a1', '4.q1.a1', '4.v1.a1', '4.ba1.a1', '4.bc1.a1', '4.bd1.a1'], 'contains': ['16.a1.a1', '16.w1.a1', '16.bm1.a1', '16.bs1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2390, 6899, 7512, 6128, 2395, 6899, 7504, 6128], 'generators': [11, 164, 64], 'label': '256.20278.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.k1.a1', '4.q1.a1', '4.ba1.a1', '4.v1.a1', '4.bc1.a1', '4.bd1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26645030
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.h1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.r1.a1', '4.y1.a1', '4.ba1.a1', '4.be1.a1', '4.bf1.a1'], 'contains': ['16.a1.a1', '16.x1.a1', '16.bn1.a1', '16.bt1.a1', '16.ck1.a1', '16.co1.a1', '16.cz1.a1', '16.df1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4581, 2497, 7240, 4631, 4590, 2497, 7232, 4631], 'generators': [17, 164, 160, 64], 'label': '256.20278.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.e1.a1', '4.h1.a1', '4.r1.a1', '4.y1.a1', '4.ba1.a1', '4.be1.a1', '4.bf1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26645031
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.264', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.l1.a1', '4.p1.a1', '4.t1.a1', '4.bc1.a1', '4.be1.a1', '4.bg1.a1'], 'contains': ['16.a1.a1', '16.y1.a1', '16.bo1.a1', '16.bu1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1995, 4766, 7619, 5528, 1999, 4766, 7611, 5528], 'generators': [19, 164, 64], 'label': '256.20278.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.f1.a1', '4.l1.a1', '4.p1.a1', '4.t1.a1', '4.bc1.a1', '4.be1.a1', '4.bg1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.49'}
  • id: 26645032
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.i1.a1', '4.q1.a1', '4.w1.a1', '4.bb1.a1', '4.be1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.h1.a1', '16.cl1.a1', '16.da1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6549, 3586, 3817, 3385, 6562, 3585, 3813, 3385], 'generators': [2, 160, 64], 'label': '256.20278.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.g1.a1', '4.i1.a1', '4.q1.a1', '4.bb1.a1', '4.w1.a1', '4.be1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '64.226', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645033
    {'ambient': '256.20278', 'aut_centralizer_order': 256, 'aut_label': '8.k1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 256, 'centralizer': '8.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.m1.a1', '4.r1.a1', '4.z1.a1', '4.bb1.a1', '4.bc1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.m1.a1', '16.cp1.a1', '16.db1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3001, 6390, 6305, 7596, 3007, 6390, 6299, 7596], 'generators': [24, 164, 64], 'label': '256.20278.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1', '4.m1.a1', '4.r1.a1', '4.z1.a1', '4.bb1.a1', '4.bc1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1', '16.l1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '64.226', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645034
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.l1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.l1.a1', '4.s1.a1', '4.w1.a1', '4.y1.a1', '4.bd1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.bp1.a1', '16.cq1.a1', '16.dg1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6021, 4130, 4083, 6703, 6034, 4129, 4079, 6702], 'generators': [18, 160, 64], 'label': '256.20278.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.d1.a1', '4.l1.a1', '4.s1.a1', '4.y1.a1', '4.w1.a1', '4.bd1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645035
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.g1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1', '4.be1.a1', '4.bf1.a1', '4.bg1.a1', '4.bh1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6407, 4494, 5700, 6692, 6271, 4494, 5694, 6478], 'generators': [17, 2, 8], 'label': '256.20278.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.f1.a1', '4.g1.a1', '4.be1.a1', '4.bf1.a1', '4.bg1.a1', '4.bh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645036
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.m1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.a1', '4.u1.a1', '4.bf1.a1', '4.bg1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.bq1.a1', '16.cm1.a1', '16.dc1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7112, 5235, 3940, 4018, 7126, 5235, 3936, 4017], 'generators': [10, 160, 64], 'label': '256.20278.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.a1', '4.u1.a1', '4.bf1.a1', '4.bg1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645037
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.n1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.m1.a1', '4.n1.a1', '4.x1.a1', '4.bd1.a1', '4.bg1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.bv1.a1', '16.cn1.a1', '16.dh1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6314, 5578, 6615, 7302, 6327, 5578, 6608, 7302], 'generators': [25, 164, 160], 'label': '256.20278.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.e1.a1', '4.m1.a1', '4.n1.a1', '4.x1.a1', '4.bd1.a1', '4.bg1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645038
    {'ambient': '256.20278', 'aut_centralizer_order': 128, 'aut_label': '8.o1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 128, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.j1.a1', '4.s1.a1', '4.v1.a1', '4.z1.a1', '4.bf1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.bw1.a1', '16.cr1.a1', '16.dd1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2542, 3049, 6041, 5829, 2546, 3049, 6035, 5828], 'generators': [27, 164, 64], 'label': '256.20278.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.f1.a1', '4.j1.a1', '4.s1.a1', '4.z1.a1', '4.v1.a1', '4.bf1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645039
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.l1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1679, 7527, 6992, 7931, 1683, 7527, 6984, 7931], 'generators': [8, 16], 'label': '256.20278.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.a1', '16.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645040
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.q1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bo1.a1', '4.bq1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.m1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1894, 7100, 8437, 8216, 1898, 7100, 8428, 8216], 'generators': [8, 180], 'label': '256.20278.8.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.k1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.q1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645041
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.r1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bj1.a1', '4.bt1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6860, 1744, 3618, 2132, 6874, 1744, 3614, 2132], 'generators': [1, 2], 'label': '256.20278.8.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': ['4.i1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645042
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.s1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bk1.a1', '4.bu1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.h1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6718, 1601, 3558, 2275, 6731, 1601, 3554, 2274], 'generators': [1, 66], 'label': '256.20278.8.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': ['4.i1.a1'], 'normal_contains': ['16.c1.a1', '16.f1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.s1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645043
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.t1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bl1.a1', '4.bv1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.h1.a1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6646, 2028, 3736, 1989, 6660, 2028, 3732, 1990], 'generators': [65, 66], 'label': '256.20278.8.t1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': ['4.i1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.a1', '16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.t1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645044
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.u1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bm1.a1', '4.bw1.a1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6790, 1886, 3677, 2416, 6803, 1886, 3673, 2416], 'generators': [65, 2], 'label': '256.20278.8.u1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': ['4.i1.a1'], 'normal_contains': ['16.f1.a1', '16.d1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.u1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645045
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.v1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.br1.a1', '4.bx1.a1'], 'contains': ['16.i1.a1', '16.j1.a1', '16.m1.a1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1822, 7243, 8497, 7790, 1826, 7242, 8488, 7789], 'generators': [172, 16], 'label': '256.20278.8.v1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.i1.a1', '16.j1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.v1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645046
    {'ambient': '256.20278', 'aut_centralizer_order': 4, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.f1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.l1.a1', '4.t1.a1', '4.w1.a1', '4.y1.a1', '4.be1.a1', '4.bt1.a1', '4.bu1.a1', '4.bv1.a1', '4.bw1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5131, 2142, 5094, 4352, 5142, 2142, 5084, 4351], 'generators': [1, 2, 16, 64], 'label': '256.20278.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.h1.a1', '4.l1.a1', '4.t1.a1', '4.y1.a1', '4.w1.a1', '4.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': '64.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
  • id: 26645047
    {'ambient': '256.20278', 'aut_centralizer_order': 64, 'aut_label': '8.w1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bs1.a1', '4.by1.a1'], 'contains': ['16.i1.a1', '16.k1.a1', '16.l1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1751, 7384, 6932, 8074, 1755, 7384, 6925, 8074], 'generators': [172, 180], 'label': '256.20278.8.w1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.w1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.i1.a1', '16.k1.a1', '16.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.w1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
  • id: 26645048
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.q1.a1', '16.r1.a1', '16.s1.a1', '16.z1.a1', '16.ba1.a1', '16.be1.a1', '16.bi1.a1', '16.cf1.a1', '16.cf1.b1', '16.cf1.c1', '16.cf1.d1', '16.cs1.a1', '16.cs1.a2', '16.cs1.b1', '16.cs1.b2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8771, -1, 1727, -1, 8789, -1, 1725, -1], 'generators': [1, 8, 228, 160], 'label': '256.20278.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.x1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645049
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.q1.a1', '16.u1.a1', '16.w1.a1', '16.bc1.a1', '16.bd1.a1', '16.bx1.a1', '16.by1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [512, -1, 9780, -1, 513, -1, 9770, -1], 'generators': [3, 8, 228], 'label': '256.20278.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.y1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645050
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.r1.a1', '16.t1.a1', '16.x1.a1', '16.bg1.a1', '16.bh1.a1', '16.bz1.a1', '16.cc1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1566, -1, 8591, -1, 1570, -1, 8581, -1], 'generators': [1, 16, 228], 'label': '256.20278.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.z1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26645051
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1'], 'contains': ['16.s1.a1', '16.v1.a1', '16.y1.a1', '16.dw1.a1', '16.dw1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [66, -1, 9379, -1, 66, -1, 9369, -1], 'generators': [9, 26, 128], 'label': '256.20278.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '8.ba1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645052
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.51', 'aut_weyl_index': 128, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1'], 'contains': ['16.t1.a1', '16.u1.a1', '16.y1.a1', '16.ca1.a1', '16.cb1.a1', '16.cd1.a1', '16.ce1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [183, -1, 9980, -1, 184, -1, 9969, -1], 'generators': [3, 16, 228], 'label': '256.20278.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '8.bb1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 26645053
    {'ambient': '256.20278', 'aut_centralizer_order': 16, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1'], 'contains': ['16.v1.a1', '16.w1.a1', '16.x1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [415, -1, 9282, -1, 416, -1, 9271, -1], 'generators': [17, 26], 'label': '256.20278.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ba1.a1', 'old_label': '8.bc1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 26645054
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.c1.a1', '16.z1.a1', '16.bb1.a1', '16.be1.a1', '16.bj1.a1', '16.di1.a1', '16.di1.b1', '16.dj1.a1', '16.dj1.b1', '16.dj1.c1', '16.dj1.d1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9148, -1, 933, -1, 9166, -1, 932, -1], 'generators': [1, 8, 164, 160], 'label': '256.20278.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bd1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645055
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.d1.a1', '16.ba1.a1', '16.bb1.a1', '16.bi1.a1', '16.bj1.a1', '16.dk1.a1', '16.dk1.b1', '16.dl1.a1', '16.dl1.b1', '16.dl1.c1', '16.dl1.d1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9021, -1, 2154, -1, 9039, -1, 2151, -1], 'generators': [65, 8, 164, 160], 'label': '256.20278.8.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.be1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 26645056
    {'ambient': '256.20278', 'aut_centralizer_order': 32, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.261', 'aut_weyl_index': 64, 'centralizer': '32.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.e1.a1', '16.bb1.a1', '16.bc1.a1', '16.bm1.a1', '16.bx1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3271, -1, 4951, -1, 3277, -1, 4945, -1], 'generators': [3, 8, 164], 'label': '256.20278.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bf1.a1', 'projective_image': '64.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}