Abstract group data - 256.5426

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 4, 2, 2, 8, 8], 'aut_gens': [[1, 2, 16], [1, 2, 112], [1, 10, 16], [1, 2, 80], [1, 2, 144], [1, 142, 16], [5, 2, 112], [1, 162, 16]], 'aut_group': None, 'aut_hash': 857334616572655192, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 48, 'aut_perms': [225044626269319742038821623319272671802780730035770432615576, 1301014750029248721617318751734171710757869272465837892221, 67623233657509695672742234807510796233694638420705690787555, 163227245504018825005590096390811311367620255943223311420133, 163641053558530447462275782733830846025235197234303317389631, 6173381894093001800660703356137200065853423012108390678169816, 5016102394375366835254617190089211040294034109254015269765], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 1, 1], [2, 32, 1, 1], [4, 2, 1, 2], [4, 4, 2, 1], [4, 8, 1, 1], [4, 32, 1, 1], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 2, 1], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 4, 1], [16, 16, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2.C_2^3.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '256.55683', 'autcentquo_hash': 55683, 'autcentquo_nilpotent': True, 'autcentquo_order': 256, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times D_4^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 8, 1], [2, 32, 1], [4, 2, 2], [4, 4, 2], [4, 8, 1], [4, 32, 1], [8, 2, 4], [8, 4, 2], [8, 8, 2], [16, 2, 4], [16, 4, 6], [16, 8, 4], [16, 16, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.399', 'commutator_count': 1, 'commutator_label': '32.3', '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': 5426, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 1, 1], [2, 32, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 8, 1, 1], [4, 32, 1, 1], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 2, 1], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 4, 1], [16, 16, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 2688, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[4, 0, 8]], 'familial': False, 'frattini_label': '32.3', 'frattini_quotient': '8.5', 'hash': 5426, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 8, 8], 'inner_gens': [[1, 142, 16], [5, 2, 112], [1, 162, 16]], 'inner_hash': 399, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_8:D_8', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 18], [4, 11]], 'label': '256.5426', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 2, 'linQ_dim': 16, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C16.D8', 'ngens': 3, 'nilpotency_class': 4, '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': 21, 'number_characteristic_subgroups': 37, 'number_conjugacy_classes': 37, 'number_divisions': 22, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 108, 'number_subgroup_classes': 112, 'number_subgroups': 415, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 43], [4, 52], [8, 32], [16, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 64, 0], 'outer_gens': [[1, 2, 112], [1, 10, 16], [1, 2, 80]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 6], [8, 2], [16, 2]], 'representations': {'PC': {'code': 10759413322934336573990107376154772478, 'gens': [1, 2, 5], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2273, 41, 3362, 66, 4355, 539, 2252, 116, 5389, 141, 5390, 166]}, 'Perm': {'d': 32, 'gens': [8864346423732048421075307945543, 186929969009818989145446659948544000, 67977995780968282257602718863923200, 42220655673452578351016333552494073, 50973977447395947166377772942641238, 16985047389861003970253793579100937, 25199055155403427461047289114002057, 8231691320578226211046411712681647]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{16}.D_8', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 109462635
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 5426, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 109462646
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 5426, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 109462657
    {'aut_label': '2B', 'centralizer': '2.d1.a1', 'counter': 3, 'group_counter': 5426, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 72, 'size': 2}
  • id: 109462666
    {'aut_label': '2C', 'centralizer': '8.q1.a1', 'counter': 4, 'group_counter': 5426, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 1, 'size': 8}
  • id: 109462667
    {'aut_label': '2D', 'centralizer': '32.g1.a1', 'counter': 5, 'group_counter': 5426, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 15, 'size': 32}
  • id: 109462668
    {'aut_label': '4A', 'centralizer': '2.g1.a1', 'counter': 6, 'group_counter': 5426, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 136, 'size': 2}
  • id: 109462669
    {'aut_label': '4B', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 5426, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 64, 'size': 2}
  • id: 109462670
    {'aut_label': '4C', 'centralizer': '4.d1.a1', 'counter': 8, 'group_counter': 5426, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [3], 'representative': 36, 'size': 4}
  • id: 109462671
    {'aut_label': '4C', 'centralizer': '4.d1.a1', 'counter': 9, 'group_counter': 5426, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [3], 'representative': 164, 'size': 4}
  • id: 109462636
    {'aut_label': '4E', 'centralizer': '8.q1.a1', 'counter': 10, 'group_counter': 5426, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 65, 'size': 8}
  • id: 109462637
    {'aut_label': '4F', 'centralizer': '32.i1.a1', 'counter': 11, 'group_counter': 5426, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [2], 'representative': 127, 'size': 32}
  • id: 109462638
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 5426, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [7], 'representative': 32, 'size': 2}
  • id: 109462639
    {'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 13, 'group_counter': 5426, 'group_order': 256, 'label': '8A3', 'order': 8, 'powers': [7], 'representative': 96, 'size': 2}
  • id: 109462640
    {'aut_label': '8B1', 'centralizer': '2.g1.a1', 'counter': 14, 'group_counter': 5426, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [6], 'representative': 4, 'size': 2}
  • id: 109462641
    {'aut_label': '8B1', 'centralizer': '2.g1.a1', 'counter': 15, 'group_counter': 5426, 'group_order': 256, 'label': '8B3', 'order': 8, 'powers': [6], 'representative': 12, 'size': 2}
  • id: 109462642
    {'aut_label': '8C', 'centralizer': '4.d1.a1', 'counter': 16, 'group_counter': 5426, 'group_order': 256, 'label': '8C', 'order': 8, 'powers': [6], 'representative': 68, 'size': 4}
  • id: 109462643
    {'aut_label': '8D', 'centralizer': '4.d1.a1', 'counter': 17, 'group_counter': 5426, 'group_order': 256, 'label': '8D', 'order': 8, 'powers': [7], 'representative': 40, 'size': 4}
  • id: 109462644
    {'aut_label': '8E1', 'centralizer': '8.q1.a1', 'counter': 18, 'group_counter': 5426, 'group_order': 256, 'label': '8E1', 'order': 8, 'powers': [7], 'representative': 33, 'size': 8}
  • id: 109462645
    {'aut_label': '8E1', 'centralizer': '8.q1.a1', 'counter': 19, 'group_counter': 5426, 'group_order': 256, 'label': '8E-1', 'order': 8, 'powers': [7], 'representative': 97, 'size': 8}
  • id: 109462647
    {'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 5426, 'group_order': 256, 'label': '16A1', 'order': 16, 'powers': [12], 'representative': 16, 'size': 2}
  • id: 109462648
    {'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 5426, 'group_order': 256, 'label': '16A-1', 'order': 16, 'powers': [12], 'representative': 144, 'size': 2}
  • id: 109462649
    {'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 22, 'group_counter': 5426, 'group_order': 256, 'label': '16A3', 'order': 16, 'powers': [13], 'representative': 80, 'size': 2}
  • id: 109462650
    {'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 5426, 'group_order': 256, 'label': '16A-3', 'order': 16, 'powers': [13], 'representative': 208, 'size': 2}
  • id: 109462651
    {'aut_label': '16B1', 'centralizer': '4.d1.a1', 'counter': 24, 'group_counter': 5426, 'group_order': 256, 'label': '16B1', 'order': 16, 'powers': [13], 'representative': 24, 'size': 4}
  • id: 109462652
    {'aut_label': '16B1', 'centralizer': '4.d1.a1', 'counter': 25, 'group_counter': 5426, 'group_order': 256, 'label': '16B3', 'order': 16, 'powers': [12], 'representative': 88, 'size': 4}
  • id: 109462653
    {'aut_label': '16C1', 'centralizer': '4.d1.a1', 'counter': 26, 'group_counter': 5426, 'group_order': 256, 'label': '16C1', 'order': 16, 'powers': [17], 'representative': 20, 'size': 4}
  • id: 109462654
    {'aut_label': '16C1', 'centralizer': '4.d1.a1', 'counter': 27, 'group_counter': 5426, 'group_order': 256, 'label': '16C-1', 'order': 16, 'powers': [17], 'representative': 148, 'size': 4}
  • id: 109462655
    {'aut_label': '16C1', 'centralizer': '4.d1.a1', 'counter': 28, 'group_counter': 5426, 'group_order': 256, 'label': '16C3', 'order': 16, 'powers': [17], 'representative': 212, 'size': 4}
  • id: 109462656
    {'aut_label': '16C1', 'centralizer': '4.d1.a1', 'counter': 29, 'group_counter': 5426, 'group_order': 256, 'label': '16C-3', 'order': 16, 'powers': [17], 'representative': 84, 'size': 4}
  • id: 109462658
    {'aut_label': '16D1', 'centralizer': '8.q1.a1', 'counter': 30, 'group_counter': 5426, 'group_order': 256, 'label': '16D1', 'order': 16, 'powers': [12], 'representative': 17, 'size': 8}
  • id: 109462659
    {'aut_label': '16D1', 'centralizer': '8.q1.a1', 'counter': 31, 'group_counter': 5426, 'group_order': 256, 'label': '16D-1', 'order': 16, 'powers': [12], 'representative': 21, 'size': 8}
  • id: 109462660
    {'aut_label': '16D1', 'centralizer': '8.q1.a1', 'counter': 32, 'group_counter': 5426, 'group_order': 256, 'label': '16D3', 'order': 16, 'powers': [13], 'representative': 49, 'size': 8}
  • id: 109462661
    {'aut_label': '16D1', 'centralizer': '8.q1.a1', 'counter': 33, 'group_counter': 5426, 'group_order': 256, 'label': '16D-3', 'order': 16, 'powers': [13], 'representative': 81, 'size': 8}
  • id: 109462662
    {'aut_label': '16E1', 'centralizer': '16.w1.a1', 'counter': 34, 'group_counter': 5426, 'group_order': 256, 'label': '16E1', 'order': 16, 'powers': [14], 'representative': 2, 'size': 16}
  • id: 109462663
    {'aut_label': '16E1', 'centralizer': '16.w1.a1', 'counter': 35, 'group_counter': 5426, 'group_order': 256, 'label': '16E3', 'order': 16, 'powers': [15], 'representative': 10, 'size': 16}
  • id: 109462664
    {'aut_label': '16F1', 'centralizer': '16.x1.a1', 'counter': 36, 'group_counter': 5426, 'group_order': 256, 'label': '16F1', 'order': 16, 'powers': [15], 'representative': 18, 'size': 16}
  • id: 109462665
    {'aut_label': '16F1', 'centralizer': '16.x1.a1', 'counter': 37, 'group_counter': 5426, 'group_order': 256, 'label': '16F3', 'order': 16, 'powers': [14], 'representative': 26, '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: 4285523
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1a', '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], 'schur_index': 1}
  • id: 4285534
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1b', '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], 'schur_index': 1}
  • id: 4285538
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1c', '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], 'schur_index': 1}
  • id: 4285539
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1d', '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], 'schur_index': 1}
  • id: 4285540
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1e', '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], 'schur_index': 1}
  • id: 4285541
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1f', '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], 'schur_index': 1}
  • id: 4285542
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1g', '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], 'schur_index': 1}
  • id: 4285543
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.1h', '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], 'schur_index': 1}
  • id: 4285544
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 0, 2, 2, -2, -2, -2, 0, 2, -2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285524
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285525
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285526
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 2, 2, -2, -2, 2, 0, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285527
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2e', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 4, -4, 0, 0, 4, 0, 4, 0, 0, 4, -4, 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: 4285528
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2f', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285529
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2g', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285530
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2h', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, 4, 0, 4, -4, 0, 0, -4, 0, 4, 0, 0, 4, -4, 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: 4285531
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 4, 4, 4, 4, 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], 'schur_index': 1}
  • id: 4285533
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 0, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4285532
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.2j', 'multiplicity': 4, 'nt': [16, 44], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 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: 4285535
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.4b', 'multiplicity': 2, 'nt': [16, 133], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, -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], 'schur_index': 1}
  • id: 4285536
    {'cdim': 4, 'counter': 21, 'faithful': True, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.4c', 'multiplicity': 4, 'nt': [32, 7468], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
  • id: 4285537
    {'cdim': 4, 'counter': 22, 'faithful': True, 'group': '256.5426', 'group_order': 256, 'image': None, 'label': '256.5426.4d', 'multiplicity': 4, 'nt': [32, 7468], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 6370273
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.5426.1a', '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]]]}
  • id: 6370284
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.5426.1b', '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]]]}
  • id: 6370295
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.5426.1c', '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]]]}
  • id: 6370304
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.5426.1d', '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]]]}
  • id: 6370305
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.5426.1e', '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]]]}
  • id: 6370306
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.5426.1f', '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]]]}
  • id: 6370307
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.5426.1g', '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]]]}
  • id: 6370308
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.5426.1h', '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]]]}
  • id: 6370309
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 32, 'label': '256.5426.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370274
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1.a1', 'kernel_order': 32, 'label': '256.5426.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370275
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 32, 'label': '256.5426.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370276
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 32, 'label': '256.5426.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370277
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.e1.a1', 'kernel_order': 16, 'label': '256.5426.2e1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370278
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.e1.a1', 'kernel_order': 16, 'label': '256.5426.2e2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370279
    {'center': '8.c1.a1', 'center_index': 8, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.g1.a1', 'kernel_order': 16, 'label': '256.5426.2f1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6370280
    {'center': '8.c1.a1', 'center_index': 8, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.g1.a1', 'kernel_order': 16, 'label': '256.5426.2f2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 6370281
    {'center': '8.c1.a1', 'center_index': 8, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.f1.a1', 'kernel_order': 16, 'label': '256.5426.2g1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 6370282
    {'center': '8.c1.a1', 'center_index': 8, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.f1.a1', 'kernel_order': 16, 'label': '256.5426.2g2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 6370283
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.d1.a1', 'kernel_order': 16, 'label': '256.5426.2h1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370285
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.d1.a1', 'kernel_order': 16, 'label': '256.5426.2h2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370286
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 16, 'label': '256.5426.2i1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370287
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 16, 'label': '256.5426.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-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]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370288
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '32.42', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 8, 'label': '256.5426.2j1', 'nt': [16, 44], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370289
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '32.42', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 8, 'label': '256.5426.2j2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370290
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 32, 'counter': 25, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '32.42', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 8, 'label': '256.5426.2j3', 'nt': [16, 44], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370291
    {'center': '8.e1.a1', 'center_index': 8, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '32.42', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 8, 'label': '256.5426.2j4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370292
    {'center': '16.b1.a1', 'center_index': 16, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '32.43', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1.a1', 'kernel_order': 8, 'label': '256.5426.4a', 'nt': [8, 15], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370293
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 28, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '64.153', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.5426.4b1', 'nt': [16, 133], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370294
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '64.153', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.5426.4b2', 'nt': [16, 133], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370296
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4c1', 'nt': [32, 7468], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370297
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4c2', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370298
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4c3', 'nt': [32, 7468], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370299
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4c4', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370300
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4d1', 'nt': [32, 7468], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370301
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4d2', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370302
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4d3', 'nt': [32, 7468], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6370303
    {'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 16, 'dim': 4, 'faithful': True, 'field': [2, 0, 4, 0, 1], 'group': '256.5426', 'group_counter': 5426, 'group_order': 256, 'image': None, 'image_isoclass': '256.5426', 'image_order': 256, 'indicator': 0, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.5426.4d4', 'nt': [32, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 7]], [[-2, 3], [-2, 5]], [[-2, 1], [-2, 7]], [[2, 3], [2, 5]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [1, 7]], [[-1, 1], [1, 3], [1, 5], [-1, 7]], [[1, 1], [-1, 3], [-1, 5], [1, 7]], [[-1, 1], [-1, 3], [-1, 5], [-1, 7]], [[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: 64576757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.5426.1.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': '256.5426', 'subgroup_hash': 5426, 'subgroup_order': 256, 'subgroup_tex': 'C_{16}.D_8', 'supersolvable': True, 'sylow': 2}
  • id: 64576781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.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': '128.945', 'subgroup_hash': 945, 'subgroup_order': 128, 'subgroup_tex': 'D_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.946', 'subgroup_hash': 946, 'subgroup_order': 128, 'subgroup_tex': 'C_8.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.902', 'subgroup_hash': 902, 'subgroup_order': 128, 'subgroup_tex': 'C_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.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': '128.980', 'subgroup_hash': 980, 'subgroup_order': 128, 'subgroup_tex': 'C_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.89', 'subgroup_hash': 89, 'subgroup_order': 128, 'subgroup_tex': 'C_8.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.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': '128.90', 'subgroup_hash': 90, 'subgroup_order': 128, 'subgroup_tex': 'C_8.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.105', 'subgroup_hash': 105, 'subgroup_order': 128, 'subgroup_tex': 'C_{16}.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.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': '64.124', 'subgroup_hash': 124, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.174', 'subgroup_hash': 174, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.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': '64.175', 'subgroup_hash': 175, 'subgroup_order': 64, 'subgroup_tex': 'C_4:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.26', 'subgroup_hash': 26, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '64.45', 'subgroup_hash': 45, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.185', 'subgroup_hash': 185, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.31', 'subgroup_hash': 31, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.190', 'subgroup_hash': 190, 'subgroup_order': 64, 'subgroup_tex': 'D_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.191', 'subgroup_hash': 191, 'subgroup_order': 64, 'subgroup_tex': 'Q_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.187', 'subgroup_hash': 187, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.187', 'subgroup_hash': 187, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.42', 'subgroup_hash': 42, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{32}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.43', 'subgroup_hash': 43, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'U1', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', '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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.18', 'subgroup_hash': 18, 'subgroup_order': 32, 'subgroup_tex': 'D_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.x1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.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': 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': '32.19', 'subgroup_hash': 19, 'subgroup_order': 32, 'subgroup_tex': '\\SD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 64576815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 64576816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], '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: 64576817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.16.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': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576820
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.16.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': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576821
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.16.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': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64576823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576840
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 64576845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'L2', '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: 64576846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 79, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.32.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': '32.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576848
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.32.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': '32.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576849
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 81, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.32.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': '32.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576850
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.32.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': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 64576853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 64576864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.32.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.5426.64.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': '64.153', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 153, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 64576867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 98, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.64.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': '64.147', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 147, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8: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: 64576868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 99, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.64.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': '64.140', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 140, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_8', '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: 64576759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64576760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64576761
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64576762
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 64576763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.64.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: 64576764
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.5426.64.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.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': 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: 64576765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 64576766
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.64.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 64576767
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 108, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.5426.128.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': '128.399', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 399, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_8', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U3', 'L3', '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: 64576768
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, '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: 64576770
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 64576771
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.5426.128.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: 64576772
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.5426', 'ambient_counter': 5426, 'ambient_order': 256, 'ambient_tex': 'C_{16}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 112, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.5426.256.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': '256.5426', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5426, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}.D_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U4', 'L4', '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: 64576757
    {'ambient': '256.5426', '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': '128.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'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5479, 5029, 5397, 4703, 5480, 5065, 5355, 4736], 'generators': [1, 2, 16], 'label': '256.5426.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '128.399', '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': '128.399'}
  • id: 64576758
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10483374', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4791, 2646, 4424, 3565, 4792, 2664, 4382, 3591], 'generators': [3, 140, 96], 'label': '256.5426.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '128.399', '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': '64.153'}
  • id: 64576759
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.j1.a1', '32.k1.a1'], 'contains': ['128.a1.a1', '128.c1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5982, -1, 5898, -1, 5984, -1, 6014, -1], 'generators': [1, 128], 'label': '256.5426.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576760
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.l1.a1', '32.m1.a1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5179, -1, 3858, -1, 5180, -1, 3858, -1], 'generators': [3, 128], 'label': '256.5426.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.i1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576761
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.j1.a1', '32.n1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5720, -1, 5644, -1, 5722, -1, 5760, -1], 'generators': [65], 'label': '256.5426.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576762
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.o1.a1', '32.p1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [6245, -1, 5407, -1, 6247, -1, 5523, -1], 'generators': [19], 'label': '256.5426.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576763
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.r1.a1', '32.r1.b1'], 'contains': ['128.b1.a1', '128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4655, -1, 2842, -1, 4656, -1, 2842, -1], 'generators': [3, 72], 'label': '256.5426.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1.a1', 'old_label': '64.h1.a1', 'projective_image': '256.5426', '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: 64576764
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.r1.a1', '32.r1.b1'], 'contains': ['128.b1.a1', '128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4655, -1, 3112, -1, 4656, -1, 3112, -1], 'generators': [3, 200], 'label': '256.5426.64.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1.a1', 'old_label': '64.h1.a2', 'projective_image': '256.5426', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576765
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.r1.a1'], 'contains': ['128.b1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4917, -1, 3366, -1, 4918, -1, 3366, -1], 'generators': [108], 'label': '256.5426.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.i1.a1', 'projective_image': '256.5426', '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: 64576766
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.r1.b1'], 'contains': ['128.b1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4917, -1, 3604, -1, 4918, -1, 3604, -1], 'generators': [236], 'label': '256.5426.64.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.i1.b1', 'projective_image': '256.5426', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576767
    {'ambient': '256.5426', 'aut_centralizer_order': 2048, 'aut_label': '128.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, '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'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5703, 5603, 5279, 5049, 5705, 5643, 5394, 5085], 'generators': [128], 'label': '256.5426.128.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'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.399', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.399', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64576768
    {'ambient': '256.5426', 'aut_centralizer_order': 1024, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.h1.a1', '64.h1.a2', '64.i1.a1', '64.i1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5441, -1, 3541, -1, 5443, -1, 3485, -1], 'generators': [72], 'label': '256.5426.128.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '128.b1.a1', 'projective_image': '256.5426', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64576769
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10483374', 'aut_weyl_index': 4, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5479, 5564, 5397, 7393, 5480, 5603, 5355, 7445], 'generators': [19, 140, 96], 'label': '256.5426.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '128.399', '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': '64.153'}
  • id: 64576770
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5966, -1, 5644, -1, 5967, -1, 5885, -1], 'generators': [1], 'label': '256.5426.128.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.q1.a1', 'old_label': '128.c1.a1', 'projective_image': '256.5426', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64576771
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.h1.a1', '64.h1.a2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [5179, -1, 3178, -1, 5180, -1, 3241, -1], 'generators': [3], 'label': '256.5426.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1.a1', 'old_label': '128.d1.a1', 'projective_image': '256.5426', '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: 64576772
    {'ambient': '256.5426', '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'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5574, 5603, 4313, 5049, 5572, 5643, 4184, 5085], 'generators': [], 'label': '256.5426.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.5426', '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: 64576773
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.45', 'aut_weyl_index': 64, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3105, 9214, 3363, 9214, 3106, 9279, 3320, 9279], 'generators': [16, 140], 'label': '256.5426.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576774
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2312', 'aut_weyl_index': 16, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.n1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4293, 7037, 4905, 5920, 4295, 7087, 4863, 5961], 'generators': [17, 140], 'label': '256.5426.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 64576775
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2312', 'aut_weyl_index': 16, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.o1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5986, 7947, 5889, 5010, 5988, 8003, 5846, 5045], 'generators': [2, 96], 'label': '256.5426.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576776
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2312', 'aut_weyl_index': 16, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.p1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6905, 4089, 6779, 2122, 6907, 4119, 6736, 2137], 'generators': [18, 96], 'label': '256.5426.4.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.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576777
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.196', 'aut_weyl_index': 32, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.n1.a1', '8.q1.a1', '8.r1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1263, -1, 3864, -1, 1264, -1, 3821, -1], 'generators': [1, 16, 8], 'label': '256.5426.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.h1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64576778
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.196', 'aut_weyl_index': 32, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.n1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1917, -1, 2941, -1, 1918, -1, 2898, -1], 'generators': [1, 156], 'label': '256.5426.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.i1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64576779
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.o1.a1', '8.s1.a1', '8.u1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7906, -1, 8177, -1, 7909, -1, 8157, -1], 'generators': [1, 2, 64], 'label': '256.5426.4.j1.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.j1.a1', 'projective_image': '128.399', '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': '64.140'}
  • id: 64576780
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '8.p1.a1', '8.t1.a1', '8.y1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8972, -1, 8622, -1, 8975, -1, 8612, -1], 'generators': [1, 18, 64], 'label': '256.5426.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '128.399', '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': '64.140'}
  • id: 64576781
    {'ambient': '256.5426', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dln', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '4.j1.a1', '4.n1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6402, 2606, 6290, 2013, 6400, 2625, 6245, 2027], 'generators': [1, 2, 96], 'label': '256.5426.2.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.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '128.399', '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': '128.399'}
  • id: 64576782
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53164', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.l1.a1', '8.v1.a1', '8.w1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2452, -1, 2358, -1, 2452, -1, 2328, -1], 'generators': [3, 16, 8], 'label': '256.5426.4.l1.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.l1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576783
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53164', 'aut_weyl_index': 8, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.l1.a1', '8.x1.a1', '8.x1.a2'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3760, -1, 1619, -1, 3760, -1, 1563, -1], 'generators': [3, 156, 8], 'label': '256.5426.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.m1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576784
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.j1.a1', '8.o1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7365, -1, 7223, -1, 7367, -1, 7181, -1], 'generators': [97, 2], 'label': '256.5426.4.n1.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.n1.a1', 'projective_image': '128.399', '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': '64.140'}
  • id: 64576785
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.54439', 'aut_weyl_index': 8, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '8.m1.a1', '8.p1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8561, -1, 7715, -1, 8563, -1, 7672, -1], 'generators': [97, 18], 'label': '256.5426.4.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.o1.a1', 'projective_image': '128.399', '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': '64.140'}
  • id: 64576786
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.254', 'aut_weyl_index': 32, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '16.h1.a1', '16.p1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7692, 3091, 8312, 2448, 7694, 3113, 8312, 2465], 'generators': [1, 140, 64], 'label': '256.5426.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576787
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5342, 5564, 5496, 5010, 5344, 5603, 5496, 5045], 'generators': [140, 96], 'label': '256.5426.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576788
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.l1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1488, 8659, 2522, 8105, 1488, 8721, 2522, 8163], 'generators': [16, 8], 'label': '256.5426.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.b1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576789
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.bb1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3160, 7047, 1984, 6494, 3161, 7097, 1985, 6539], 'generators': [156, 8], 'label': '256.5426.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576790
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.254', 'aut_weyl_index': 32, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.l1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6568, 4218, 6683, 3624, 6570, 4248, 6683, 3651], 'generators': [97, 140], 'label': '256.5426.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 64576791
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.l1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5837, -1, 6278, -1, 5838, -1, 6278, -1], 'generators': [1, 236], 'label': '256.5426.8.f1.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.f1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64576792
    {'ambient': '256.5426', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dln', 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.g1.a1', '4.k1.a1', '4.o1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6862, 1399, 6736, 806, 6860, 1409, 6690, 812], 'generators': [1, 18, 96], 'label': '256.5426.2.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'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '128.399'}
  • id: 64576793
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.l1.a1', '16.n1.a1', '16.o1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2660, -1, 5054, -1, 2660, -1, 5054, -1], 'generators': [1, 96, 8], 'label': '256.5426.8.g1.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.g1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576794
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1751', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4954, -1, 2944, -1, 4956, -1, 2944, -1], 'generators': [3, 236, 64], 'label': '256.5426.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.h1.a1', 'projective_image': '128.399', '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': '32.7'}
  • id: 64576795
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.s1.a1', '16.t1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3670, -1, 1491, -1, 3672, -1, 1490, -1], 'generators': [3, 96, 8], 'label': '256.5426.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.i1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576796
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.q1.a1', '16.r1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6960, -1, 7062, -1, 6962, -1, 7062, -1], 'generators': [3, 140, 64], 'label': '256.5426.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.43'}
  • id: 64576797
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.1751', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.m1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6255, -1, 5872, -1, 6257, -1, 5872, -1], 'generators': [19, 236, 64], 'label': '256.5426.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.k1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.7'}
  • id: 64576798
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.y1.a1', '16.z1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4185, -1, 3366, -1, 4186, -1, 3366, -1], 'generators': [19, 96, 8], 'label': '256.5426.8.l1.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.l1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576799
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2317', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.k1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.u1.a1', '16.v1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8768, -1, 7559, -1, 8770, -1, 7560, -1], 'generators': [19, 140, 64], 'label': '256.5426.8.m1.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.m1.a1', 'projective_image': '128.399', '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': '32.43'}
  • id: 64576800
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.b1.a1', '16.ba1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1039, -1, 3801, -1, 1039, -1, 3802, -1], 'generators': [17, 8], 'label': '256.5426.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.n1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576801
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.j1.a1', '4.n1.a1'], 'contains': ['16.c1.a1', '16.w1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7365, -1, 7995, -1, 7367, -1, 7995, -1], 'generators': [2, 64], 'label': '256.5426.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '128.399', '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': '16.11'}
  • id: 64576802
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.48', 'aut_weyl_index': 64, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.k1.a1', '4.o1.a1'], 'contains': ['16.c1.a1', '16.x1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9217, -1, 8628, -1, 9220, -1, 8628, -1], 'generators': [18, 64], 'label': '256.5426.8.p1.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.p1.a1', 'projective_image': '128.399', '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': '16.11'}
  • id: 64576803
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53144', 'aut_weyl_index': 8, 'centralizer': '16.f1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.h1.a1', '4.i1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3296, 6522, 4299, 4703, 3236, 6569, 4257, 4736], 'generators': [1, 16, 140], 'label': '256.5426.2.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.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 64576804
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.f1.a1', '16.n1.a1', '16.ba1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [589, -1, 4236, -1, 589, -1, 4237, -1], 'generators': [1, 16], 'label': '256.5426.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.q1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576805
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.g1.a1', '16.n1.a1', '16.ba1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [139, -1, 4672, -1, 140, -1, 4672, -1], 'generators': [1, 24], 'label': '256.5426.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.r1.a1', 'projective_image': '128.399', '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': '4.2'}
  • id: 64576806
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.d1.a1', '16.q1.a1', '16.w1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8336, -1, 9264, -1, 8338, -1, 9265, -1], 'generators': [1, 2], 'label': '256.5426.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.s1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576807
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.d1.a1', '16.u1.a1', '16.x1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9861, -1, 9868, -1, 9864, -1, 9868, -1], 'generators': [1, 18], 'label': '256.5426.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '8.t1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576808
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.e1.a1', '16.q1.a1', '16.w1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8016, -1, 8954, -1, 8018, -1, 8955, -1], 'generators': [65, 2], 'label': '256.5426.8.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.u1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576809
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.f1.a1', '16.s1.a1', '16.y1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2267, -1, 779, -1, 2268, -1, 778, -1], 'generators': [3, 16], 'label': '256.5426.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.v1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576810
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.g1.a1', '16.s1.a1', '16.y1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1934, -1, 1101, -1, 1935, -1, 1101, -1], 'generators': [3, 24], 'label': '256.5426.8.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.w1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576811
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1'], 'contains': ['16.t1.a1', '16.z1.a1', '16.bb1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4631, -1, 132, -1, 4632, -1, 132, -1], 'generators': [3, 20], 'label': '256.5426.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '8.x1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576812
    {'ambient': '256.5426', 'aut_centralizer_order': 4, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1'], 'contains': ['16.t1.a1', '16.z1.a1', '16.bb1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4631, -1, 455, -1, 4632, -1, 455, -1], 'generators': [3, 156], 'label': '256.5426.8.x1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '8.x1.a2', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.a2', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 64576813
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.123', 'aut_weyl_index': 32, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.e1.a1', '16.u1.a1', '16.x1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9541, -1, 9558, -1, 9544, -1, 9558, -1], 'generators': [65, 18], 'label': '256.5426.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '8.y1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576814
    {'ambient': '256.5426', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '64.a1.a1', 'complements': ['128.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.l1.a1', '4.m1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4322, 5029, 3481, 8610, 4261, 5065, 3439, 8670], 'generators': [3, 16, 140], 'label': '256.5426.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '128.399', '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': '64.153'}
  • id: 64576815
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.f1.a1', '8.h1.a1', '8.k1.a1'], 'contains': ['32.a1.a1', '32.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5537, 5603, 5229, 5049, 5538, 5643, 5229, 5085], 'generators': [236, 64], 'label': '256.5426.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576816
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '8.g1.a1', '8.i1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3037, 6680, 3801, 6128, 3038, 6728, 3802, 6171], 'generators': [96, 8], 'label': '256.5426.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'normal_contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576817
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.e1.a1', '8.j1.a1', '8.m1.a1', '8.o1.a1', '8.p1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7583, 4525, 7514, 3971, 7585, 4557, 7514, 3999], 'generators': [140, 64], 'label': '256.5426.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.e1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576818
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.s1.a1', '8.t1.a1'], 'contains': ['32.b1.a1', '32.k1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8789, 3496, 9297, 2052, 8791, 3521, 9298, 2067], 'generators': [1, 140], 'label': '256.5426.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576819
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.u1.a1', '8.y1.a1'], 'contains': ['32.b1.a1', '32.n1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8513, 2695, 8737, 2854, 8515, 2714, 8737, 2874], 'generators': [65, 140], 'label': '256.5426.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576820
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.q1.a1', '8.v1.a1'], 'contains': ['32.d1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1764, 7789, 2687, 7235, 1764, 7844, 2687, 7286], 'generators': [16], 'label': '256.5426.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576821
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '16.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.r1.a1', '8.w1.a1'], 'contains': ['32.d1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1001, 8659, 2977, 8105, 1001, 8721, 2977, 8163], 'generators': [24], 'label': '256.5426.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576822
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.j1.a1', '32.k1.a1', '32.n1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6146, -1, 6604, -1, 6148, -1, 6604, -1], 'generators': [1, 8, 64], 'label': '256.5426.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.h1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64576823
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '32.g1.a1', '32.l1.a1', '32.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5162, -1, 3349, -1, 5164, -1, 3350, -1], 'generators': [3, 8, 64], 'label': '256.5426.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.i1.a1', 'projective_image': '128.399', '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': '16.11'}
  • id: 64576824
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.r1.a1', '32.r1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4352, -1, 956, -1, 4353, -1, 956, -1], 'generators': [3, 236, 128], 'label': '256.5426.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '16.j1.a1', 'projective_image': '128.399', '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': '8.5'}
  • id: 64576825
    {'ambient': '256.5426', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4927, 3812, 4952, 3220, 4935, 3840, 4909, 3242], 'generators': [17, 18], 'label': '256.5426.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '128.399', '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': '128.399'}
  • id: 64576826
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.l1.a1', '8.m1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '32.o1.a1', '32.p1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6538, -1, 6225, -1, 6540, -1, 6225, -1], 'generators': [19, 8, 64], 'label': '256.5426.16.k1.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.k1.a1', 'projective_image': '128.399', '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: 64576827
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.q1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4757, -1, 5833, -1, 4758, -1, 5832, -1], 'generators': [97, 8], 'label': '256.5426.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.l1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 64576828
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1'], 'contains': ['32.h1.a1', '32.i1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5834, -1, 5516, -1, 5835, -1, 5516, -1], 'generators': [19, 236], 'label': '256.5426.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1.a1', 'old_label': '16.m1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 64576829
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.d1.a1', '32.j1.a1', '32.q1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1383, -1, 4540, -1, 1383, -1, 4540, -1], 'generators': [1, 160], 'label': '256.5426.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.n1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576830
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.e1.a1', '32.j1.a1', '32.q1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2636, -1, 4929, -1, 2636, -1, 4929, -1], 'generators': [1, 168], 'label': '256.5426.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.o1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576831
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.c1.a1', '32.k1.a1', '32.n1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7185, -1, 7899, -1, 7187, -1, 7900, -1], 'generators': [1, 204], 'label': '256.5426.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.p1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576832
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.s1.a1', '8.u1.a1'], 'contains': ['32.b1.a1', '32.l1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7938, -1, 8180, -1, 7939, -1, 8180, -1], 'generators': [3, 140], 'label': '256.5426.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.q1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576833
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1'], 'contains': ['32.c1.a1', '32.l1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6895, -1, 6874, -1, 6897, -1, 6874, -1], 'generators': [3, 204], 'label': '256.5426.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.r1.a1', 'projective_image': '128.399', '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': '16.8'}
  • id: 64576834
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.d1.a1', '32.m1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2036, -1, 2127, -1, 2037, -1, 2127, -1], 'generators': [3, 96], 'label': '256.5426.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.s1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576835
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.x1.a1', '8.x1.a2'], 'contains': ['32.e1.a1', '32.m1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3691, -1, 1302, -1, 3692, -1, 1302, -1], 'generators': [3, 104], 'label': '256.5426.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '16.t1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576836
    {'ambient': '256.5426', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '128.a1.a1', 'complements': ['128.c1.a1', '128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5479, 8006, 5397, 7393, 5480, 8063, 5355, 7445], 'generators': [17, 2], 'label': '256.5426.2.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.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '128.399', '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': '128.399'}
  • id: 64576837
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.t1.a1', '8.y1.a1'], 'contains': ['32.b1.a1', '32.o1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9367, -1, 9030, -1, 9370, -1, 9031, -1], 'generators': [19, 140], 'label': '256.5426.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.u1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576838
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1'], 'contains': ['32.c1.a1', '32.o1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9065, -1, 7141, -1, 9067, -1, 7141, -1], 'generators': [19, 204], 'label': '256.5426.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.a1', 'old_label': '16.v1.a1', 'projective_image': '128.399', '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': '16.8'}
  • id: 64576839
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.s1.a1', '8.u1.a1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8209, -1, 8443, -1, 8212, -1, 8444, -1], 'generators': [2], 'label': '256.5426.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.w1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576840
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.t1.a1', '8.y1.a1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9670, -1, 9561, -1, 9673, -1, 9562, -1], 'generators': [18], 'label': '256.5426.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '16.x1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576841
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.v1.a1', '8.w1.a1'], 'contains': ['32.d1.a1', '32.p1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2312, -1, 2394, -1, 2313, -1, 2394, -1], 'generators': [19, 96], 'label': '256.5426.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.y1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576842
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.x1.a1', '8.x1.a2'], 'contains': ['32.e1.a1', '32.p1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3967, -1, 1860, -1, 3968, -1, 1860, -1], 'generators': [19, 104], 'label': '256.5426.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '16.z1.a1', 'projective_image': '128.399', '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': '16.7'}
  • id: 64576843
    {'ambient': '256.5426', 'aut_centralizer_order': 64, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.q1.a1', '8.r1.a1'], 'contains': ['32.d1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [658, -1, 4170, -1, 657, -1, 4171, -1], 'generators': [17], 'label': '256.5426.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.ba1.a1', 'projective_image': '128.399', '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': '2.1'}
  • id: 64576844
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.x1.a1', '8.x1.a2'], 'contains': ['32.e1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3418, -1, 1567, -1, 3419, -1, 1566, -1], 'generators': [156], 'label': '256.5426.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bb1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576845
    {'ambient': '256.5426', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.h1.a1', '16.i1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5537, 5603, 5538, 5049, 5538, 5643, 5539, 5085], 'generators': [8, 64], 'label': '256.5426.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576846
    {'ambient': '256.5426', 'aut_centralizer_order': 512, 'aut_label': '32.b1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '16.q1.a1', '16.u1.a1', '16.w1.a1', '16.x1.a1'], 'contains': ['64.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8359, 3674, 8591, 3081, 8362, 3700, 8589, 3103], 'generators': [140], 'label': '256.5426.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.c1.a1', '16.d1.a1', '16.e1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576847
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53143', 'aut_weyl_index': 8, 'centralizer': '32.b1.a1', 'complements': ['128.c1.a1', '128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.a1', '4.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5942, 9214, 5845, 6187, 5940, 9279, 5800, 6230], 'generators': [2, 16], 'label': '256.5426.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.f1.a1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '128.399', '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': '32.39'}
  • id: 64576848
    {'ambient': '256.5426', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.p1.a1', '16.r1.a1', '16.v1.a1'], 'contains': ['64.b1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7335, 4545, 7141, 3991, 7337, 4577, 7141, 4019], 'generators': [204], 'label': '256.5426.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '128.399', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576849
    {'ambient': '256.5426', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.f1.a1', '16.g1.a1', '16.n1.a1', '16.s1.a1', '16.y1.a1', '16.ba1.a1'], 'contains': ['64.c1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1900, 7581, 3824, 7027, 1901, 7625, 3825, 7067], 'generators': [96], 'label': '256.5426.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1', '16.f1.a1', '16.g1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576850
    {'ambient': '256.5426', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.o1.a1', '16.t1.a1', '16.z1.a1', '16.bb1.a1'], 'contains': ['64.c1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3582, 6661, 3587, 6108, 3583, 6698, 3587, 6141], 'generators': [104], 'label': '256.5426.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '128.399', '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: 64576851
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.f1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5891, -1, 6331, -1, 5892, -1, 6330, -1], 'generators': [1, 72], 'label': '256.5426.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.f1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576852
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '32.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.h1.a1', '64.h1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4702, -1, 3096, -1, 4704, -1, 3096, -1], 'generators': [3, 72, 128], 'label': '256.5426.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.g1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576853
    {'ambient': '256.5426', 'aut_centralizer_order': 256, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '64.i1.a1', '64.i1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5074, -1, 4167, -1, 5075, -1, 4168, -1], 'generators': [236, 128], 'label': '256.5426.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.h1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576854
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '32.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '64.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6245, -1, 5988, -1, 6247, -1, 5987, -1], 'generators': [19, 72], 'label': '256.5426.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.k1.a1', 'old_label': '32.i1.a1', 'projective_image': '128.399', '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': '4.2'}
  • id: 64576855
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.n1.a1', '16.o1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.f1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3228, -1, 5090, -1, 3229, -1, 5091, -1], 'generators': [1, 64], 'label': '256.5426.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.j1.a1', 'projective_image': '128.399', '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: 64576856
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.h1.a1', '16.p1.a1'], 'contains': ['64.b1.a1', '64.d1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7089, -1, 7615, -1, 7091, -1, 7616, -1], 'generators': [1, 8], 'label': '256.5426.32.k1.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.k1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576857
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.q1.a1', '16.r1.a1'], 'contains': ['64.b1.a1', '64.e1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6599, -1, 6666, -1, 6601, -1, 6667, -1], 'generators': [3, 8], 'label': '256.5426.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1.a1', 'old_label': '32.l1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576858
    {'ambient': '256.5426', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2310', 'aut_weyl_index': 16, 'centralizer': '16.f1.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.e1.a1', '8.f1.a1', '8.g1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6446, 786, 6334, 786, 6448, 792, 6291, 792], 'generators': [1, 140, 96], 'label': '256.5426.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '128.399', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
  • id: 64576859
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.s1.a1', '16.t1.a1'], 'contains': ['64.c1.a1', '64.e1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3827, -1, 3349, -1, 3828, -1, 3350, -1], 'generators': [3, 64], 'label': '256.5426.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.m1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576860
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.h1.a1', '16.p1.a1'], 'contains': ['64.b1.a1', '64.f1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6844, -1, 7378, -1, 6846, -1, 7379, -1], 'generators': [65, 8], 'label': '256.5426.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.n1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576861
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.u1.a1', '16.v1.a1'], 'contains': ['64.b1.a1', '64.g1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7580, -1, 6903, -1, 7582, -1, 6904, -1], 'generators': [19, 8], 'label': '256.5426.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1.a1', 'old_label': '32.o1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576862
    {'ambient': '256.5426', 'aut_centralizer_order': 32, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.y1.a1', '16.z1.a1'], 'contains': ['64.c1.a1', '64.g1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4073, -1, 4510, -1, 4074, -1, 4510, -1], 'generators': [19, 64], 'label': '256.5426.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.l1.a1', 'old_label': '32.p1.a1', 'projective_image': '128.399', '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': '8.3'}
  • id: 64576863
    {'ambient': '256.5426', 'aut_centralizer_order': 128, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.n1.a1', '16.o1.a1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2810, -1, 4747, -1, 2755, -1, 4748, -1], 'generators': [161], 'label': '256.5426.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '32.q1.a1', 'projective_image': '128.399', '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': '2.1'}
  • id: 64576864
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1'], 'contains': ['64.h1.a1', '64.h1.a2', '64.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T7468', 'count': 16, 'diagramx': [4440, -1, 2605, -1, 4441, -1, 2605, -1], 'generators': [3, 108], 'label': '256.5426.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1.a1', 'old_label': '32.r1.a1', 'projective_image': '256.5426', '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: 64576865
    {'ambient': '256.5426', 'aut_centralizer_order': 8, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1'], 'contains': ['64.h1.a1', '64.h1.a2', '64.i1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T7468', 'count': 16, 'diagramx': [4440, -1, 2842, -1, 4441, -1, 2842, -1], 'generators': [3, 236], 'label': '256.5426.32.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1.a1', 'old_label': '32.r1.b1', 'projective_image': '256.5426', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 64576866
    {'ambient': '256.5426', 'aut_centralizer_order': 1024, 'aut_label': '64.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '128.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5458, 5603, 5153, 5049, 5460, 5643, 5269, 5085], 'generators': [72, 128], 'label': '256.5426.64.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.39', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576867
    {'ambient': '256.5426', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.k1.a1', '32.l1.a1', '32.n1.a1', '32.o1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6967, 4683, 7022, 4129, 6969, 4716, 7023, 4158], 'generators': [8], 'label': '256.5426.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.14', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64576868
    {'ambient': '256.5426', 'aut_centralizer_order': 1024, 'aut_label': '64.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '32.j1.a1', '32.m1.a1', '32.p1.a1', '32.q1.a1'], 'contains': ['128.a1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3704, 6512, 4629, 5959, 3706, 6549, 4629, 5991], 'generators': [64], 'label': '256.5426.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.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.c1.a1', 'projective_image': '128.399', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.25', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}