Abstract group data - 256.12509

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 4, 4, 4, 4, 4], 'aut_gens': [[1, 2, 4, 32], [129, 10, 156, 112], [17, 154, 28, 112], [17, 130, 148, 240], [145, 67, 141, 104], [145, 138, 220, 32], [17, 154, 4, 32], [129, 2, 220, 176], [145, 203, 93, 232]], 'aut_group': None, 'aut_hash': 5881906593575344611, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 48, 'aut_perms': [7937101482942227503746333454431119931530246126323833099964128, 2384688650769100178979655843873248212040347293521878064929248, 5291856004995458059690824267973006971725641817112821681620165, 2620527253998221229142994783952371532031054653888748300981711, 2443087770591139662453800790717113970304064376594149019194229, 11623881476522574833791081074607517298695116311658470558713161, 3964409943419644123646862046440451104424186199587400949230782, 6644892343978855621545741384409573172618034901587468819417851], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 16, 1, 1], [4, 2, 2, 2], [4, 4, 1, 4], [4, 8, 2, 2], [4, 16, 1, 3], [8, 4, 4, 1], [8, 8, 2, 1], [8, 8, 4, 2], [8, 16, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '32.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 16, 1], [4, 2, 4], [4, 4, 4], [4, 8, 4], [4, 16, 3], [8, 4, 4], [8, 8, 10], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.203', 'commutator_count': 1, 'commutator_label': '16.2', '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': 12509, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 16, 1, 1], [4, 2, 1, 4], [4, 4, 1, 4], [4, 8, 1, 4], [4, 16, 1, 3], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 4], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 161280, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '16.14', 'hash': 12509, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 4], 'inner_gens': [[1, 130, 132, 48], [129, 2, 140, 32], [129, 154, 4, 96], [17, 2, 196, 32]], 'inner_hash': 203, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': True, 'inner_tex': 'C_2^3:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 8], [8, 1]], 'label': '256.12509', 'linC_count': 16, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 8, 'linQ_dim': 16, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 16, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.C2^4', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 47, 'number_conjugacy_classes': 37, 'number_divisions': 31, 'number_normal_subgroups': 105, 'number_subgroup_autclasses': 205, 'number_subgroup_classes': 291, 'number_subgroups': 727, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 23], [4, 104], [8, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 112], [129, 130, 4, 32], [17, 2, 4, 32], [1, 2, 20, 32], [1, 130, 4, 32], [17, 195, 21, 184]], 'outer_group': '128.1009', 'outer_hash': 1009, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 14, 'outer_perms': [14377673521, 19239897655, 21196264375, 288, 21196264608, 32627710206], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 2], [8, 5]], 'representations': {'PC': {'code': 10718209585077369834943883663686814190, 'gens': [1, 2, 3, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2081, 137, 3170, 1690, 66, 395, 91, 2309, 1173, 141, 2710, 166]}, 'Perm': {'d': 32, 'gens': [9620189608523220657277537279019806, 17268312130521262350485277730445136, 25207874400137674715523130071627653, 34538973774836392403927035693471009, 43051836646078837836722321827071649, 5794634545962, 51550024053101171754201062105088000, 4315567359649]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.C_2^4', 'transitive_degree': 128, '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: 101091631
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 12509, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 101091642
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 12509, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 144, 'size': 1}
  • id: 101091653
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 12509, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 101091662
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 12509, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 101091663
    {'aut_label': '2D', 'centralizer': '4.c1.a1', 'counter': 5, 'group_counter': 12509, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 101091664
    {'aut_label': '2E', 'centralizer': '16.p1.a1', 'counter': 6, 'group_counter': 12509, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 38, 'size': 16}
  • id: 101091665
    {'aut_label': '4A', 'centralizer': '2.e1.a1', 'counter': 7, 'group_counter': 12509, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [3], 'representative': 64, 'size': 2}
  • id: 101091666
    {'aut_label': '4A', 'centralizer': '2.e1.a1', 'counter': 8, 'group_counter': 12509, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [3], 'representative': 80, 'size': 2}
  • id: 101091667
    {'aut_label': '4C', 'centralizer': '2.g1.a1', 'counter': 9, 'group_counter': 12509, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 8, 'size': 2}
  • id: 101091632
    {'aut_label': '4C', 'centralizer': '2.g1.a1', 'counter': 10, 'group_counter': 12509, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 136, 'size': 2}
  • id: 101091633
    {'aut_label': '4E', 'centralizer': '4.d1.a1', 'counter': 11, 'group_counter': 12509, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 72, 'size': 4}
  • id: 101091634
    {'aut_label': '4F', 'centralizer': '4.e1.a1', 'counter': 12, 'group_counter': 12509, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 65, 'size': 4}
  • id: 101091635
    {'aut_label': '4G', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 12509, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 9, 'size': 4}
  • id: 101091636
    {'aut_label': '4H', 'centralizer': '4.e1.a1', 'counter': 14, 'group_counter': 12509, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [2], 'representative': 73, 'size': 4}
  • id: 101091637
    {'aut_label': '4I', 'centralizer': '8.bl1.a1', 'counter': 15, 'group_counter': 12509, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 2, 'size': 8}
  • id: 101091638
    {'aut_label': '4J', 'centralizer': '8.bl1.a1', 'counter': 16, 'group_counter': 12509, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [2], 'representative': 66, 'size': 8}
  • id: 101091639
    {'aut_label': '4J', 'centralizer': '8.bl1.b1', 'counter': 17, 'group_counter': 12509, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [2], 'representative': 3, 'size': 8}
  • id: 101091640
    {'aut_label': '4I', 'centralizer': '8.bl1.b1', 'counter': 18, 'group_counter': 12509, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 67, 'size': 8}
  • id: 101091641
    {'aut_label': '4M', 'centralizer': '16.n1.a1', 'counter': 19, 'group_counter': 12509, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [3], 'representative': 6, 'size': 16}
  • id: 101091643
    {'aut_label': '4N', 'centralizer': '16.n1.a1', 'counter': 20, 'group_counter': 12509, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [3], 'representative': 7, 'size': 16}
  • id: 101091644
    {'aut_label': '4O', 'centralizer': '16.p1.a1', 'counter': 21, 'group_counter': 12509, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [4], 'representative': 39, 'size': 16}
  • id: 101091645
    {'aut_label': '8A1', 'centralizer': '4.o1.a1', 'counter': 22, 'group_counter': 12509, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [7], 'representative': 32, 'size': 4}
  • id: 101091646
    {'aut_label': '8A1', 'centralizer': '4.o1.a1', 'counter': 23, 'group_counter': 12509, 'group_order': 256, 'label': '8A-1', 'order': 8, 'powers': [7], 'representative': 160, 'size': 4}
  • id: 101091647
    {'aut_label': '8A1', 'centralizer': '4.o1.b1', 'counter': 24, 'group_counter': 12509, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [8], 'representative': 40, 'size': 4}
  • id: 101091648
    {'aut_label': '8A1', 'centralizer': '4.o1.b1', 'counter': 25, 'group_counter': 12509, 'group_order': 256, 'label': '8B-1', 'order': 8, 'powers': [8], 'representative': 168, 'size': 4}
  • id: 101091649
    {'aut_label': '8C', 'centralizer': '8.j1.a1', 'counter': 26, 'group_counter': 12509, 'group_order': 256, 'label': '8C', 'order': 8, 'powers': [8], 'representative': 33, 'size': 8}
  • id: 101091650
    {'aut_label': '8C', 'centralizer': '8.j1.a1', 'counter': 27, 'group_counter': 12509, 'group_order': 256, 'label': '8D', 'order': 8, 'powers': [7], 'representative': 41, 'size': 8}
  • id: 101091651
    {'aut_label': '8E1', 'centralizer': '8.bq1.a1', 'counter': 28, 'group_counter': 12509, 'group_order': 256, 'label': '8E1', 'order': 8, 'powers': [9], 'representative': 4, 'size': 8}
  • id: 101091652
    {'aut_label': '8E1', 'centralizer': '8.bq1.a1', 'counter': 29, 'group_counter': 12509, 'group_order': 256, 'label': '8E-1', 'order': 8, 'powers': [9], 'representative': 20, 'size': 8}
  • id: 101091654
    {'aut_label': '8F1', 'centralizer': '8.bl1.a1', 'counter': 30, 'group_counter': 12509, 'group_order': 256, 'label': '8F1', 'order': 8, 'powers': [8], 'representative': 34, 'size': 8}
  • id: 101091655
    {'aut_label': '8F1', 'centralizer': '8.bl1.a1', 'counter': 31, 'group_counter': 12509, 'group_order': 256, 'label': '8F-1', 'order': 8, 'powers': [8], 'representative': 98, 'size': 8}
  • id: 101091656
    {'aut_label': '8E1', 'centralizer': '8.bq1.a1', 'counter': 32, 'group_counter': 12509, 'group_order': 256, 'label': '8G1', 'order': 8, 'powers': [10], 'representative': 5, 'size': 8}
  • id: 101091657
    {'aut_label': '8E1', 'centralizer': '8.bq1.a1', 'counter': 33, 'group_counter': 12509, 'group_order': 256, 'label': '8G-1', 'order': 8, 'powers': [10], 'representative': 69, 'size': 8}
  • id: 101091658
    {'aut_label': '8F1', 'centralizer': '8.bl1.b1', 'counter': 34, 'group_counter': 12509, 'group_order': 256, 'label': '8H1', 'order': 8, 'powers': [7], 'representative': 35, 'size': 8}
  • id: 101091659
    {'aut_label': '8F1', 'centralizer': '8.bl1.b1', 'counter': 35, 'group_counter': 12509, 'group_order': 256, 'label': '8H-1', 'order': 8, 'powers': [7], 'representative': 99, 'size': 8}
  • id: 101091660
    {'aut_label': '8I', 'centralizer': '16.bd1.a1', 'counter': 36, 'group_counter': 12509, 'group_order': 256, 'label': '8I', 'order': 8, 'powers': [10], 'representative': 36, 'size': 16}
  • id: 101091661
    {'aut_label': '8I', 'centralizer': '16.bd1.b1', 'counter': 37, 'group_counter': 12509, 'group_order': 256, 'label': '8J', 'order': 8, 'powers': [9], 'representative': 37, '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: 372902
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1a', '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: 372913
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1b', '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: 372924
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1c', '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: 372927
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1d', '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: 372928
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1e', '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: 372929
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1f', '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: 372930
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1g', '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: 372931
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1h', '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: 372932
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 372903
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 372904
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 372905
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 372906
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 372907
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 372908
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 372909
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 372910
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372911
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372912
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 2, 2, -2, -2, -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, 0], 'schur_index': 1}
  • id: 372914
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 2, 2, -2, -2, -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, 0], 'schur_index': 1}
  • id: 372915
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, -2, -2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372916
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, -2, -2, 2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372917
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 2, 2, -2, -2, -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, 0], 'schur_index': 1}
  • id: 372918
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 2, 2, -2, -2, -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, 0], 'schur_index': 1}
  • id: 372919
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, 0, -4, -4, -4, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372920
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.2j', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 0, -4, -4, -4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 372921
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.4a', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -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], 'schur_index': 1}
  • id: 372922
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.4b', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -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], 'schur_index': 1}
  • id: 372923
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.4c', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 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], 'schur_index': 1}
  • id: 372925
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.4d', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 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], 'schur_index': 1}
  • id: 372926
    {'cdim': 8, 'counter': 31, 'faithful': False, 'group': '256.12509', 'group_order': 256, 'image': None, 'label': '256.12509.8a', 'multiplicity': 1, 'nt': [32, 1869], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 541913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.12509.1a', '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: 541924
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.b1', 'kernel_order': 128, 'label': '256.12509.1b', '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: 541935
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.b1', 'kernel_order': 128, 'label': '256.12509.1c', '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: 541944
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 128, 'label': '256.12509.1d', '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: 541945
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 128, 'label': '256.12509.1e', '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: 541946
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.b1', 'kernel_order': 128, 'label': '256.12509.1f', '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: 541947
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.b1', 'kernel_order': 128, 'label': '256.12509.1g', '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: 541948
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 128, 'label': '256.12509.1h', '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: 541949
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 128, 'label': '256.12509.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 541914
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.12509.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 541915
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.12509.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 541916
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.12509.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 541917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.12509.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 541918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.12509.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 541919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.12509.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 541920
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.12509.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 541921
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.n1.b1', 'kernel_order': 32, 'label': '256.12509.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541922
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.n1.a1', 'kernel_order': 32, 'label': '256.12509.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541923
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.o1.a1', 'kernel_order': 32, 'label': '256.12509.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[-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]], [[0, 0]]]}
  • id: 541925
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.p1.a1', 'kernel_order': 32, 'label': '256.12509.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[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]], [[0, 0]]]}
  • id: 541926
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 32, 'label': '256.12509.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541927
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 32, 'label': '256.12509.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541928
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 32, 'label': '256.12509.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[-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]], [[0, 0]]]}
  • id: 541929
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.b1', 'kernel_order': 32, 'label': '256.12509.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[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]], [[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]], [[0, 0]]]}
  • id: 541930
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.k1.a1', 'kernel_order': 16, 'label': '256.12509.2i1', 'nt': [8, 11], 'q_character': None, 'values': [[[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]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 541931
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.k1.a1', 'kernel_order': 16, 'label': '256.12509.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[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]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 541932
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 16, 'label': '256.12509.2j1', 'nt': [8, 11], 'q_character': None, 'values': [[[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]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 541933
    {'center': '4.f1.a1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 16, 'label': '256.12509.2j2', 'nt': [8, 2], 'q_character': None, 'values': [[[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]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]]]}
  • id: 541934
    {'center': '32.c1.a1', 'center_index': 32, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 4, 'label': '256.12509.4a1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-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]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[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: 541936
    {'center': '32.c1.a1', 'center_index': 32, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 4, 'label': '256.12509.4a2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-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]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[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: 541937
    {'center': '32.c1.a1', 'center_index': 32, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.b1', 'kernel_order': 4, 'label': '256.12509.4b1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-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]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[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: 541938
    {'center': '32.c1.a1', 'center_index': 32, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.b1', 'kernel_order': 4, 'label': '256.12509.4b2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-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]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[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: 541939
    {'center': '32.b1.a1', 'center_index': 32, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 4, 'label': '256.12509.4c1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541940
    {'center': '32.b1.a1', 'center_index': 32, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 4, 'label': '256.12509.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541941
    {'center': '32.b1.a1', 'center_index': 32, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.b1', 'kernel_order': 4, 'label': '256.12509.4d1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541942
    {'center': '32.b1.a1', 'center_index': 32, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.b1', 'kernel_order': 4, 'label': '256.12509.4d2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 541943
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '256.12509', 'group_counter': 12509, 'group_order': 256, 'image': None, 'image_isoclass': '128.1801', 'image_order': 128, 'indicator': -1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.12509.8a', 'nt': [32, 1869], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 24109088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.12509.1.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': '256.12509', 'subgroup_hash': 12509, 'subgroup_order': 256, 'subgroup_tex': 'C_4^2.C_2^4', 'supersolvable': True, 'sylow': 2}
  • id: 24109199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.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': '128.1948', 'subgroup_hash': 1948, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1938', 'subgroup_hash': 1938, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.285', 'subgroup_hash': 285, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.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': '128.1961', 'subgroup_hash': 1961, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.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': '128.1717', 'subgroup_hash': 1717, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.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': '128.288', 'subgroup_hash': 288, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.304', 'subgroup_hash': 304, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.398', 'subgroup_hash': 398, 'subgroup_order': 128, 'subgroup_tex': 'C_8:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.h1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.398', 'subgroup_hash': 398, 'subgroup_order': 128, 'subgroup_tex': 'C_8:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.418', 'subgroup_hash': 418, 'subgroup_order': 128, 'subgroup_tex': 'C_8:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.i1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.418', 'subgroup_hash': 418, 'subgroup_order': 128, 'subgroup_tex': 'C_8:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.432', 'subgroup_hash': 432, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.j1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.432', 'subgroup_hash': 432, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.412', 'subgroup_hash': 412, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.2.k1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.412', 'subgroup_hash': 412, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.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': '64.213', 'subgroup_hash': 213, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.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': '64.214', 'subgroup_hash': 214, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.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': '64.212', 'subgroup_hash': 212, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.112', 'subgroup_hash': 112, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.112', 'subgroup_hash': 112, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.113', 'subgroup_hash': 113, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.113', 'subgroup_hash': 113, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.12', 'subgroup_hash': 12, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.156', 'subgroup_hash': 156, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.156', 'subgroup_hash': 156, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.156', 'subgroup_hash': 156, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.156', 'subgroup_hash': 156, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.143', 'subgroup_hash': 143, 'subgroup_order': 64, 'subgroup_tex': 'C_4:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.143', 'subgroup_hash': 143, 'subgroup_order': 64, 'subgroup_tex': 'C_4:Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.126', 'subgroup_hash': 126, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 64, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.126', 'subgroup_hash': 126, 'subgroup_order': 64, 'subgroup_tex': 'C_8\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.168', 'subgroup_hash': 168, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.168', 'subgroup_hash': 168, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.15', 'subgroup_hash': 15, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.15', 'subgroup_hash': 15, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.16', 'subgroup_hash': 16, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.16', 'subgroup_hash': 16, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.164', 'subgroup_hash': 164, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.164', 'subgroup_hash': 164, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.142', 'subgroup_hash': 142, 'subgroup_order': 64, 'subgroup_tex': 'C_4:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.178', 'subgroup_hash': 178, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.170', 'subgroup_hash': 170, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.127', 'subgroup_hash': 127, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.168', 'subgroup_hash': 168, 'subgroup_order': 64, 'subgroup_tex': 'C_4.Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.179', 'subgroup_hash': 179, 'subgroup_order': 64, 'subgroup_tex': 'C_8:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 24109351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['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: 24109358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', '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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109372
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109374
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bl2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bl2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bm2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bm2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109121
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.8.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109140
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109141
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.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': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C4'], '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: 24109143
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109145
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109146
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.b1', '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: 24109147
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.b1', '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: 24109149
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', '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: 24109156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109159
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 24109180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 24109201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 24109203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.16.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 24109212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 210, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['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: 24109214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 24109215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 213, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 214, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 215, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109218
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 216, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109219
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 24109220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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: 24109221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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: 24109224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 24109225
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109226
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.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: 24109231
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.r1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109242
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 238, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109245
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109246
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109247
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109248
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.y1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.z1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109253
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109254
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109256
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bb1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 24109260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 24109262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bd2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd2.a1', 'outer_equivalence': False, 'perfect': False, '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: 24109263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.bd2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd2.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.32.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109267
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109268
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109269
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 262, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109270
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.32.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 24109271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.12509.64.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': '64.203', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 203, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2', 'L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109272
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 265, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.64.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': '64.258', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 258, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109273
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.258', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 258, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.64.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': '64.258', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 258, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109275
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 268, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.64.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.258', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 258, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109276
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.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: 24109278
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.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: 24109279
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.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: 24109280
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 272, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.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: 24109281
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109282
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109283
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109284
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109285
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109286
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109287
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.12509.64.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 24109291
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109292
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109293
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 24109294
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.64.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 24109295
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 286, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.128.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': '128.1801', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1801, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109296
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 287, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.1775', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1775, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['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: 24109297
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 288, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.12509.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.1789', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1789, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2\\times C_8):D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109298
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.128.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: 24109300
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.12509.128.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 24109301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.12509', 'ambient_counter': 12509, 'ambient_order': 256, 'ambient_tex': 'C_4^2.C_2^4', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 291, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.12509.256.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': '256.12509', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12509, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 24109088
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.h1.b1', '2.i1.a1', '2.i1.b1', '2.j1.a1', '2.j1.b1', '2.k1.a1', '2.k1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4853, 5992, 5244, 4510, 4872, 5974, 5260, 4520], 'generators': [1, 2, 4, 32], 'label': '256.12509.1.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', '2.h1.b1', '2.h1.a1', '2.i1.b1', '2.i1.a1', '2.j1.b1', '2.j1.a1', '2.k1.b1', '2.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': None, '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': None}
  • id: 24109089
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.b1', '4.i1.a1', '4.k1.b1', '4.l1.b1', '4.o1.b1', '4.r1.b1', '4.v1.b1'], 'core': '2.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5047, 6786, 5381, 6645, 5066, 6765, 5397, 6659], 'generators': [5, 6, 32], 'label': '256.12509.2.h1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.b1', '4.i1.a1', '4.k1.b1', '4.l1.b1', '4.o1.b1', '4.r1.b1', '4.v1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109090
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.c1.a1', '16.m1.a1', '16.m1.b1', '16.be1.a1', '16.be1.b1', '16.bn1.a1', '16.bo1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3126, -1, 5609, -1, 3138, -1, 5625, -1], 'generators': [1, 2, 200], 'label': '256.12509.8.z1.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.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109091
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.c1.a1', '16.n1.a1', '16.bf1.a1', '16.bg1.a1', '16.bp1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5984, -1, 4016, -1, 6007, -1, 4028, -1], 'generators': [1, 6, 200], 'label': '256.12509.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109092
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bb1.a1', '4.bb1.b1'], 'contains': ['16.e1.a1', '16.p1.a1', '16.q1.a1', '16.r1.a1', '16.x1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6351, -1, 2109, -1, 6376, -1, 2115, -1], 'generators': [137, 38, 64], 'label': '256.12509.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109093
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.f1.a1', '16.r1.a1', '16.v1.a1', '16.br1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8317, -1, 439, -1, 8349, -1, 440, -1], 'generators': [6, 32, 16], 'label': '256.12509.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109094
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.b1', '4.bb1.b1'], 'contains': ['16.f1.b1', '16.r1.a1', '16.v1.a1', '16.br1.b1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8317, -1, 672, -1, 8349, -1, 674, -1], 'generators': [6, 168, 16], 'label': '256.12509.8.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109095
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.a1', '4.bb1.b1'], 'contains': ['16.g1.a1', '16.r1.a1', '16.w1.a1', '16.bs1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7986, -1, 906, -1, 8017, -1, 909, -1], 'generators': [33, 38, 16], 'label': '256.12509.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109096
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.x1.b1', '4.bb1.a1'], 'contains': ['16.g1.b1', '16.r1.a1', '16.w1.a1', '16.bs1.a1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7986, -1, 107, -1, 8017, -1, 108, -1], 'generators': [169, 38, 16], 'label': '256.12509.8.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109097
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bc1.a1', '4.bd1.a1'], 'contains': ['16.h1.a1', '16.o1.a1', '16.q1.a1', '16.s1.a1', '16.bb1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2972, -1, 7060, -1, 2983, -1, 7081, -1], 'generators': [65, 38, 136], 'label': '256.12509.8.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109098
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.i1.a1', '16.s1.a1', '16.bd1.a1', '16.bu1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [399, -1, 9689, -1, 400, -1, 9719, -1], 'generators': [2, 36, 128], 'label': '256.12509.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109099
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.y1.b1', '4.bc1.a1'], 'contains': ['16.i1.b1', '16.s1.a1', '16.bd1.b1', '16.bu1.a1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [399, -1, 9456, -1, 400, -1, 9484, -1], 'generators': [101, 38, 128], 'label': '256.12509.8.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109100
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.k1.b1', '4.m1.a1', '4.p1.a1', '4.t1.b1', '4.w1.b1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4853, 6389, 5522, 7287, 4872, 6370, 5538, 7303], 'generators': [33, 2, 36], 'label': '256.12509.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.j1.a1', '4.k1.b1', '4.m1.a1', '4.p1.a1', '4.t1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109101
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.y1.b1', '4.bd1.a1'], 'contains': ['16.j1.a1', '16.s1.a1', '16.bd1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [772, -1, 8810, -1, 775, -1, 8836, -1], 'generators': [66, 36], 'label': '256.12509.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109102
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '4.y1.a1', '4.bd1.a1'], 'contains': ['16.j1.b1', '16.s1.a1', '16.bd1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [772, -1, 8518, -1, 775, -1, 8543, -1], 'generators': [37, 38], 'label': '256.12509.8.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109103
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.k1.a1', '16.o1.a1', '16.p1.a1', '16.t1.a1', '16.bh1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4700, -1, 5233, -1, 4718, -1, 5249, -1], 'generators': [65, 38, 200], 'label': '256.12509.8.bh1.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.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109104
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.be1.a1', '4.be1.b1'], 'contains': ['16.e1.a1', '16.u1.a1', '16.u1.b1', '16.bl1.a1', '16.bl1.b1', '16.bn1.a1', '16.bo1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3797, -1, 5379, -1, 3811, -1, 5394, -1], 'generators': [137, 2, 64], 'label': '256.12509.8.bi1.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.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109105
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bb1.a1', '4.bb1.b1'], 'contains': ['16.e1.a1', '16.v1.a1', '16.w1.a1', '16.bm1.a1', '16.bp1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7238, -1, 1868, -1, 7266, -1, 1874, -1], 'generators': [137, 6, 64], 'label': '256.12509.8.bj1.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.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109106
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.be1.a1', '4.be1.b1'], 'contains': ['16.e1.a1', '16.y1.a1', '16.y1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8925, -1, 3591, -1, 8960, -1, 3603, -1], 'generators': [137, 34], 'label': '256.12509.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109107
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.z1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.u1.a1', '16.y1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9565, -1, 3141, -1, 9602, -1, 3150, -1], 'generators': [2, 32], 'label': '256.12509.8.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109108
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '4.z1.b1', '4.be1.b1'], 'contains': ['16.f1.b1', '16.u1.b1', '16.y1.b1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9565, -1, 2998, -1, 9602, -1, 3006, -1], 'generators': [3, 168], 'label': '256.12509.8.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109109
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.z1.b1', '4.be1.b1'], 'contains': ['16.f1.b1', '16.u1.a1', '16.y1.a1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9736, -1, 3735, -1, 9774, -1, 3746, -1], 'generators': [2, 168], 'label': '256.12509.8.bl2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bl2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109110
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bl2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '4.z1.a1', '4.be1.a1'], 'contains': ['16.f1.a1', '16.u1.b1', '16.y1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9736, -1, 2877, -1, 9774, -1, 2885, -1], 'generators': [3, 32], 'label': '256.12509.8.bl2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bl2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl2.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109111
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.b1', '4.j1.a1', '4.k1.a1', '4.m1.b1', '4.p1.b1', '4.t1.a1', '4.w1.a1'], 'core': '2.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4853, 6389, 4830, 5252, 4872, 6370, 4845, 5226], 'generators': [33, 34, 4], 'label': '256.12509.2.i1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.b1', '4.j1.a1', '4.k1.a1', '4.m1.b1', '4.p1.b1', '4.t1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109112
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.z1.b1', '4.be1.a1'], 'contains': ['16.g1.b1', '16.u1.a1', '16.y1.b1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9395, -1, 2327, -1, 9431, -1, 2335, -1], 'generators': [169, 2], 'label': '256.12509.8.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109113
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '4.z1.a1', '4.be1.b1'], 'contains': ['16.g1.a1', '16.u1.b1', '16.y1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9395, -1, 3449, -1, 9431, -1, 3460, -1], 'generators': [33, 34], 'label': '256.12509.8.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109114
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.z1.a1', '4.be1.b1'], 'contains': ['16.g1.a1', '16.u1.a1', '16.y1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 3307, -1, 9228, -1, 3317, -1], 'generators': [33, 2], 'label': '256.12509.8.bm2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bm2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109115
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bm2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '4.z1.b1', '4.be1.a1'], 'contains': ['16.g1.b1', '16.u1.b1', '16.y1.a1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 2734, -1, 9228, -1, 2742, -1], 'generators': [169, 34], 'label': '256.12509.8.bm2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bm2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm2.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109116
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.a1', '4.bb1.b1'], 'contains': ['16.g1.a1', '16.v1.a1', '16.x1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7751, -1, 1336, -1, 7781, -1, 1340, -1], 'generators': [33, 6], 'label': '256.12509.8.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109117
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.b1', '4.bb1.a1'], 'contains': ['16.g1.b1', '16.v1.a1', '16.x1.a1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7751, -1, 273, -1, 7781, -1, 274, -1], 'generators': [169, 6], 'label': '256.12509.8.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109118
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.x1.a1', '4.bb1.a1'], 'contains': ['16.f1.a1', '16.w1.a1', '16.x1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7613, -1, 1239, -1, 7642, -1, 1242, -1], 'generators': [7, 32], 'label': '256.12509.8.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109119
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.x1.b1', '4.bb1.b1'], 'contains': ['16.f1.b1', '16.w1.a1', '16.x1.a1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7613, -1, 1433, -1, 7642, -1, 1437, -1], 'generators': [7, 168], 'label': '256.12509.8.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109120
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bf1.a1', '4.bg1.a1'], 'contains': ['16.h1.a1', '16.z1.a1', '16.ba1.a1', '16.bk1.a1', '16.bp1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4359, -1, 6493, -1, 4375, -1, 6513, -1], 'generators': [65, 6, 136], 'label': '256.12509.8.bp1.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.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109121
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bf1.a1', '4.bg1.a1'], 'contains': ['16.h1.a1', '16.bc1.a1', '16.bc1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1997, -1, 7614, -1, 2005, -1, 7638, -1], 'generators': [65, 4], 'label': '256.12509.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109122
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1', '128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.n1.a1', '4.p1.a1', '4.q1.a1', '4.r1.b1', '4.u1.a1', '4.w1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4648, 5556, 4541, 3954, 4666, 5539, 4554, 3962], 'generators': [33, 2, 4], 'label': '256.12509.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.n1.a1', '4.p1.a1', '4.q1.a1', '4.r1.b1', '4.u1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109123
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bc1.a1', '4.bd1.a1'], 'contains': ['16.h1.a1', '16.bd1.a1', '16.bd1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1145, -1, 9125, -1, 1149, -1, 9152, -1], 'generators': [65, 36], 'label': '256.12509.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109124
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.ba1.a1', '4.bf1.a1'], 'contains': ['16.i1.a1', '16.z1.a1', '16.bc1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1655, -1, 8031, -1, 1662, -1, 8056, -1], 'generators': [2, 4], 'label': '256.12509.8.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109125
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '4.ba1.b1', '4.bf1.a1'], 'contains': ['16.i1.b1', '16.z1.a1', '16.bc1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1655, -1, 8421, -1, 1662, -1, 8446, -1], 'generators': [69, 6], 'label': '256.12509.8.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109126
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.ba1.a1', '4.bf1.a1'], 'contains': ['16.i1.a1', '16.ba1.a1', '16.bc1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1347, -1, 8129, -1, 1352, -1, 8153, -1], 'generators': [5, 2], 'label': '256.12509.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109127
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '4.ba1.b1', '4.bf1.a1'], 'contains': ['16.i1.b1', '16.ba1.a1', '16.bc1.a1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1347, -1, 8323, -1, 1352, -1, 8348, -1], 'generators': [67, 4], 'label': '256.12509.8.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109128
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.y1.a1', '4.bc1.a1'], 'contains': ['16.i1.a1', '16.bb1.a1', '16.bd1.b1', '16.bv1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [110, -1, 8944, -1, 110, -1, 8971, -1], 'generators': [37, 2, 128], 'label': '256.12509.8.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109129
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '4.y1.b1', '4.bc1.a1'], 'contains': ['16.i1.b1', '16.bb1.a1', '16.bd1.a1', '16.bv1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [110, -1, 9893, -1, 110, -1, 9923, -1], 'generators': [67, 36, 128], 'label': '256.12509.8.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109130
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.ba1.b1', '4.bg1.a1'], 'contains': ['16.j1.a1', '16.z1.a1', '16.bc1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2306, -1, 7397, -1, 2315, -1, 7419, -1], 'generators': [66, 4], 'label': '256.12509.8.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109131
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '4.ba1.a1', '4.bg1.a1'], 'contains': ['16.j1.b1', '16.z1.a1', '16.bc1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2306, -1, 6963, -1, 2315, -1, 6984, -1], 'generators': [5, 6], 'label': '256.12509.8.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109132
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.ba1.b1', '4.bg1.a1'], 'contains': ['16.j1.a1', '16.ba1.a1', '16.bc1.b1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2168, -1, 7494, -1, 2176, -1, 7517, -1], 'generators': [5, 66], 'label': '256.12509.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109133
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1', '128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.b1', '4.n1.b1', '4.p1.b1', '4.q1.a1', '4.r1.a1', '4.u1.b1', '4.w1.b1'], 'core': '2.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4648, 5556, 5671, 3082, 4666, 5539, 5689, 3108], 'generators': [33, 34, 36], 'label': '256.12509.2.j1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.b1', '4.n1.b1', '4.p1.b1', '4.q1.a1', '4.r1.a1', '4.u1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109134
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '4.ba1.a1', '4.bg1.a1'], 'contains': ['16.j1.b1', '16.ba1.a1', '16.bc1.a1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2168, -1, 6866, -1, 2176, -1, 6886, -1], 'generators': [3, 4], 'label': '256.12509.8.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109135
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.y1.b1', '4.bd1.a1'], 'contains': ['16.j1.a1', '16.bb1.a1', '16.bd1.b1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [634, -1, 8712, -1, 636, -1, 8738, -1], 'generators': [37, 66], 'label': '256.12509.8.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109136
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '4.y1.a1', '4.bd1.a1'], 'contains': ['16.j1.b1', '16.bb1.a1', '16.bd1.a1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [634, -1, 8615, -1, 636, -1, 8641, -1], 'generators': [3, 36], 'label': '256.12509.8.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109137
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.k1.a1', '16.be1.a1', '16.be1.b1', '16.bi1.a1', '16.bj1.a1', '16.bl1.a1', '16.bl1.b1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3970, -1, 5717, -1, 3984, -1, 5735, -1], 'generators': [65, 2, 200], 'label': '256.12509.8.by1.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.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109138
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.k1.a1', '16.bf1.a1', '16.bg1.a1', '16.bk1.a1', '16.bm1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6180, -1, 4153, -1, 6203, -1, 4165, -1], 'generators': [65, 6, 200], 'label': '256.12509.8.bz1.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.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109139
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.q1.a1', '8.t1.a1', '8.u1.a1', '8.v1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.e1.a1', '32.q1.a1', '32.q1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7335, 4060, 2782, 6017, 7363, 4047, 2790, 6023], 'generators': [1, 64, 16], 'label': '256.12509.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109140
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.r1.a1', '8.w1.a1', '8.x1.a1', '8.y1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.f1.a1', '32.ba1.a1', '32.ba1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2442, 5563, 7102, 4019, 2452, 5545, 7122, 4030], 'generators': [1, 136, 128], 'label': '256.12509.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'normal_contains': ['32.a1.a1', '32.c1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109141
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.s1.a1', '8.z1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.g1.a1', '32.n1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5064, 5074, 4524, 4578, 5084, 5049, 4537, 4588], 'generators': [1, 200, 128], 'label': '256.12509.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '32.d1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109158
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.t1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.i1.b1', '32.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3252, -1, 5685, -1, 3264, -1, 5701, -1], 'generators': [1, 66], 'label': '256.12509.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109142
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1'], 'contains': ['32.b1.a1', '32.c1.a1', '32.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5574, 4428, 4883, 4865, 5595, 4415, 4896, 4876], 'generators': [136, 64], 'label': '256.12509.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.b1', '8.e1.a1', '8.f1.a1', '8.h1.a1', '8.g1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.k1.b1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1'], 'normal_contains': ['32.c1.a1', '32.b1.a1', '32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': None, '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': None}
  • id: 24109143
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.n1.a1', '8.n1.b1', '8.bb1.a1', '8.bi1.a1', '8.bj1.a1', '8.bk1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '32.g1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6385, 3691, 3834, 5438, 6410, 3680, 3842, 5211], 'generators': [137, 64], 'label': '256.12509.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.a1', '8.n1.b1', '8.n1.a1'], 'normal_contains': ['32.b1.a1', '32.g1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': None, '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': None}
  • id: 24109144
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1', '128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.t1.a1', '4.u1.b1', '4.v1.b1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4435, 5992, 5822, 3419, 4452, 5974, 5839, 3426], 'generators': [5, 2, 32], 'label': '256.12509.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.m1.a1', '4.o1.a1', '4.s1.a1', '4.u1.b1', '4.t1.a1', '4.v1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109145
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.o1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.i1.a1', '8.n1.a1', '8.bc1.a1', '8.bl1.a1', '8.bl2.b1', '8.bo1.a1'], 'contains': ['32.b1.a1', '32.v1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8667, 3073, 2339, 7065, 8701, 3064, 2346, 7221], 'generators': [32, 16], 'label': '256.12509.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.b1.a1', '8.i1.a1', '8.n1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109146
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.o1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.i1.a1', '8.n1.b1', '8.bc1.b1', '8.bl1.b1', '8.bl2.a1', '8.bo1.b1'], 'contains': ['32.b1.a1', '32.v1.b1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8667, 3073, 2626, 5706, 8701, 3064, 2634, 5711], 'generators': [168, 16], 'label': '256.12509.16.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': ['8.b1.b1', '8.i1.a1', '8.n1.b1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109147
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.j1.a1', '8.n1.b1', '8.bd1.a1', '8.bm1.b1', '8.bm2.a1', '8.bn1.a1'], 'contains': ['32.b1.a1', '32.w1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8317, 2560, 2483, 6344, 8349, 2549, 2490, 6351], 'generators': [33, 16], 'label': '256.12509.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.b1.a1', '8.j1.a1', '8.n1.b1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109148
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '8.j1.a1', '8.n1.a1', '8.bd1.b1', '8.bm1.a1', '8.bm2.b1', '8.bn1.b1'], 'contains': ['32.b1.a1', '32.w1.a1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8317, 2560, 2195, 6681, 8349, 2549, 2202, 6835], 'generators': [169, 16], 'label': '256.12509.16.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.b1', 'normal_contained_in': ['8.b1.b1', '8.j1.a1', '8.n1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109149
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.a1', '8.p1.a1', '8.be1.a1', '8.bp1.a1', '8.bq1.a1', '8.br1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.g1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2622, 5932, 6878, 3748, 2632, 5913, 6898, 3742], 'generators': [65, 136], 'label': '256.12509.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.a1.a1', '8.p1.a1', '8.o1.a1'], 'normal_contains': ['32.c1.a1', '32.g1.a1', '32.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': None, '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': None}
  • id: 24109150
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.o1.a1', '8.bf1.a1', '8.bs1.a1', '8.bt1.a1', '8.bu1.a1'], 'contains': ['32.c1.a1', '32.i1.a1', '32.bd1.b1', '32.bd2.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1331, 7268, 8126, 3450, 1336, 7246, 8150, 3477], 'generators': [2, 136, 128], 'label': '256.12509.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.o1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': None, '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': None}
  • id: 24109151
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.e1.b1', '8.o1.a1', '8.bf1.b1', '8.bs1.b1', '8.bt1.b1', '8.bu1.b1'], 'contains': ['32.c1.a1', '32.i1.b1', '32.bd1.a1', '32.bd2.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1331, 7268, 8271, 3161, 1336, 7246, 8295, 3186], 'generators': [67, 136, 128], 'label': '256.12509.16.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': ['8.c1.b1', '8.e1.b1', '8.o1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109152
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.e1.a1', '8.p1.a1', '8.bg1.a1', '8.bv1.a1', '8.bw1.a1', '8.bx1.a1'], 'contains': ['32.c1.a1', '32.j1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1845, 7779, 7234, 2638, 1852, 7754, 7255, 2627], 'generators': [66, 136], 'label': '256.12509.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.c1.b1', '8.e1.a1', '8.p1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': None, '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': None}
  • id: 24109153
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.b1', '8.p1.a1', '8.bg1.b1', '8.bv1.b1', '8.bw1.b1', '8.bx1.b1'], 'contains': ['32.c1.a1', '32.j1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1845, 7779, 6970, 2917, 1852, 7754, 6990, 2943], 'generators': [3, 136], 'label': '256.12509.16.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': ['8.c1.a1', '8.e1.b1', '8.p1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109154
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bh1.a1', '8.by1.a1', '8.bz1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5244, 4695, 4796, 4307, 5264, 4672, 4810, 4316], 'generators': [65, 200], 'label': '256.12509.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': None, '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': None}
  • id: 24109155
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1', '128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.m1.b1', '4.n1.b1', '4.o1.b1', '4.s1.a1', '4.t1.b1', '4.u1.a1', '4.v1.a1'], 'core': '2.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4435, 5992, 4967, 4510, 4452, 5974, 4981, 4520], 'generators': [3, 4, 32], 'label': '256.12509.2.k1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.b1', '4.m1.b1', '4.o1.b1', '4.s1.a1', '4.u1.a1', '4.t1.b1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109156
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.r1.a1', '8.s1.a1'], 'contains': ['32.a1.a1', '32.h1.a1', '32.m1.a1', '32.z1.a1', '32.z1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4089, -1, 5915, -1, 4105, -1, 5932, -1], 'generators': [1, 38, 128], 'label': '256.12509.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.l1.a1', 'projective_image': None, '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': None}
  • id: 24109157
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.t1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '32.j1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3252, -1, 5420, -1, 3264, -1, 5436, -1], 'generators': [1, 2], 'label': '256.12509.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.m1.a1', 'projective_image': None, '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': None}
  • id: 24109159
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.w1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.k1.a1', '32.l1.a1', '32.r1.a1', '32.r1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6689, -1, 3708, -1, 6714, -1, 3715, -1], 'generators': [1, 6, 16], 'label': '256.12509.16.n1.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.n1.a1', 'projective_image': None, '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': None}
  • id: 24109160
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.be1.a1', '8.bh1.a1'], 'contains': ['32.e1.a1', '32.h1.a1', '32.m1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4723, -1, 4986, -1, 4741, -1, 5000, -1], 'generators': [65, 38], 'label': '256.12509.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.o1.a1', 'projective_image': None, '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': None}
  • id: 24109161
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.bb1.a1', '8.bh1.a1'], 'contains': ['32.f1.a1', '32.h1.a1', '32.m1.a1', '32.bb1.a1', '32.bb1.a2'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3868, -1, 6168, -1, 3884, -1, 6186, -1], 'generators': [137, 38, 128], 'label': '256.12509.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.p1.a1', 'projective_image': None, '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': None}
  • id: 24109162
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.bb1.a1', '8.be1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.m1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4554, -1, 5106, -1, 4571, -1, 5120, -1], 'generators': [201, 38], 'label': '256.12509.16.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.q1.a1', 'projective_image': None, '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': None}
  • id: 24109163
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.q1.a1', '8.bb1.a1', '8.bc1.a1', '8.bc1.b1', '8.bd1.a1', '8.bd1.b1'], 'contains': ['32.b1.a1', '32.h1.a1', '32.s1.a1', '32.s1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7114, -1, 1809, -1, 7141, -1, 1814, -1], 'generators': [38, 64, 16], 'label': '256.12509.16.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.r1.a1', 'projective_image': None, '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': None}
  • id: 24109164
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.r1.a1', '8.be1.a1', '8.bf1.a1', '8.bf1.b1', '8.bg1.a1', '8.bg1.b1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.bc1.a1', '32.bc1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2222, -1, 7837, -1, 2231, -1, 7859, -1], 'generators': [38, 136, 128], 'label': '256.12509.16.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.s1.a1', 'projective_image': None, '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': None}
  • id: 24109165
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.s1.a1', '8.bh1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.o1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5409, -1, 4680, -1, 5430, -1, 4693, -1], 'generators': [38, 200, 128], 'label': '256.12509.16.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.t1.a1', 'projective_image': None, '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': None}
  • id: 24109166
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.h1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1', '8.bb1.a1', '8.be1.a1', '8.bh1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4511, 3475, 5412, 1542, 4529, 3465, 5428, 1545], 'generators': [1, 38, 136, 64], 'label': '256.12509.4.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.d1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': None, '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': None}
  • id: 24109167
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.t1.a1', '8.bi1.a1', '8.bl1.a1', '8.bl2.a1', '8.bm1.a1', '8.bm2.a1'], 'contains': ['32.b1.a1', '32.i1.a1', '32.j1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6509, -1, 4298, -1, 6534, -1, 4308, -1], 'generators': [2, 64], 'label': '256.12509.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.u1.a1', 'projective_image': None, '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': None}
  • id: 24109168
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.t1.a1', '8.bi1.a1', '8.bl1.b1', '8.bl2.b1', '8.bm1.b1', '8.bm2.b1'], 'contains': ['32.b1.a1', '32.i1.b1', '32.j1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6509, -1, 4018, -1, 6534, -1, 4027, -1], 'generators': [3, 64], 'label': '256.12509.16.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109169
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.u1.a1', '8.bc1.a1', '8.bc1.b1', '8.bj1.a1', '8.bn1.a1', '8.bn1.b1'], 'contains': ['32.b1.a1', '32.k1.a1', '32.t1.a1', '32.t1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7760, -1, 1664, -1, 7790, -1, 1669, -1], 'generators': [6, 64, 16], 'label': '256.12509.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.v1.a1', 'projective_image': None, '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': None}
  • id: 24109170
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.u1.a1', '8.bd1.a1', '8.bd1.b1', '8.bj1.a1', '8.bo1.a1', '8.bo1.b1'], 'contains': ['32.b1.a1', '32.l1.a1', '32.u1.a1', '32.u1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7555, -1, 1954, -1, 7584, -1, 1960, -1], 'generators': [7, 64, 16], 'label': '256.12509.16.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.w1.a1', 'projective_image': None, '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': None}
  • id: 24109171
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.q1.a1', '8.bb1.a1', '8.bn1.a1', '8.bn1.b1', '8.bo1.a1', '8.bo1.b1'], 'contains': ['32.b1.a1', '32.m1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6256, -1, 2075, -1, 6280, -1, 2081, -1], 'generators': [39, 64], 'label': '256.12509.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.x1.a1', 'projective_image': None, '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': None}
  • id: 24109172
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.v1.a1', '8.bk1.a1', '8.bl1.a1', '8.bl2.a1', '8.bm1.b1', '8.bm2.b1'], 'contains': ['32.b1.a1', '32.x1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 3141, -1, 9228, -1, 3150, -1], 'generators': [34, 16], 'label': '256.12509.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.y1.a1', 'projective_image': None, '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': None}
  • id: 24109173
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '8.v1.a1', '8.bk1.a1', '8.bl1.b1', '8.bl2.b1', '8.bm1.a1', '8.bm2.a1'], 'contains': ['32.b1.a1', '32.x1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9192, -1, 2937, -1, 9228, -1, 2946, -1], 'generators': [35, 16], 'label': '256.12509.16.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109174
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.w1.a1', '8.bp1.a1', '8.bs1.a1', '8.bs1.b1', '8.bv1.a1', '8.bv1.b1'], 'contains': ['32.c1.a1', '32.k1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3682, -1, 6689, -1, 3696, -1, 6708, -1], 'generators': [6, 136], 'label': '256.12509.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.z1.a1', 'projective_image': None, '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': None}
  • id: 24109175
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.w1.a1', '8.bp1.a1', '8.bt1.a1', '8.bt1.b1', '8.bw1.a1', '8.bw1.b1'], 'contains': ['32.c1.a1', '32.l1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3544, -1, 6786, -1, 3557, -1, 6806, -1], 'generators': [7, 136], 'label': '256.12509.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.ba1.a1', 'projective_image': None, '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': None}
  • id: 24109176
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.r1.a1', '8.be1.a1', '8.bu1.a1', '8.bu1.b1', '8.bx1.a1', '8.bx1.b1'], 'contains': ['32.c1.a1', '32.m1.a1', '32.be1.a1', '32.be1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2016, -1, 7982, -1, 2024, -1, 8005, -1], 'generators': [39, 136, 128], 'label': '256.12509.16.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bb1.a1', 'projective_image': None, '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': None}
  • id: 24109177
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.e1.a1', '8.e1.b1', '8.o1.a1', '8.p1.a1', '8.t1.a1', '8.z1.a1', '8.bi1.a1', '8.by1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3846, 9755, 6137, 190, 3861, 9724, 6155, 191], 'generators': [1, 2, 136, 64], 'label': '256.12509.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '8.e1.b1', '8.e1.a1', '8.p1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': None, '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': None}
  • id: 24109178
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.x1.a1', '8.bq1.a1', '8.bs1.a1', '8.bt1.b1', '8.bv1.a1', '8.bw1.b1'], 'contains': ['32.c1.a1', '32.bf1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1535, -1, 7548, -1, 1542, -1, 7571, -1], 'generators': [4, 128], 'label': '256.12509.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109179
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.b1', '8.x1.a1', '8.bq1.a1', '8.bs1.b1', '8.bt1.a1', '8.bv1.b1', '8.bw1.a1'], 'contains': ['32.c1.a1', '32.bf1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1535, -1, 7693, -1, 1542, -1, 7715, -1], 'generators': [5, 128], 'label': '256.12509.16.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109180
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.y1.a1', '8.bf1.a1', '8.bg1.a1', '8.br1.a1', '8.bu1.b1', '8.bx1.b1'], 'contains': ['32.c1.a1', '32.bg1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1126, -1, 8655, -1, 1130, -1, 8680, -1], 'generators': [36, 128], 'label': '256.12509.16.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109181
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bd1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '8.y1.a1', '8.bf1.b1', '8.bg1.b1', '8.br1.a1', '8.bu1.a1', '8.bx1.a1'], 'contains': ['32.c1.a1', '32.bg1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1126, -1, 8416, -1, 1130, -1, 8441, -1], 'generators': [37, 128], 'label': '256.12509.16.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109182
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.z1.a1', '8.by1.a1'], 'contains': ['32.d1.a1', '32.i1.a1', '32.j1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3406, -1, 6036, -1, 3419, -1, 6053, -1], 'generators': [2, 200], 'label': '256.12509.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109183
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.z1.a1', '8.by1.a1'], 'contains': ['32.d1.a1', '32.i1.b1', '32.j1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3406, -1, 5794, -1, 3419, -1, 5810, -1], 'generators': [3, 200], 'label': '256.12509.16.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109184
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.ba1.a1', '8.bz1.a1'], 'contains': ['32.d1.a1', '32.k1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5980, -1, 4109, -1, 6003, -1, 4119, -1], 'generators': [6, 200], 'label': '256.12509.16.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109185
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.ba1.a1', '8.bz1.a1'], 'contains': ['32.d1.a1', '32.l1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5704, -1, 4390, -1, 5726, -1, 4401, -1], 'generators': [7, 200], 'label': '256.12509.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109186
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.s1.a1', '8.bh1.a1'], 'contains': ['32.d1.a1', '32.m1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4877, -1, 5214, -1, 4896, -1, 5229, -1], 'generators': [39, 200], 'label': '256.12509.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109187
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.t1.a1', '8.by1.a1'], 'contains': ['32.e1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4262, -1, 6397, -1, 4278, -1, 6416, -1], 'generators': [65, 2], 'label': '256.12509.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109188
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.g1.a1', '8.u1.a1', '8.w1.a1', '8.ba1.a1', '8.bj1.a1', '8.bp1.a1', '8.bz1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5445, 2944, 4264, 2676, 5466, 2935, 4277, 2682], 'generators': [1, 6, 136, 64], 'label': '256.12509.4.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.a1.a1', '8.f1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': None, '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': None}
  • id: 24109189
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.t1.a1', '8.by1.a1'], 'contains': ['32.e1.a1', '32.j1.a1', '32.j1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4399, -1, 5312, -1, 4416, -1, 5327, -1], 'generators': [65, 66], 'label': '256.12509.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109190
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.bp1.a1', '8.bz1.a1'], 'contains': ['32.e1.a1', '32.k1.a1', '32.l1.a1', '32.y1.a1', '32.y1.a2'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6909, -1, 3552, -1, 6935, -1, 3559, -1], 'generators': [65, 6, 16], 'label': '256.12509.16.bk1.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.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109191
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.bi1.a1', '8.by1.a1'], 'contains': ['32.f1.a1', '32.i1.a1', '32.j1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3097, -1, 6300, -1, 3109, -1, 6318, -1], 'generators': [137, 2], 'label': '256.12509.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109192
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '8.bi1.a1', '8.by1.a1'], 'contains': ['32.f1.a1', '32.i1.b1', '32.j1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3097, -1, 6592, -1, 3109, -1, 6611, -1], 'generators': [137, 66], 'label': '256.12509.16.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109193
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '8.bj1.a1', '8.bz1.a1'], 'contains': ['32.f1.a1', '32.k1.a1', '32.l1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6118, -1, 4206, -1, 6141, -1, 4216, -1], 'generators': [137, 6], 'label': '256.12509.16.bm1.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.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109194
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.z1.a1', '8.bi1.a1'], 'contains': ['32.g1.a1', '32.i1.a1', '32.i1.b1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2753, -1, 6494, -1, 2763, -1, 6513, -1], 'generators': [201, 2], 'label': '256.12509.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109195
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.z1.a1', '8.bi1.a1'], 'contains': ['32.g1.a1', '32.j1.a1', '32.j1.b1', '32.p1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2925, -1, 5552, -1, 2936, -1, 5568, -1], 'generators': [201, 66, 128], 'label': '256.12509.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109196
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.bj1.a1', '8.bp1.a1'], 'contains': ['32.g1.a1', '32.k1.a1', '32.l1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5842, -1, 3926, -1, 5865, -1, 3934, -1], 'generators': [201, 6], 'label': '256.12509.16.bp1.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.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109197
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.q1.a1', '32.r1.a1', '32.r1.a2', '32.t1.a1', '32.u1.a1', '32.y1.a1', '32.y1.a2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7965, -1, 1166, -1, 7996, -1, 1170, -1], 'generators': [1, 6, 64], 'label': '256.12509.16.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109198
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1'], 'contains': ['32.q1.b1', '32.r1.a1', '32.r1.a2', '32.t1.b1', '32.u1.b1', '32.y1.a1', '32.y1.a2'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7965, -1, 1312, -1, 7996, -1, 1315, -1], 'generators': [1, 6, 80], 'label': '256.12509.16.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '16.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109199
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1', '4.h1.a1', '4.h1.b1', '4.n1.a1', '4.n1.b1', '4.y1.a1', '4.y1.b1', '4.bc1.a1', '4.bd1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2742, 7658, 7206, 2765, 2753, 7635, 7228, 2771], 'generators': [1, 2, 36, 64], 'label': '256.12509.2.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.g1.a1', '4.h1.b1', '4.h1.a1', '4.n1.b1', '4.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': None, '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': None}
  • id: 24109200
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.i1.a1', '8.j1.a1', '8.n1.a1', '8.n1.b1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6761, 245, 2129, 9810, 6787, 245, 2135, 9830], 'generators': [1, 32, 136], 'label': '256.12509.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1', '8.i1.a1', '8.j1.a1', '8.n1.b1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109201
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1'], 'contains': ['32.s1.a1', '32.t1.a1', '32.v1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8493, -1, 938, -1, 8525, -1, 941, -1], 'generators': [6, 32], 'label': '256.12509.16.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '16.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109202
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.b1'], 'contains': ['32.s1.b1', '32.t1.b1', '32.v1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8493, -1, 1436, -1, 8525, -1, 1440, -1], 'generators': [6, 168], 'label': '256.12509.16.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.b1', 'old_label': '16.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109203
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.b1'], 'contains': ['32.s1.a1', '32.u1.a1', '32.w1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8142, -1, 1042, -1, 8173, -1, 1045, -1], 'generators': [169, 38], 'label': '256.12509.16.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1.b1', 'old_label': '16.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109204
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1'], 'contains': ['32.s1.b1', '32.u1.b1', '32.w1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8142, -1, 1540, -1, 8173, -1, 1544, -1], 'generators': [33, 38], 'label': '256.12509.16.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bd1.a1', 'old_label': '16.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109205
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1'], 'contains': ['32.z1.a1', '32.z1.a2', '32.ba1.a1', '32.bb1.a1', '32.bb1.a2', '32.bc1.a1', '32.be1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1707, -1, 7331, -1, 1713, -1, 7352, -1], 'generators': [1, 38, 8], 'label': '256.12509.16.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '16.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109206
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1'], 'contains': ['32.z1.a1', '32.z1.a2', '32.ba1.b1', '32.bb1.a1', '32.bb1.a2', '32.bc1.b1', '32.be1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1707, -1, 7428, -1, 1713, -1, 7450, -1], 'generators': [1, 38, 136], 'label': '256.12509.16.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '16.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109207
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.b1'], 'contains': ['32.bc1.a1', '32.bd1.a1', '32.bg1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [950, -1, 8778, -1, 954, -1, 8804, -1], 'generators': [101, 38], 'label': '256.12509.16.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bf1.b1', 'old_label': '16.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109208
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1'], 'contains': ['32.bc1.b1', '32.bd1.b1', '32.bg1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [950, -1, 8881, -1, 954, -1, 8908, -1], 'generators': [2, 36], 'label': '256.12509.16.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bf1.a1', 'old_label': '16.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109209
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1'], 'contains': ['32.bd2.a1', '32.be1.a1', '32.bg1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [809, -1, 8536, -1, 812, -1, 8561, -1], 'generators': [37, 2], 'label': '256.12509.16.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bu1.a1', 'old_label': '16.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109210
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.b1'], 'contains': ['32.bd2.b1', '32.be1.b1', '32.bg1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [809, -1, 8981, -1, 812, -1, 9008, -1], 'generators': [67, 36], 'label': '256.12509.16.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bu1.b1', 'old_label': '16.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109211
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '8.k1.b1', '8.x1.a1', '8.bq1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3284, 4022, 6533, 3042, 3297, 4011, 6552, 3049], 'generators': [1, 4, 64], 'label': '256.12509.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.k1.a1', '8.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': None, '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': None}
  • id: 24109212
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.l1.a1', '16.m1.a1', '16.m1.b1', '16.n1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.i1.a1', '64.n1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4683, 5596, 5075, 5096, 4700, 5579, 5089, 5107], 'generators': [1, 16, 128], 'label': '256.12509.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.a1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109213
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.f1.b1', '16.g1.a1', '16.g1.b1', '16.r1.a1', '16.u1.a1', '16.u1.b1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1', '16.y1.b1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.b1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6927, 3590, 2581, 5572, 6953, 3578, 2589, 5372], 'generators': [64, 16], 'label': '256.12509.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.f1.b1', '16.f1.a1', '16.g1.b1', '16.g1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.a1', '64.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109214
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.h1.a1', '16.i1.a1', '16.i1.b1', '16.j1.a1', '16.j1.b1', '16.s1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1', '16.bc1.b1', '16.bd1.a1', '16.bd1.b1'], 'contains': ['64.a1.a1', '64.c1.a1', '64.c1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2332, 5932, 7551, 3714, 2340, 5913, 7573, 3723], 'generators': [136, 128], 'label': '256.12509.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.b1.a1', '16.d1.a1', '16.h1.a1', '16.j1.b1', '16.j1.a1', '16.i1.a1', '16.i1.b1'], 'normal_contains': ['64.a1.a1', '64.c1.b1', '64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109215
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.k1.a1', '16.t1.a1', '16.be1.a1', '16.be1.b1', '16.bf1.a1', '16.bg1.a1', '16.bh1.a1'], 'contains': ['64.a1.a1', '64.f1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5253, 4425, 4816, 4865, 5273, 4412, 4830, 4876], 'generators': [200, 128], 'label': '256.12509.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.c1.a1', '16.d1.a1', '16.k1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109216
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.k1.a1', '16.o1.a1', '16.bi1.a1', '16.bj1.a1', '16.bk1.a1'], 'contains': ['64.a1.a1', '64.k1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5050, 4843, 4960, 4290, 5069, 4828, 4974, 4299], 'generators': [65, 16], 'label': '256.12509.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.a1.a1', '16.h1.a1', '16.k1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109217
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.k1.a1', '16.p1.a1', '16.bl1.a1', '16.bl1.b1', '16.bm1.a1'], 'contains': ['64.a1.a1', '64.p1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4397, 4007, 5784, 4578, 4413, 3995, 5800, 4588], 'generators': [137, 128], 'label': '256.12509.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.b1.a1', '16.e1.a1', '16.k1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': None, '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': None}
  • id: 24109218
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.e1.a1', '16.h1.a1', '16.q1.a1', '16.bn1.a1', '16.bo1.a1', '16.bp1.a1'], 'contains': ['64.a1.a1', '64.g1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4193, 5261, 5190, 4003, 4208, 5245, 5205, 4011], 'generators': [201, 128], 'label': '256.12509.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.c1.a1', '16.h1.a1', '16.e1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': None, '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': None}
  • id: 24109219
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.o1.a1', '16.p1.a1', '16.q1.a1', '16.r1.a1', '16.s1.a1', '16.t1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.j1.a1', '64.o1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4560, -1, 5305, -1, 4577, -1, 5320, -1], 'generators': [38, 16, 128], 'label': '256.12509.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.h1.a1', 'projective_image': None, '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': None}
  • id: 24109220
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.m1.a1', '16.u1.a1', '16.be1.a1', '16.bi1.a1', '16.bl1.a1', '16.bn1.a1'], 'contains': ['64.a1.a1', '64.q1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3328, -1, 6277, -1, 3342, -1, 6295, -1], 'generators': [2, 128], 'label': '256.12509.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.i1.a1', 'projective_image': None, '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': None}
  • id: 24109221
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.m1.b1', '16.u1.b1', '16.be1.b1', '16.bi1.a1', '16.bl1.b1', '16.bn1.a1'], 'contains': ['64.a1.a1', '64.q1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3328, -1, 6421, -1, 3342, -1, 6439, -1], 'generators': [67, 128], 'label': '256.12509.32.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109222
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '8.l1.b1', '8.v1.a1', '8.bk1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8237, 7925, 3827, 6063, 8270, 7901, 3838, 6076], 'generators': [1, 34, 136], 'label': '256.12509.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.l1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': None, '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': None}
  • id: 24109223
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.m1.b1', '16.u1.a1', '16.be1.a1', '16.bj1.a1', '16.bl1.b1', '16.bo1.a1'], 'contains': ['64.a1.a1', '64.h1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3531, -1, 5928, -1, 3547, -1, 5944, -1], 'generators': [66, 128], 'label': '256.12509.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.j1.a1', 'projective_image': None, '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': None}
  • id: 24109224
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.m1.a1', '16.u1.b1', '16.be1.b1', '16.bj1.a1', '16.bl1.a1', '16.bo1.a1'], 'contains': ['64.a1.a1', '64.h1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3531, -1, 5420, -1, 3547, -1, 5436, -1], 'generators': [3, 128], 'label': '256.12509.32.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109225
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.v1.a1', '16.z1.a1', '16.bf1.a1', '16.bk1.a1', '16.bm1.a1', '16.bp1.a1'], 'contains': ['64.a1.a1', '64.l1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6219, -1, 3854, -1, 6244, -1, 3862, -1], 'generators': [6, 16], 'label': '256.12509.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.k1.a1', 'projective_image': None, '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': None}
  • id: 24109226
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.w1.a1', '16.ba1.a1', '16.bg1.a1', '16.bk1.a1', '16.bm1.a1', '16.bp1.a1'], 'contains': ['64.a1.a1', '64.m1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6016, -1, 3997, -1, 6039, -1, 4006, -1], 'generators': [7, 16], 'label': '256.12509.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.l1.a1', 'projective_image': None, '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': None}
  • id: 24109227
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.o1.a1', '16.p1.a1', '16.q1.a1', '16.x1.a1', '16.bb1.a1', '16.bh1.a1'], 'contains': ['64.a1.a1', '64.r1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3989, -1, 5640, -1, 4004, -1, 5656, -1], 'generators': [39, 128], 'label': '256.12509.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.m1.a1', 'projective_image': None, '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': None}
  • id: 24109228
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1'], 'contains': ['64.d1.a1', '64.f1.a1', '64.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4846, -1, 4596, -1, 4864, -1, 4609, -1], 'generators': [1, 200], 'label': '256.12509.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.n1.a1', 'projective_image': None, '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': None}
  • id: 24109229
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1'], 'contains': ['64.e1.a1', '64.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5409, -1, 4706, -1, 5430, -1, 4720, -1], 'generators': [182, 200], 'label': '256.12509.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bh1.a1', 'old_label': '32.o1.a1', 'projective_image': None, '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': None}
  • id: 24109230
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1'], 'contains': ['64.g1.a1', '64.h1.a1', '64.h1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3172, -1, 5530, -1, 3186, -1, 5546, -1], 'generators': [201, 66], 'label': '256.12509.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bi1.a1', 'old_label': '32.p1.a1', 'projective_image': None, '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': None}
  • id: 24109231
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bq1.a1'], 'contains': ['64.b1.a1', '64.i1.a1', '64.k1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7335, -1, 1581, -1, 7363, -1, 1586, -1], 'generators': [1, 64], 'label': '256.12509.32.q1.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.q1.a1', 'projective_image': None, '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': None}
  • id: 24109232
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bq1.b1'], 'contains': ['64.b1.b1', '64.i1.a1', '64.k1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7335, -1, 2164, -1, 7363, -1, 2170, -1], 'generators': [1, 80], 'label': '256.12509.32.q1.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': '32.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109233
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '8.m1.b1', '8.y1.a1', '8.br1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2742, 7578, 7269, 6677, 2753, 7555, 7291, 6691], 'generators': [1, 36, 64], 'label': '256.12509.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.m1.a1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': None, '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': None}
  • id: 24109234
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bq1.a1', '16.bq1.b1'], 'contains': ['64.i1.a1', '64.l1.a1', '64.m1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7131, -1, 1725, -1, 7158, -1, 1730, -1], 'generators': [1, 6], 'label': '256.12509.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.r1.a1', 'projective_image': None, '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': None}
  • id: 24109235
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bq1.a1', '16.bq1.b1'], 'contains': ['64.i1.a1', '64.l1.a1', '64.m1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7131, -1, 1868, -1, 7158, -1, 1874, -1], 'generators': [17, 6], 'label': '256.12509.32.r1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.r1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109236
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.br1.a1', '16.bs1.a1'], 'contains': ['64.b1.a1', '64.j1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7781, -1, 1090, -1, 7811, -1, 1094, -1], 'generators': [38, 64], 'label': '256.12509.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '32.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109237
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.br1.b1', '16.bs1.b1'], 'contains': ['64.b1.b1', '64.j1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7781, -1, 2274, -1, 7811, -1, 2281, -1], 'generators': [38, 80], 'label': '256.12509.32.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.b1', 'old_label': '32.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109238
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bq1.a1', '16.br1.a1'], 'contains': ['64.b1.a1', '64.l1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7888, -1, 938, -1, 7919, -1, 941, -1], 'generators': [6, 64], 'label': '256.12509.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '32.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109239
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.bq1.b1', '16.br1.b1'], 'contains': ['64.b1.b1', '64.l1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7888, -1, 1978, -1, 7919, -1, 1984, -1], 'generators': [6, 80], 'label': '256.12509.32.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '32.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109240
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.bq1.a1', '16.bs1.a1'], 'contains': ['64.b1.a1', '64.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7672, -1, 1243, -1, 7703, -1, 1246, -1], 'generators': [7, 64], 'label': '256.12509.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.b1', 'old_label': '32.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109241
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.bq1.b1', '16.bs1.b1'], 'contains': ['64.b1.b1', '64.m1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7672, -1, 2054, -1, 7703, -1, 2060, -1], 'generators': [7, 80], 'label': '256.12509.32.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '32.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109242
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.br1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8493, -1, 1015, -1, 8525, -1, 1018, -1], 'generators': [32], 'label': '256.12509.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109243
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '16.br1.b1'], 'contains': ['64.b1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8493, -1, 2426, -1, 8525, -1, 2433, -1], 'generators': [168], 'label': '256.12509.32.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '32.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109244
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.m1.a1', '8.bf1.a1', '8.bg1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3058, 9260, 7145, 4923, 3070, 9231, 7166, 4933], 'generators': [2, 36, 64], 'label': '256.12509.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': None, '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': None}
  • id: 24109245
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '16.bs1.a1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8142, -1, 1166, -1, 8173, -1, 1170, -1], 'generators': [169], 'label': '256.12509.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.b1', 'old_label': '32.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109246
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.bs1.b1'], 'contains': ['64.b1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8142, -1, 2350, -1, 8173, -1, 2357, -1], 'generators': [33], 'label': '256.12509.32.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '32.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109247
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.b1'], 'contains': ['64.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8894, -1, 1319, -1, 8933, -1, 1323, -1], 'generators': [35], 'label': '256.12509.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.b1', 'old_label': '32.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109248
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1'], 'contains': ['64.b1.b1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8894, -1, 2911, -1, 8933, -1, 2942, -1], 'generators': [34], 'label': '256.12509.32.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109249
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.bq1.a1', '16.bq1.b1'], 'contains': ['64.k1.a1', '64.l1.a1', '64.m1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7490, -1, 1394, -1, 7519, -1, 1399, -1], 'generators': [65, 6], 'label': '256.12509.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109250
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.bq1.a1', '16.bq1.b1'], 'contains': ['64.k1.a1', '64.l1.a1', '64.m1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7490, -1, 1471, -1, 7519, -1, 1475, -1], 'generators': [81, 6], 'label': '256.12509.32.y1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.y1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109251
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.bt1.a1', '16.bt1.b1'], 'contains': ['64.n1.a1', '64.o1.a1', '64.r1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3064, -1, 6935, -1, 3077, -1, 6954, -1], 'generators': [1, 38], 'label': '256.12509.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '32.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109252
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.bt1.a1', '16.bt1.b1'], 'contains': ['64.n1.a1', '64.o1.a1', '64.r1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3064, -1, 7010, -1, 3077, -1, 7030, -1], 'generators': [129, 38], 'label': '256.12509.32.z1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '32.z1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109253
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bt1.a1'], 'contains': ['64.c1.a1', '64.n1.a1', '64.p1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2128, -1, 6825, -1, 2136, -1, 6844, -1], 'generators': [1, 8], 'label': '256.12509.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109254
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bt1.b1'], 'contains': ['64.c1.b1', '64.n1.a1', '64.p1.a1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2128, -1, 7120, -1, 2136, -1, 7140, -1], 'generators': [1, 136], 'label': '256.12509.32.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109255
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.b1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.e1.b1', '8.m1.b1', '8.bf1.b1', '8.bg1.b1'], 'core': '4.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3058, 9260, 6889, 5813, 3070, 9231, 6909, 5826], 'generators': [37, 38, 64], 'label': '256.12509.4.h1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.b1', 'normal_contained_in': ['2.a1.a1', '2.h1.b1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.e1.b1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109256
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bt1.a1', '16.bt1.b1'], 'contains': ['64.o1.a1', '64.p1.a1', '64.r1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2908, -1, 7407, -1, 2921, -1, 7429, -1], 'generators': [9, 38], 'label': '256.12509.32.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '32.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109257
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bt1.a1', '16.bt1.b1'], 'contains': ['64.o1.a1', '64.p1.a1', '64.r1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2908, -1, 7264, -1, 2921, -1, 7285, -1], 'generators': [137, 38], 'label': '256.12509.32.bb1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '32.bb1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109258
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.bt1.a1', '16.bu1.a1'], 'contains': ['64.c1.a1', '64.o1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1814, -1, 7737, -1, 1821, -1, 7760, -1], 'generators': [38, 8], 'label': '256.12509.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.b1', 'old_label': '32.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109259
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.bt1.b1', '16.bu1.b1'], 'contains': ['64.c1.b1', '64.o1.a1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1814, -1, 7889, -1, 1821, -1, 7912, -1], 'generators': [38, 136], 'label': '256.12509.32.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '32.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109260
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.bu1.a1'], 'contains': ['64.c1.a1', '64.q1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1472, -1, 8269, -1, 1457, -1, 8294, -1], 'generators': [67, 8], 'label': '256.12509.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '32.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109261
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.bu1.b1'], 'contains': ['64.c1.b1', '64.q1.a1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1472, -1, 8345, -1, 1457, -1, 8370, -1], 'generators': [2, 136], 'label': '256.12509.32.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109262
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.bv1.a1'], 'contains': ['64.c1.a1', '64.q1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1338, -1, 8117, -1, 1342, -1, 8141, -1], 'generators': [2, 8], 'label': '256.12509.32.bd2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '32.bd2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109263
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '16.bv1.b1'], 'contains': ['64.c1.b1', '64.q1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1338, -1, 8422, -1, 1342, -1, 8446, -1], 'generators': [67, 136], 'label': '256.12509.32.bd2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.b1', 'old_label': '32.bd2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd2.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109264
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bt1.a1', '16.bv1.a1'], 'contains': ['64.c1.a1', '64.r1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1707, -1, 7813, -1, 1713, -1, 7836, -1], 'generators': [39, 8], 'label': '256.12509.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '32.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109265
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bt1.b1', '16.bv1.b1'], 'contains': ['64.c1.b1', '64.r1.a1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1707, -1, 7965, -1, 1713, -1, 7988, -1], 'generators': [39, 136], 'label': '256.12509.32.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.b1', 'old_label': '32.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109266
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.h1.b1'], 'contains': ['8.d1.a1', '8.f1.a1', '8.i1.a1', '8.bc1.a1', '8.bc1.b1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6495, 2419, 3110, 6370, 6520, 2411, 3120, 6383], 'generators': [6, 32, 136], 'label': '256.12509.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.h1.b1', '2.h1.a1'], 'normal_contains': ['8.d1.a1', '8.f1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': None, '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': None}
  • id: 24109267
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1585, -1, 7661, -1, 1591, -1, 7683, -1], 'generators': [4], 'label': '256.12509.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bg1.a1', 'old_label': '32.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109268
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.b1'], 'contains': ['64.c1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1585, -1, 8041, -1, 1591, -1, 8065, -1], 'generators': [5], 'label': '256.12509.32.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bg1.a1', 'old_label': '32.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109269
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bd1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.b1', '16.bu1.a1', '16.bv1.a1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1039, -1, 8194, -1, 1042, -1, 8217, -1], 'generators': [37], 'label': '256.12509.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bc1.a1', 'old_label': '32.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109270
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.bu1.b1', '16.bv1.b1'], 'contains': ['64.c1.b1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1039, -1, 8767, -1, 1042, -1, 8793, -1], 'generators': [36], 'label': '256.12509.32.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bc1.a1', 'old_label': '32.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109271
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1', '32.h1.a1', '32.i1.a1', '32.i1.b1', '32.j1.a1', '32.j1.b1', '32.k1.a1', '32.l1.a1', '32.m1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4565, 4843, 5289, 4578, 4583, 4828, 5303, 4588], 'generators': [16, 128], 'label': '256.12509.64.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.c1.a1', '32.b1.a1', '32.d1.a1', '32.g1.a1', '32.e1.a1', '32.f1.a1'], 'normal_contains': ['128.c1.a1', '128.a1.a1', '128.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109272
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.q1.a1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.v1.a1', '32.w1.a1', '32.x1.a1'], 'contains': ['128.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7781, 4099, 1243, 5430, 7811, 4087, 1246, 5228], 'generators': [64], 'label': '256.12509.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.b1.a1'], 'normal_contains': ['128.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109273
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.q1.b1', '32.s1.b1', '32.t1.b1', '32.u1.b1', '32.v1.b1', '32.w1.b1', '32.x1.b1'], 'contains': ['128.b1.a1'], 'core': '64.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7781, 4099, 2247, 5206, 7811, 4087, 2233, 4967], 'generators': [80], 'label': '256.12509.64.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.b1', 'normal_contained_in': ['32.b1.a1'], 'normal_contains': ['128.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109274
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.ba1.a1', '32.bc1.a1', '32.bd1.a1', '32.bd2.a1', '32.be1.a1', '32.bf1.a1', '32.bg1.a1'], 'contains': ['128.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1707, 5507, 7737, 4212, 1713, 5487, 7760, 4287], 'generators': [8], 'label': '256.12509.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.c1.a1'], 'normal_contains': ['128.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109275
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.ba1.b1', '32.bc1.b1', '32.bd1.b1', '32.bd2.b1', '32.be1.b1', '32.bf1.b1', '32.bg1.b1'], 'contains': ['128.c1.a1'], 'core': '64.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1707, 5507, 7965, 3988, 1713, 5487, 7988, 3861], 'generators': [136], 'label': '256.12509.64.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.b1', 'normal_contained_in': ['32.c1.a1'], 'normal_contains': ['128.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109276
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.n1.a1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4700, -1, 4840, -1, 4712, -1, 4854, -1], 'generators': [1, 144], 'label': '256.12509.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '64.d1.a1', 'projective_image': None, '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': None}
  • id: 24109277
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.j1.a1', '8.bd1.a1', '8.bd1.b1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6231, 1878, 1755, 7430, 6256, 1872, 1760, 7445], 'generators': [33, 38, 136], 'label': '256.12509.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.b1.a1', '2.i1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': None, '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': None}
  • id: 24109278
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.o1.a1'], 'contains': ['128.a1.a1', '128.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4955, -1, 5109, -1, 4968, -1, 5123, -1], 'generators': [38, 144], 'label': '256.12509.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bh1.a1', 'old_label': '64.e1.a1', 'projective_image': None, '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': None}
  • id: 24109279
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.n1.a1', '32.o1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4840, -1, 4922, -1, 4852, -1, 4936, -1], 'generators': [200], 'label': '256.12509.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.f1.a1', 'projective_image': None, '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': None}
  • id: 24109280
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.n1.a1', '32.p1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4331, -1, 5190, -1, 4335, -1, 5205, -1], 'generators': [201], 'label': '256.12509.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.g1.a1', 'projective_image': None, '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': None}
  • id: 24109281
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.p1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3531, -1, 5530, -1, 3547, -1, 5546, -1], 'generators': [66], 'label': '256.12509.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '64.h1.a1', 'projective_image': None, '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': None}
  • id: 24109282
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.b1', '32.p1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3531, -1, 5420, -1, 3547, -1, 5436, -1], 'generators': [3], 'label': '256.12509.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.b1', 'old_label': '64.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109283
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.q1.a1', '32.q1.b1', '32.r1.a1', '32.r1.a2'], 'contains': ['128.b1.a1', '128.d1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6784, -1, 2138, -1, 6811, -1, 2138, -1], 'generators': [1, 128], 'label': '256.12509.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.i1.a1', 'projective_image': None, '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': None}
  • id: 24109284
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.s1.a1', '32.s1.b1'], 'contains': ['128.b1.a1', '128.e1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6908, -1, 2327, -1, 6934, -1, 2314, -1], 'generators': [38, 128], 'label': '256.12509.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '64.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109285
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.q1.a1', '32.q1.b1', '32.y1.a1', '32.y1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7022, -1, 2029, -1, 7050, -1, 1995, -1], 'generators': [65], 'label': '256.12509.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '64.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109286
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.r1.a1', '32.r1.a2', '32.t1.a1', '32.t1.b1', '32.y1.a1', '32.y1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7238, -1, 1758, -1, 7266, -1, 1764, -1], 'generators': [6], 'label': '256.12509.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109287
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.r1.a1', '32.r1.a2', '32.u1.a1', '32.u1.b1', '32.y1.a1', '32.y1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7131, -1, 1851, -1, 7158, -1, 1857, -1], 'generators': [7], 'label': '256.12509.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '64.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109288
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'contains': ['8.d1.a1', '8.k1.a1', '8.l1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5251, 5879, 5173, 4695, 5270, 5861, 5188, 4704], 'generators': [34, 4], 'label': '256.12509.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.i1.b1'], 'normal_contains': ['8.d1.a1', '8.k1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': None, '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': None}
  • id: 24109289
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.z1.a1', '32.z1.a2', '32.ba1.a1', '32.ba1.b1'], 'contains': ['128.c1.a1', '128.d1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3220, -1, 6935, -1, 3235, -1, 6954, -1], 'generators': [1, 16], 'label': '256.12509.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109290
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.z1.a1', '32.z1.a2', '32.bb1.a1', '32.bb1.a2', '32.bc1.a1', '32.bc1.b1'], 'contains': ['128.c1.a1', '128.e1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3097, -1, 7201, -1, 3112, -1, 7222, -1], 'generators': [38, 16], 'label': '256.12509.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '64.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109291
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.ba1.a1', '32.ba1.b1', '32.bb1.a1', '32.bb1.a2'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2982, -1, 7120, -1, 2996, -1, 7140, -1], 'generators': [137], 'label': '256.12509.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109292
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.bd1.b1', '32.bd2.a1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2345, -1, 7813, -1, 2355, -1, 7836, -1], 'generators': [2], 'label': '256.12509.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.a1', 'old_label': '64.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109293
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bl1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.bd1.a1', '32.bd2.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2345, -1, 7889, -1, 2355, -1, 7912, -1], 'generators': [67], 'label': '256.12509.64.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.b1', 'old_label': '64.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109294
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.z1.a1', '32.z1.a2', '32.bb1.a1', '32.bb1.a2', '32.be1.a1', '32.be1.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2874, -1, 7283, -1, 2888, -1, 7304, -1], 'generators': [39], 'label': '256.12509.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.r1.a1', 'old_label': '64.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109295
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.h1.a1', '64.h1.b1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4634, 4843, 5187, 4578, 4646, 4828, 5202, 4588], 'generators': [144], 'label': '256.12509.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109296
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.b1.b1', '64.i1.a1', '64.j1.a1', '64.k1.a1', '64.l1.a1', '64.m1.a1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6965, 4623, 2138, 4923, 6991, 4608, 2138, 4744], 'generators': [128], 'label': '256.12509.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.a1.a1', '64.b1.a1', '64.b1.b1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': None, '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': None}
  • id: 24109297
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.c1.a1', '64.c1.b1', '64.n1.a1', '64.o1.a1', '64.p1.a1', '64.q1.a1', '64.q1.b1', '64.r1.a1'], 'contains': ['256.a1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3041, 5064, 7242, 4284, 3055, 5049, 7262, 4431], 'generators': [16], 'label': '256.12509.128.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.c1.a1', 'normal_contained_in': ['64.a1.a1', '64.c1.b1', '64.c1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.c1.a1', 'projective_image': None, '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': None}
  • id: 24109298
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '128.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '64.i1.a1', '64.n1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4742, -1, 4990, -1, 4754, -1, 5003, -1], 'generators': [1], 'label': '256.12509.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '128.d1.a1', 'projective_image': None, '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': None}
  • id: 24109299
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'contains': ['8.d1.a1', '8.k1.b1', '8.l1.b1'], 'core': '4.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5251, 5879, 5270, 7146, 5270, 5861, 5285, 7161], 'generators': [5, 38], 'label': '256.12509.4.k1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.b1', 'normal_contained_in': ['2.c1.a1', '2.h1.b1', '2.i1.a1'], 'normal_contains': ['8.d1.a1', '8.k1.b1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109300
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '128.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '64.j1.a1', '64.o1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4912, -1, 5109, -1, 4924, -1, 5123, -1], 'generators': [38], 'label': '256.12509.128.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.p1.a1', 'old_label': '128.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109301
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.c1.a1', '128.d1.a1', '128.e1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4742, 4843, 5109, 4578, 4754, 4828, 5123, 4588], 'generators': [], 'label': '256.12509.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.c1.a1', '128.a1.a1', '128.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': None, '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': None}
  • id: 24109302
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.i1.a1', '4.j1.a1', '4.q1.a1', '4.s1.a1', '4.x1.a1', '4.x1.b1', '4.bb1.a1', '4.bb1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6099, 2149, 2035, 4227, 6123, 2142, 2041, 4236], 'generators': [1, 6, 32, 136], 'label': '256.12509.2.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.d1.a1', '4.i1.a1', '4.j1.a1', '4.q1.a1', '4.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109303
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.e1.a1', '8.f1.a1', '8.k1.a1', '8.bs1.a1', '8.bv1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3628, 6165, 6389, 2204, 3641, 6146, 6408, 2209], 'generators': [2, 4, 64], 'label': '256.12509.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.e1.a1', '8.f1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': None, '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': None}
  • id: 24109304
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'contains': ['8.e1.b1', '8.f1.a1', '8.k1.b1', '8.bs1.b1', '8.bv1.b1'], 'core': '4.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3628, 6165, 6676, 1003, 3641, 6146, 6697, 1005], 'generators': [5, 6, 64], 'label': '256.12509.4.l1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.b1', 'normal_contained_in': ['2.d1.a1', '2.h1.b1', '2.j1.b1'], 'normal_contains': ['8.e1.b1', '8.f1.a1', '8.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109305
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.g1.a1', '8.k1.b1', '8.bt1.a1', '8.bw1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3488, 5593, 6775, 2402, 3502, 5576, 6795, 2406], 'generators': [5, 2, 64], 'label': '256.12509.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.g1.a1', '8.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': None, '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': None}
  • id: 24109306
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'contains': ['8.e1.b1', '8.g1.a1', '8.k1.a1', '8.bt1.b1', '8.bw1.b1'], 'core': '4.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3488, 5593, 6290, 3704, 3502, 5576, 6310, 3712], 'generators': [3, 4, 64], 'label': '256.12509.4.m1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.b1', 'normal_contained_in': ['2.d1.a1', '2.i1.b1', '2.k1.b1'], 'normal_contains': ['8.e1.b1', '8.g1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109307
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.m1.b1', '8.bu1.a1', '8.bx1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2568, 6490, 7016, 779, 2578, 6471, 7038, 780], 'generators': [37, 2, 64], 'label': '256.12509.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': None, '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': None}
  • id: 24109308
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.b1', '2.k1.b1'], 'contains': ['8.e1.b1', '8.h1.a1', '8.m1.a1', '8.bu1.b1', '8.bx1.b1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2568, 6490, 7392, 527, 2578, 6471, 7414, 528], 'generators': [3, 36, 64], 'label': '256.12509.4.n1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.a1.a1', '2.j1.b1', '2.k1.b1'], 'normal_contains': ['8.e1.b1', '8.h1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109309
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.i1.a1', '8.l1.a1', '8.bl1.a1', '8.bl2.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7264, 8860, 4103, 4451, 7292, 8833, 4116, 4460], 'generators': [2, 32, 136], 'label': '256.12509.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.i1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': None, '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': None}
  • id: 24109310
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.b1', '2.k1.b1'], 'contains': ['8.e1.b1', '8.i1.a1', '8.l1.b1', '8.bl1.b1', '8.bl2.b1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7264, 8860, 3959, 9217, 7292, 8833, 3970, 9237], 'generators': [3, 32, 136], 'label': '256.12509.4.o1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.e1.a1', '2.h1.b1', '2.k1.b1'], 'normal_contains': ['8.e1.b1', '8.i1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109311
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.e1.a1', '8.j1.a1', '8.l1.b1', '8.bm1.a1', '8.bm2.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7027, 8375, 3484, 8058, 7054, 8349, 3495, 8075], 'generators': [33, 2, 136], 'label': '256.12509.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.e1.a1', '8.j1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109312
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.b1', '2.j1.b1'], 'contains': ['8.e1.b1', '8.j1.a1', '8.l1.a1', '8.bm1.b1', '8.bm2.b1'], 'core': '4.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7027, 8375, 3672, 5494, 7054, 8349, 3683, 5506], 'generators': [33, 34, 136], 'label': '256.12509.4.p1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.b1', 'normal_contained_in': ['2.e1.a1', '2.i1.b1', '2.j1.b1'], 'normal_contains': ['8.e1.b1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109313
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.f1.a1', '4.k1.a1', '4.k1.b1', '4.u1.a1', '4.u1.b1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5239, 4755, 5244, 3692, 5260, 4740, 5260, 3699], 'generators': [1, 34, 4], 'label': '256.12509.2.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.e1.a1', '4.f1.a1', '4.k1.a1', '4.k1.b1', '4.u1.a1', '4.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109314
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.j1.a1', '2.j1.b1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.j1.a1', '8.bn1.a1', '8.bn1.b1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5968, 792, 1941, 1919, 5991, 790, 1947, 1923], 'generators': [33, 6, 136], 'label': '256.12509.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.b1.a1', '2.j1.b1', '2.j1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109315
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.b1'], 'contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5091, 7222, 4934, 4180, 5111, 7200, 4949, 4189], 'generators': [34, 36], 'label': '256.12509.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.b1'], 'normal_contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109316
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.b1', '2.j1.a1'], 'contains': ['8.f1.a1', '8.l1.b1', '8.m1.b1'], 'core': '4.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5091, 7222, 4541, 6922, 5111, 7200, 4554, 6937], 'generators': [37, 6], 'label': '256.12509.4.r1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.b1', 'normal_contained_in': ['2.f1.a1', '2.h1.b1', '2.j1.a1'], 'normal_contains': ['8.f1.a1', '8.l1.b1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109317
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.k1.a1', '2.k1.b1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.i1.a1', '8.bo1.a1', '8.bo1.b1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5703, 1336, 3297, 3419, 5725, 1333, 3306, 3426], 'generators': [7, 32, 136], 'label': '256.12509.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.b1.a1', '2.k1.b1', '2.k1.a1'], 'normal_contains': ['8.h1.a1', '8.g1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109318
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.b1', '2.k1.a1'], 'contains': ['8.g1.a1', '8.l1.a1', '8.m1.b1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4913, 6856, 5061, 5179, 4932, 6835, 5076, 5190], 'generators': [37, 34], 'label': '256.12509.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.b1', '2.k1.a1'], 'normal_contains': ['8.g1.a1', '8.l1.a1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109319
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.b1'], 'contains': ['8.g1.a1', '8.l1.b1', '8.m1.a1'], 'core': '4.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4913, 6856, 4809, 7743, 4932, 6835, 4823, 7759], 'generators': [35, 36], 'label': '256.12509.4.t1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.b1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.b1'], 'normal_contains': ['8.g1.a1', '8.l1.b1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109320
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'contains': ['8.h1.a1', '8.k1.a1', '8.l1.b1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4734, 5267, 4414, 3928, 4753, 5251, 4428, 3937], 'generators': [35, 4], 'label': '256.12509.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.c1.a1', '2.j1.a1', '2.k1.b1'], 'normal_contains': ['8.h1.a1', '8.k1.a1', '8.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109321
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'contains': ['8.h1.a1', '8.k1.b1', '8.l1.a1'], 'core': '4.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4734, 5267, 5699, 1227, 4753, 5251, 5715, 1230], 'generators': [5, 34], 'label': '256.12509.4.u1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.b1', 'normal_contained_in': ['2.c1.a1', '2.j1.b1', '2.k1.a1'], 'normal_contains': ['8.h1.a1', '8.k1.b1', '8.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109322
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'contains': ['8.i1.a1', '8.k1.a1', '8.m1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4287, 4896, 5570, 8659, 4303, 4881, 5587, 8677], 'generators': [4, 32], 'label': '256.12509.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.b1'], 'normal_contains': ['8.i1.a1', '8.k1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109323
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'contains': ['8.i1.a1', '8.k1.b1', '8.m1.b1'], 'core': '4.v1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4287, 4896, 5967, 9491, 4303, 4881, 5986, 9512], 'generators': [5, 32], 'label': '256.12509.4.v1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.b1', 'normal_contained_in': ['2.g1.a1', '2.h1.b1', '2.k1.a1'], 'normal_contains': ['8.i1.a1', '8.k1.b1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109324
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.a1', '4.l1.a1', '4.l1.b1', '4.m1.a1', '4.m1.b1', '4.ba1.a1', '4.ba1.b1', '4.bf1.a1', '4.bg1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3488, 5135, 6604, 2420, 3502, 5119, 6624, 2425], 'generators': [1, 2, 4, 64], 'label': '256.12509.2.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.e1.a1', '4.l1.b1', '4.l1.a1', '4.m1.b1', '4.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109325
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'contains': ['8.j1.a1', '8.k1.a1', '8.m1.b1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4095, 4502, 4675, 8930, 4111, 4488, 4689, 8948], 'generators': [33, 4], 'label': '256.12509.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.b1', '2.j1.a1'], 'normal_contains': ['8.j1.a1', '8.k1.a1', '8.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109326
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'contains': ['8.j1.a1', '8.k1.b1', '8.m1.a1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4095, 4502, 5832, 8387, 4111, 4488, 5850, 8406], 'generators': [33, 36], 'label': '256.12509.4.w1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.b1'], 'normal_contains': ['8.j1.a1', '8.k1.b1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109327
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.q1.a1', '8.u1.a1', '8.bc1.a1', '8.bd1.a1', '8.bn1.a1', '8.bo1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7956, -1, 1247, -1, 7987, -1, 1251, -1], 'generators': [1, 6, 32], 'label': '256.12509.4.x1.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.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109328
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.b1', '8.q1.a1', '8.u1.a1', '8.bc1.b1', '8.bd1.b1', '8.bn1.b1', '8.bo1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7956, -1, 694, -1, 7987, -1, 696, -1], 'generators': [1, 6, 168], 'label': '256.12509.4.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109329
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.r1.a1', '8.y1.a1', '8.bf1.a1', '8.bg1.b1', '8.bu1.a1', '8.bx1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [853, -1, 8604, -1, 853, -1, 8629, -1], 'generators': [1, 2, 36], 'label': '256.12509.4.y1.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.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109330
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.b1', '8.r1.a1', '8.y1.a1', '8.bf1.b1', '8.bg1.a1', '8.bu1.b1', '8.bx1.a1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [853, -1, 8820, -1, 853, -1, 8847, -1], 'generators': [1, 66, 36], 'label': '256.12509.4.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109331
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.b1.a1', '8.t1.a1', '8.v1.a1', '8.bl1.a1', '8.bl2.b1', '8.bm1.b1', '8.bm2.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9348, -1, 2725, -1, 9383, -1, 2733, -1], 'generators': [1, 2, 32], 'label': '256.12509.4.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109332
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.b1.b1', '8.t1.a1', '8.v1.a1', '8.bl1.b1', '8.bl2.a1', '8.bm1.a1', '8.bm2.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9348, -1, 2327, -1, 9383, -1, 2335, -1], 'generators': [1, 2, 168], 'label': '256.12509.4.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109333
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.w1.a1', '8.x1.a1', '8.bs1.a1', '8.bt1.a1', '8.bv1.b1', '8.bw1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1884, -1, 7628, -1, 1966, -1, 7651, -1], 'generators': [1, 2, 4], 'label': '256.12509.4.ba1.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.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109334
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.b1', '8.w1.a1', '8.x1.a1', '8.bs1.b1', '8.bt1.b1', '8.bv1.a1', '8.bw1.a1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1884, -1, 7779, -1, 1966, -1, 7802, -1], 'generators': [1, 66, 4], 'label': '256.12509.4.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109335
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': ['128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.o1.a1', '4.o1.b1', '4.p1.a1', '4.p1.b1', '4.z1.a1', '4.z1.b1', '4.be1.a1', '4.be1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7145, 8224, 3578, 5917, 7173, 8196, 3589, 6002], 'generators': [1, 2, 32, 136], 'label': '256.12509.2.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.d1.a1', '4.f1.a1', '4.o1.b1', '4.o1.a1', '4.p1.b1', '4.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109336
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.n1.a1', '8.bb1.a1', '8.bc1.a1', '8.bd1.b1', '8.bj1.a1', '8.bn1.b1', '8.bo1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7564, -1, 970, -1, 7593, -1, 973, -1], 'generators': [137, 6, 32], 'label': '256.12509.4.bb1.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.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109337
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.n1.b1', '8.bb1.a1', '8.bc1.b1', '8.bd1.a1', '8.bj1.a1', '8.bn1.a1', '8.bo1.b1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7564, -1, 1524, -1, 7593, -1, 1528, -1], 'generators': [137, 6, 168], 'label': '256.12509.4.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109338
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.o1.a1', '8.be1.a1', '8.bf1.a1', '8.bf1.b1', '8.br1.a1', '8.bu1.a1', '8.bu1.b1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1197, -1, 9079, -1, 1426, -1, 9117, -1], 'generators': [65, 2, 36], 'label': '256.12509.4.bc1.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.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109339
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.p1.a1', '8.be1.a1', '8.bg1.a1', '8.bg1.b1', '8.br1.a1', '8.bx1.a1', '8.bx1.b1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1558, -1, 8430, -1, 1739, -1, 8455, -1], 'generators': [65, 66, 36], 'label': '256.12509.4.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109340
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.n1.a1', '8.bi1.a1', '8.bk1.a1', '8.bl1.a1', '8.bl2.b1', '8.bm1.a1', '8.bm2.b1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8974, -1, 2526, -1, 9007, -1, 2534, -1], 'generators': [137, 2, 32], 'label': '256.12509.4.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109341
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.n1.b1', '8.bi1.a1', '8.bk1.a1', '8.bl1.b1', '8.bl2.a1', '8.bm1.b1', '8.bm2.a1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8974, -1, 2923, -1, 9007, -1, 2932, -1], 'generators': [137, 2, 168], 'label': '256.12509.4.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109342
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.o1.a1', '8.bp1.a1', '8.bq1.a1', '8.bs1.a1', '8.bs1.b1', '8.bt1.a1', '8.bt1.b1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2198, -1, 8080, -1, 2282, -1, 8104, -1], 'generators': [65, 2, 4], 'label': '256.12509.4.bf1.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.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109343
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '4.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.p1.a1', '8.bp1.a1', '8.bq1.a1', '8.bv1.a1', '8.bv1.b1', '8.bw1.a1', '8.bw1.b1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 7503, -1, 2907, -1, 7526, -1], 'generators': [65, 66, 4], 'label': '256.12509.4.bg1.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.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109344
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.h1.a1', '16.k1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5060, 4755, 4959, 4212, 5079, 4737, 4974, 4221], 'generators': [1, 136, 64], 'label': '256.12509.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.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.b1.a1', '16.a1.a1', '16.c1.a1', '16.d1.a1', '16.h1.a1', '16.e1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': None, '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': None}
  • id: 24109345
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.x1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8707, 2369, 1759, 7478, 8740, 2359, 1765, 7488], 'generators': [1, 32], 'label': '256.12509.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109346
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1', '4.t1.b1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5445, 7222, 4685, 5579, 5466, 7200, 4699, 5554], 'generators': [1, 34, 36], 'label': '256.12509.2.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.f1.a1', '4.g1.a1', '4.r1.a1', '4.r1.b1', '4.t1.a1', '4.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109347
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.x1.b1', '4.z1.b1'], 'contains': ['16.a1.a1', '16.f1.b1', '16.g1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8707, 2369, 1542, 7042, 8740, 2359, 1546, 7051], 'generators': [1, 168], 'label': '256.12509.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.b1', '16.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109348
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.y1.a1', '4.ba1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.j1.b1', '16.m1.a1', '16.bl1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1810, 7858, 7169, 2953, 1817, 7834, 7190, 2960], 'generators': [1, 2, 136], 'label': '256.12509.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.b1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109349
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.y1.b1', '4.ba1.b1'], 'contains': ['16.b1.a1', '16.i1.b1', '16.j1.a1', '16.m1.b1', '16.bl1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1810, 7858, 7288, 2517, 1817, 7834, 7310, 2523], 'generators': [1, 66, 136], 'label': '256.12509.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.a1', '16.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109350
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.h1.b1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'contains': ['16.d1.a1', '16.r1.a1', '16.s1.a1', '16.t1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5247, 4370, 4826, 5339, 5267, 4354, 4841, 5351], 'generators': [38, 136, 64], 'label': '256.12509.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.b1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.k1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109351
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.m1.a1', '4.n1.a1', '4.o1.a1', '4.p1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '16.j1.a1', '16.u1.a1', '16.be1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3452, 7188, 6177, 3415, 3465, 7166, 6196, 3422], 'generators': [2, 136, 64], 'label': '256.12509.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.l1.a1', '4.n1.a1', '4.m1.a1', '4.o1.a1', '4.p1.a1'], 'normal_contains': ['16.d1.a1', '16.j1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': None, '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': None}
  • id: 24109352
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.b1', '4.l1.b1', '4.m1.b1', '4.n1.b1', '4.o1.b1', '4.p1.b1'], 'contains': ['16.d1.a1', '16.i1.b1', '16.j1.b1', '16.u1.b1', '16.be1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3452, 7188, 6033, 3704, 3465, 7166, 6051, 3712], 'generators': [3, 136, 64], 'label': '256.12509.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.b1.a1', '4.h1.b1', '4.l1.b1', '4.n1.b1', '4.m1.b1', '4.o1.b1', '4.p1.b1'], 'normal_contains': ['16.d1.a1', '16.j1.b1', '16.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109353
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.l1.a1', '4.l1.b1', '4.q1.a1', '4.r1.a1', '4.r1.b1'], 'contains': ['16.d1.a1', '16.v1.a1', '16.z1.a1', '16.bf1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5789, 4087, 4536, 3948, 5812, 4072, 4549, 3956], 'generators': [6, 136, 64], 'label': '256.12509.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.l1.b1', '4.l1.a1', '4.q1.a1', '4.r1.a1', '4.r1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': None, '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': None}
  • id: 24109354
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.m1.a1', '4.m1.b1', '4.s1.a1', '4.t1.a1', '4.t1.b1'], 'contains': ['16.d1.a1', '16.w1.a1', '16.ba1.a1', '16.bg1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5652, 3804, 4729, 4671, 5673, 3790, 4744, 4681], 'generators': [7, 136, 64], 'label': '256.12509.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.j1.a1', '4.m1.b1', '4.m1.a1', '4.s1.a1', '4.t1.a1', '4.t1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': None, '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': None}
  • id: 24109355
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.n1.b1', '4.q1.a1', '4.s1.a1', '4.u1.a1', '4.u1.b1'], 'contains': ['16.d1.a1', '16.x1.a1', '16.bb1.a1', '16.bh1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4872, 3522, 5500, 3171, 4891, 3508, 5516, 3178], 'generators': [39, 136, 64], 'label': '256.12509.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.a1.a1', '4.n1.b1', '4.n1.a1', '4.q1.a1', '4.s1.a1', '4.u1.a1', '4.u1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': None, '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': None}
  • id: 24109356
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.o1.a1', '4.o1.b1', '4.s1.a1', '4.v1.a1', '4.v1.b1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.f1.b1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6930, 3172, 3855, 6583, 6956, 3159, 3867, 6591], 'generators': [32, 136], 'label': '256.12509.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.d1.a1', '4.i1.a1', '4.o1.b1', '4.o1.a1', '4.s1.a1', '4.v1.a1', '4.v1.b1'], 'normal_contains': ['16.d1.a1', '16.f1.b1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': None, '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': None}
  • id: 24109357
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': ['128.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1', '4.v1.a1', '4.v1.b1', '4.w1.a1', '4.w1.b1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4165, 4357, 5963, 8523, 4181, 4344, 5981, 8541], 'generators': [1, 4, 32], 'label': '256.12509.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1', '4.v1.a1', '4.v1.b1', '4.w1.a1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109358
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.a1', '4.p1.b1', '4.q1.a1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.g1.a1', '16.g1.b1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6726, 2754, 2449, 6296, 6752, 2742, 2455, 6303], 'generators': [33, 136], 'label': '256.12509.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.b1', '4.p1.a1', '4.q1.a1', '4.w1.a1', '4.w1.b1'], 'normal_contains': ['16.d1.a1', '16.g1.b1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': None, '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': None}
  • id: 24109359
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.k1.a1', '4.l1.a1', '4.m1.b1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.d1.a1', '16.bc1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3625, 5225, 5815, 4865, 3638, 5205, 5832, 4876], 'generators': [4, 64], 'label': '256.12509.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.e1.a1', '4.k1.a1', '4.l1.a1', '4.m1.b1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': None, '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': None}
  • id: 24109360
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.k1.b1', '4.l1.b1', '4.m1.a1', '4.u1.b1', '4.v1.b1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.bc1.b1'], 'core': '8.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3625, 5225, 5912, 4477, 3638, 5205, 5929, 4486], 'generators': [5, 64], 'label': '256.12509.8.k1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.b1', 'normal_contained_in': ['4.e1.a1', '4.k1.b1', '4.l1.b1', '4.m1.a1', '4.u1.b1', '4.v1.b1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109361
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.r1.a1', '4.t1.a1', '4.u1.b1'], 'contains': ['16.d1.a1', '16.y1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7100, 6834, 4632, 5060, 7128, 6814, 4646, 5071], 'generators': [34, 136], 'label': '256.12509.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.p1.b1', '4.r1.a1', '4.u1.b1', '4.t1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': None, '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': None}
  • id: 24109362
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.f1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.r1.b1', '4.t1.b1', '4.u1.a1'], 'contains': ['16.d1.a1', '16.y1.b1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7100, 6834, 4438, 6054, 7128, 6814, 4451, 6061], 'generators': [35, 136], 'label': '256.12509.8.l1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.f1.a1', '4.k1.b1', '4.o1.b1', '4.p1.a1', '4.r1.b1', '4.u1.a1', '4.t1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109363
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.h1.a1', '4.n1.b1', '4.r1.a1', '4.t1.b1', '4.v1.a1', '4.w1.b1'], 'contains': ['16.d1.a1', '16.bd1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3280, 6512, 6396, 5577, 3293, 6492, 6416, 5588], 'generators': [36, 64], 'label': '256.12509.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.g1.a1', '4.h1.a1', '4.n1.b1', '4.r1.a1', '4.t1.b1', '4.v1.a1', '4.w1.b1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': None, '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': None}
  • id: 24109364
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.h1.b1', '4.n1.a1', '4.r1.b1', '4.t1.a1', '4.v1.b1', '4.w1.a1'], 'contains': ['16.d1.a1', '16.bd1.b1'], 'core': '8.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3280, 6512, 6299, 5836, 3293, 6492, 6318, 5838], 'generators': [37, 64], 'label': '256.12509.8.m1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.b1', 'normal_contained_in': ['4.g1.a1', '4.h1.b1', '4.n1.a1', '4.r1.b1', '4.t1.a1', '4.v1.b1', '4.w1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109365
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bb1.a1', '4.be1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.g1.b1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8553, 2053, 1651, 7260, 8585, 2044, 1655, 7269], 'generators': [137, 32], 'label': '256.12509.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.e1.a1', '16.f1.a1', '16.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': None, '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': None}
  • id: 24109366
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bb1.b1', '4.be1.b1'], 'contains': ['16.e1.a1', '16.f1.b1', '16.g1.a1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8553, 2053, 2230, 6825, 8585, 2044, 2237, 6833], 'generators': [137, 168], 'label': '256.12509.8.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.e1.a1', '16.f1.b1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109367
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bc1.a1', '4.bf1.a1'], 'contains': ['16.h1.a1', '16.i1.a1', '16.i1.b1', '16.bi1.a1', '16.bn1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2696, 7542, 8226, 2735, 2706, 7518, 8251, 2741], 'generators': [65, 2, 136], 'label': '256.12509.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.h1.a1', '16.i1.a1', '16.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': None, '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': None}
  • id: 24109368
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.k1.a1', '4.l1.a1', '4.o1.a1', '4.r1.a1', '4.v1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5047, 6786, 5108, 4794, 5066, 6765, 5123, 4804], 'generators': [2, 4, 32], 'label': '256.12509.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.a1', '4.k1.a1', '4.l1.a1', '4.o1.a1', '4.r1.a1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 24109369
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bd1.a1', '4.bg1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.j1.b1', '16.bj1.a1', '16.bo1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2834, 8175, 6768, 2299, 2844, 8149, 6789, 2304], 'generators': [65, 66, 136], 'label': '256.12509.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.h1.a1', '16.j1.b1', '16.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': None, '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': None}
  • id: 24109370
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.x1.b1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.o1.a1', '16.r1.a1', '16.x1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6539, -1, 1977, -1, 6564, -1, 1983, -1], 'generators': [1, 38, 64], 'label': '256.12509.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.q1.a1', 'projective_image': None, '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': None}
  • id: 24109371
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.y1.a1', '4.y1.b1'], 'contains': ['16.b1.a1', '16.l1.a1', '16.p1.a1', '16.s1.a1', '16.bb1.a1', '16.bt1.a1', '16.bt1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2501, -1, 7775, -1, 2510, -1, 7798, -1], 'generators': [1, 38, 136, 128], 'label': '256.12509.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.r1.a1', 'projective_image': None, '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': None}
  • id: 24109372
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.c1.a1', '16.l1.a1', '16.q1.a1', '16.t1.a1', '16.bh1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4513, -1, 5101, -1, 4530, -1, 5117, -1], 'generators': [1, 38, 200], 'label': '256.12509.8.s1.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.s1.a1', 'projective_image': None, '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': None}
  • id: 24109373
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.z1.a1', '4.z1.b1'], 'contains': ['16.a1.a1', '16.m1.a1', '16.m1.b1', '16.u1.a1', '16.u1.b1', '16.bi1.a1', '16.bj1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5449, -1, 4295, -1, 5470, -1, 4308, -1], 'generators': [1, 2, 64], 'label': '256.12509.8.t1.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.t1.a1', 'projective_image': None, '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': None}
  • id: 24109374
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.x1.a1', '4.x1.b1'], 'contains': ['16.a1.a1', '16.n1.a1', '16.v1.a1', '16.w1.a1', '16.bk1.a1', '16.bq1.a1', '16.bq1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7426, -1, 1107, -1, 7454, -1, 1110, -1], 'generators': [1, 6, 64, 16], 'label': '256.12509.8.u1.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.u1.a1', 'projective_image': None, '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': None}
  • id: 24109375
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.z1.a1', '4.z1.b1'], 'contains': ['16.a1.a1', '16.y1.a1', '16.y1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9890, -1, 2580, -1, 9929, -1, 2588, -1], 'generators': [1, 34], 'label': '256.12509.8.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.v1.a1', 'projective_image': None, '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': None}
  • id: 24109376
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.ba1.a1', '4.ba1.b1'], 'contains': ['16.b1.a1', '16.n1.a1', '16.z1.a1', '16.ba1.a1', '16.bm1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4163, -1, 6631, -1, 4180, -1, 6651, -1], 'generators': [1, 6, 136], 'label': '256.12509.8.w1.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.w1.a1', 'projective_image': None, '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': None}
  • id: 24109377
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.ba1.a1', '4.ba1.b1'], 'contains': ['16.b1.a1', '16.bc1.a1', '16.bc1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1501, -1, 7922, -1, 1507, -1, 7946, -1], 'generators': [1, 4], 'label': '256.12509.8.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.x1.a1', 'projective_image': None, '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': None}
  • id: 24109378
    {'ambient': '256.12509', 'aut_centralizer_order': None, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.y1.a1', '4.y1.b1'], 'contains': ['16.b1.a1', '16.bd1.a1', '16.bd1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [926, -1, 9279, -1, 930, -1, 9307, -1], 'generators': [1, 36], 'label': '256.12509.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.y1.a1', 'projective_image': None, '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': None}