Abstract group data - 256.18790

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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, 4, 4, 2, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 2, 4, 16, 32], [1, 18, 92, 16, 32], [193, 130, 28, 144, 48], [89, 82, 20, 16, 160], [153, 130, 84, 144, 32], [137, 66, 20, 144, 224], [201, 66, 204, 16, 48], [209, 66, 68, 144, 32], [217, 194, 68, 16, 240], [81, 194, 140, 144, 32], [81, 2, 140, 144, 48]], 'aut_group': None, 'aut_hash': 261240470784066402, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 40, 'aut_perms': [418618386280766402309875396754638163621011766836, 550175091081820123427947838578666089644880066404, 479442006075834923123824384075984511044018424802, 142127333603286156610335864486913506680125593788, 142648916075182481742466505864957627839746947085, 591174148412152378447584852842719643059000627968, 183168042680040558890273225966586917619689557368, 426631209080406859739206128687821979618137643649, 79928297802270799804688818553528296381436911119, 408639637842194668565838873562096848124404400710], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 4, 2, 1], [2, 8, 1, 2], [2, 8, 2, 1], [2, 16, 1, 1], [4, 2, 1, 4], [4, 4, 2, 1], [4, 4, 4, 1], [4, 8, 1, 2], [4, 8, 2, 2], [4, 16, 1, 1], [8, 2, 4, 1], [8, 4, 2, 1], [8, 4, 4, 1], [8, 8, 2, 2], [8, 16, 1, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.C_2^6.C_2', '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, 2, 2], [2, 4, 2], [2, 8, 4], [2, 16, 1], [4, 2, 4], [4, 4, 6], [4, 8, 6], [4, 16, 1], [8, 2, 4], [8, 4, 6], [8, 8, 4], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.226', 'commutator_count': 1, 'commutator_label': '16.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 18790, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 2], [2, 8, 1, 4], [2, 16, 1, 1], [4, 2, 1, 4], [4, 4, 1, 6], [4, 8, 1, 6], [4, 16, 1, 1], [8, 2, 2, 2], [8, 4, 1, 2], [8, 4, 2, 2], [8, 8, 1, 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': '16.10', 'frattini_quotient': '16.14', 'hash': 18790, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 1, 4], 'inner_gens': [[1, 18, 220, 16, 32], [17, 2, 84, 16, 96], [89, 210, 4, 16, 32], [1, 2, 4, 16, 32], [1, 194, 4, 16, 32]], 'inner_hash': 226, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': True, 'inner_tex': 'D_4^2', 'inner_used': [1, 2, 3, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 10]], 'label': '256.18790', 'linC_count': 96, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 48, 'linQ_dim': 10, 'linQ_dim_count': 48, 'linR_count': 48, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4.D4^2', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 95, 'number_conjugacy_classes': 46, 'number_divisions': 42, 'number_normal_subgroups': 143, 'number_subgroup_autclasses': 450, 'number_subgroup_classes': 738, 'number_subgroups': 2039, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 63], [4, 96], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [64, 64, 64, 0, 0, 0], 'outer_gens': [[17, 82, 4, 16, 32], [1, 82, 4, 16, 32], [1, 82, 20, 16, 32], [17, 82, 68, 16, 112], [1, 2, 132, 16, 32], [193, 2, 20, 144, 112]], 'outer_group': '128.2163', 'outer_hash': 2163, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [7, 41091263, 41818456, 1134120, 172046880, 94888080], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 20], [4, 2], [8, 4]], 'representations': {'PC': {'code': 41863552016730566467276331461034981, 'gens': [1, 2, 3, 5, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 128, 289, 5282, 1018, 66, 4355, 2187, 2317, 141, 5390, 166]}, 'Perm': {'d': 20, 'gens': [122887418446438562, 154813062295871410, 244511593586643610, 406269022550924173, 534080716528556183, 621599096076270623, 540483091630606080, 621599096076270600]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4.D_4^2', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 101461818
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 18790, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 101461829
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 18790, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
  • id: 101461840
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 18790, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 101461851
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 18790, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 144, 'size': 1}
  • id: 101461859
    {'aut_label': '2D', 'centralizer': '2.n1.a1', 'counter': 5, 'group_counter': 18790, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 24, 'size': 2}
  • id: 101461860
    {'aut_label': '2E', 'centralizer': '2.n1.a1', 'counter': 6, 'group_counter': 18790, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 8, 'size': 2}
  • id: 101461861
    {'aut_label': '2F', 'centralizer': '4.bl1.a1', 'counter': 7, 'group_counter': 18790, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 37, 'size': 4}
  • id: 101461862
    {'aut_label': '2F', 'centralizer': '4.bl1.a1', 'counter': 8, 'group_counter': 18790, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 53, 'size': 4}
  • id: 101461863
    {'aut_label': '2H', 'centralizer': '8.bp1.a1', 'counter': 9, 'group_counter': 18790, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 2, 'size': 8}
  • id: 101461819
    {'aut_label': '2I', 'centralizer': '8.bl1.a1', 'counter': 10, 'group_counter': 18790, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 42, 'size': 8}
  • id: 101461820
    {'aut_label': '2J', 'centralizer': '8.z1.a1', 'counter': 11, 'group_counter': 18790, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 7, 'size': 8}
  • id: 101461821
    {'aut_label': '2J', 'centralizer': '8.z1.a1', 'counter': 12, 'group_counter': 18790, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 23, 'size': 8}
  • id: 101461822
    {'aut_label': '2L', 'centralizer': '16.y1.a1', 'counter': 13, 'group_counter': 18790, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 3, 'size': 16}
  • id: 101461823
    {'aut_label': '4A', 'centralizer': '2.g1.a1', 'counter': 14, 'group_counter': 18790, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 64, 'size': 2}
  • id: 101461824
    {'aut_label': '4B', 'centralizer': '2.i1.a1', 'counter': 15, 'group_counter': 18790, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 72, 'size': 2}
  • id: 101461825
    {'aut_label': '4C', 'centralizer': '2.g1.a1', 'counter': 16, 'group_counter': 18790, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 80, 'size': 2}
  • id: 101461826
    {'aut_label': '4D', 'centralizer': '2.i1.a1', 'counter': 17, 'group_counter': 18790, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 88, 'size': 2}
  • id: 101461827
    {'aut_label': '4E', 'centralizer': '4.bc1.a1', 'counter': 18, 'group_counter': 18790, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [6], 'representative': 4, 'size': 4}
  • id: 101461828
    {'aut_label': '4E', 'centralizer': '4.bc1.a1', 'counter': 19, 'group_counter': 18790, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [6], 'representative': 132, 'size': 4}
  • id: 101461830
    {'aut_label': '4E', 'centralizer': '4.bc1.a1', 'counter': 20, 'group_counter': 18790, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [6], 'representative': 68, 'size': 4}
  • id: 101461831
    {'aut_label': '4E', 'centralizer': '4.bc1.a1', 'counter': 21, 'group_counter': 18790, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [6], 'representative': 196, 'size': 4}
  • id: 101461832
    {'aut_label': '4I', 'centralizer': '4.bk1.a1', 'counter': 22, 'group_counter': 18790, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [2], 'representative': 101, 'size': 4}
  • id: 101461833
    {'aut_label': '4I', 'centralizer': '4.bk1.a1', 'counter': 23, 'group_counter': 18790, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [2], 'representative': 45, 'size': 4}
  • id: 101461834
    {'aut_label': '4K', 'centralizer': '8.cm1.a1', 'counter': 24, 'group_counter': 18790, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [3], 'representative': 1, 'size': 8}
  • id: 101461835
    {'aut_label': '4L', 'centralizer': '8.bu1.a1', 'counter': 25, 'group_counter': 18790, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [2], 'representative': 34, 'size': 8}
  • id: 101461836
    {'aut_label': '4M', 'centralizer': '8.bk1.a1', 'counter': 26, 'group_counter': 18790, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 10, 'size': 8}
  • id: 101461837
    {'aut_label': '4K', 'centralizer': '8.cm1.a1', 'counter': 27, 'group_counter': 18790, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [4], 'representative': 65, 'size': 8}
  • id: 101461838
    {'aut_label': '4O', 'centralizer': '8.y1.a1', 'counter': 28, 'group_counter': 18790, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [2], 'representative': 39, 'size': 8}
  • id: 101461839
    {'aut_label': '4O', 'centralizer': '8.y1.a1', 'counter': 29, 'group_counter': 18790, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [2], 'representative': 55, 'size': 8}
  • id: 101461841
    {'aut_label': '4Q', 'centralizer': '16.bc1.a1', 'counter': 30, 'group_counter': 18790, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [2], 'representative': 35, 'size': 16}
  • id: 101461842
    {'aut_label': '8A1', 'centralizer': '2.g1.a1', 'counter': 31, 'group_counter': 18790, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [14], 'representative': 32, 'size': 2}
  • id: 101461843
    {'aut_label': '8A1', 'centralizer': '2.g1.a1', 'counter': 32, 'group_counter': 18790, 'group_order': 256, 'label': '8A-1', 'order': 8, 'powers': [14], 'representative': 160, 'size': 2}
  • id: 101461844
    {'aut_label': '8A1', 'centralizer': '2.g1.a1', 'counter': 33, 'group_counter': 18790, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [14], 'representative': 48, 'size': 2}
  • id: 101461845
    {'aut_label': '8A1', 'centralizer': '2.g1.a1', 'counter': 34, 'group_counter': 18790, 'group_order': 256, 'label': '8B-1', 'order': 8, 'powers': [14], 'representative': 176, 'size': 2}
  • id: 101461846
    {'aut_label': '8C', 'centralizer': '4.bc1.a1', 'counter': 35, 'group_counter': 18790, 'group_order': 256, 'label': '8C', 'order': 8, 'powers': [14], 'representative': 40, 'size': 4}
  • id: 101461847
    {'aut_label': '8C', 'centralizer': '4.bc1.a1', 'counter': 36, 'group_counter': 18790, 'group_order': 256, 'label': '8D', 'order': 8, 'powers': [14], 'representative': 56, 'size': 4}
  • id: 101461848
    {'aut_label': '8E1', 'centralizer': '4.bc1.a1', 'counter': 37, 'group_counter': 18790, 'group_order': 256, 'label': '8E1', 'order': 8, 'powers': [15], 'representative': 36, 'size': 4}
  • id: 101461849
    {'aut_label': '8E1', 'centralizer': '4.bc1.a1', 'counter': 38, 'group_counter': 18790, 'group_order': 256, 'label': '8E-1', 'order': 8, 'powers': [15], 'representative': 164, 'size': 4}
  • id: 101461850
    {'aut_label': '8E1', 'centralizer': '4.bc1.a1', 'counter': 39, 'group_counter': 18790, 'group_order': 256, 'label': '8F1', 'order': 8, 'powers': [15], 'representative': 100, 'size': 4}
  • id: 101461852
    {'aut_label': '8E1', 'centralizer': '4.bc1.a1', 'counter': 40, 'group_counter': 18790, 'group_order': 256, 'label': '8F-1', 'order': 8, 'powers': [15], 'representative': 228, 'size': 4}
  • id: 101461853
    {'aut_label': '8G', 'centralizer': '8.cm1.a1', 'counter': 41, 'group_counter': 18790, 'group_order': 256, 'label': '8G', 'order': 8, 'powers': [16], 'representative': 33, 'size': 8}
  • id: 101461854
    {'aut_label': '8H', 'centralizer': '8.bi1.a1', 'counter': 42, 'group_counter': 18790, 'group_order': 256, 'label': '8H', 'order': 8, 'powers': [14], 'representative': 5, 'size': 8}
  • id: 101461855
    {'aut_label': '8G', 'centralizer': '8.cm1.a1', 'counter': 43, 'group_counter': 18790, 'group_order': 256, 'label': '8I', 'order': 8, 'powers': [16], 'representative': 97, 'size': 8}
  • id: 101461856
    {'aut_label': '8H', 'centralizer': '8.bi1.a1', 'counter': 44, 'group_counter': 18790, 'group_order': 256, 'label': '8J', 'order': 8, 'powers': [14], 'representative': 21, 'size': 8}
  • id: 101461857
    {'aut_label': '8K', 'centralizer': '16.cb1.a1', 'counter': 45, 'group_counter': 18790, 'group_order': 256, 'label': '8K', 'order': 8, 'powers': [17], 'representative': 6, 'size': 16}
  • id: 101461858
    {'aut_label': '8L', 'centralizer': '16.cc1.a1', 'counter': 46, 'group_counter': 18790, 'group_order': 256, 'label': '8L', 'order': 8, 'powers': [17], 'representative': 38, '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: 605489
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 605500
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 605511
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 605522
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 605526
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 605527
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 605528
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 605529
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 605530
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 605490
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 605491
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 605492
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 605493
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 605494
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 605495
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 605496
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 605497
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 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, 2, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 605498
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 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, -2, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 605499
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605501
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605502
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605503
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605504
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2g', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 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, -2, 0, 2, 0, 0, 0], 'schur_index': 1}
  • id: 605505
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2h', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 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, 2, 0, -2, 0, 0, 0], 'schur_index': 1}
  • id: 605506
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2i', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0], 'schur_index': 1}
  • id: 605507
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2j', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0], 'schur_index': 1}
  • id: 605508
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2k', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0], 'schur_index': 1}
  • id: 605509
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2l', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0], 'schur_index': 1}
  • id: 605510
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2m', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 2, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605512
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2n', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 2, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605513
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2o', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, -2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605514
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2p', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605515
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2q', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, -2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605516
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2r', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605517
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2s', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, -2, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605518
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.2t', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605519
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4a', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605520
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4b', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 605521
    {'cdim': 4, 'counter': 39, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4c', 'multiplicity': 2, 'nt': [16, 328], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 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], 'schur_index': 1}
  • id: 605523
    {'cdim': 4, 'counter': 40, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4d', 'multiplicity': 2, 'nt': [16, 328], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, -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], 'schur_index': 1}
  • id: 605524
    {'cdim': 4, 'counter': 41, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4e', 'multiplicity': 2, 'nt': [16, 328], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 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], 'schur_index': 1}
  • id: 605525
    {'cdim': 4, 'counter': 42, 'faithful': False, 'group': '256.18790', 'group_order': 256, 'image': None, 'label': '256.18790.4f', 'multiplicity': 2, 'nt': [16, 328], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, -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], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 867916
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.18790.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 867927
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.o1.a1', 'kernel_order': 128, 'label': '256.18790.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 867938
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.n1.a1', 'kernel_order': 128, 'label': '256.18790.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 867949
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.m1.a1', 'kernel_order': 128, 'label': '256.18790.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 867957
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.l1.a1', 'kernel_order': 128, 'label': '256.18790.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 867958
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 128, 'label': '256.18790.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 867959
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 128, 'label': '256.18790.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 867960
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 128, 'label': '256.18790.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 867961
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 128, 'label': '256.18790.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 867917
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.18790.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 867918
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.18790.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 867919
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.18790.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 867920
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.18790.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 867921
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.18790.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 867922
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.18790.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 867923
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.18790.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 867924
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.w1.d1', 'kernel_order': 32, 'label': '256.18790.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867925
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.w1.c1', 'kernel_order': 32, 'label': '256.18790.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867926
    {'center': '4.u1.a1', 'center_index': 4, 'center_order': 64, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.x1.c1', 'kernel_order': 32, 'label': '256.18790.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-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]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867928
    {'center': '4.u1.a1', 'center_index': 4, 'center_order': 64, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.x1.d1', 'kernel_order': 32, 'label': '256.18790.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-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]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867929
    {'center': '4.u1.a1', 'center_index': 4, 'center_order': 64, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.x1.a1', 'kernel_order': 32, 'label': '256.18790.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-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]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867930
    {'center': '4.u1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.x1.b1', 'kernel_order': 32, 'label': '256.18790.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-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]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867931
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.w1.b1', 'kernel_order': 32, 'label': '256.18790.2g', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867932
    {'center': '4.d1.a1', 'center_index': 4, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.w1.a1', 'kernel_order': 32, 'label': '256.18790.2h', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867933
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.v1.c1', 'kernel_order': 32, 'label': '256.18790.2i', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867934
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.v1.d1', 'kernel_order': 32, 'label': '256.18790.2j', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867935
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.v1.a1', 'kernel_order': 32, 'label': '256.18790.2k', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867936
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.v1.b1', 'kernel_order': 32, 'label': '256.18790.2l', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867937
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 29, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.u1.b1', 'kernel_order': 32, 'label': '256.18790.2m', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867939
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 30, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.u1.a1', 'kernel_order': 32, 'label': '256.18790.2n', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867940
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 64, 'counter': 31, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.t1.a1', 'kernel_order': 32, 'label': '256.18790.2o', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867941
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 64, 'counter': 32, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.s1.a1', 'kernel_order': 32, 'label': '256.18790.2p', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867942
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.r1.a1', 'kernel_order': 32, 'label': '256.18790.2q', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867943
    {'center': '4.h1.a1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.q1.a1', 'kernel_order': 32, 'label': '256.18790.2r', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867944
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.p1.b1', 'kernel_order': 32, 'label': '256.18790.2s', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867945
    {'center': '4.e1.a1', 'center_index': 4, 'center_order': 64, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.p1.a1', 'kernel_order': 32, 'label': '256.18790.2t', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867946
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.e1.a1', 'kernel_order': 8, 'label': '256.18790.4a', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867947
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.18790.4b', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867948
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.18790.4c1', 'nt': [16, 328], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867950
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.18790.4c2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867951
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.18790.4d1', 'nt': [16, 328], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867952
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 42, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.b1', 'kernel_order': 2, 'label': '256.18790.4d2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867953
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 43, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.18790.4e1', 'nt': [16, 328], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867954
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.18790.4e2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867955
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.18790.4f1', 'nt': [16, 328], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 867956
    {'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '256.18790', 'group_counter': 18790, 'group_order': 256, 'image': None, 'image_isoclass': '128.2023', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.18790.4f2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[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: 26057119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.18790.1.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': '256.18790', 'subgroup_hash': 18790, 'subgroup_order': 256, 'subgroup_tex': 'C_4.D_4^2', 'supersolvable': True, 'sylow': 2}
  • id: 26057230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2314', 'subgroup_hash': 2314, 'subgroup_order': 128, 'subgroup_tex': 'D_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1742', 'subgroup_hash': 1742, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times Q_8):D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1749', 'subgroup_hash': 1749, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.1746', 'subgroup_hash': 1746, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.1741', 'subgroup_hash': 1741, 'subgroup_order': 128, 'subgroup_tex': '(C_2\\times Q_{16}):C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.1796', 'subgroup_hash': 1796, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.496', 'subgroup_hash': 496, 'subgroup_order': 128, 'subgroup_tex': 'D_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1886', 'subgroup_hash': 1886, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.706', 'subgroup_hash': 706, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.734', 'subgroup_hash': 734, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.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': '128.751', 'subgroup_hash': 751, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.l1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.751', 'subgroup_hash': 751, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.m1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.737', 'subgroup_hash': 737, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.n1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1875', 'subgroup_hash': 1875, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.2.o1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.709', 'subgroup_hash': 709, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{16}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.265', 'subgroup_hash': 265, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26057208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.97', 'subgroup_hash': 97, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.248', 'subgroup_hash': 248, 'subgroup_order': 64, 'subgroup_tex': 'C_8.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.253', 'subgroup_hash': 253, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.89', 'subgroup_hash': 89, 'subgroup_order': 64, 'subgroup_tex': '(C_2^2\\times C_8):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.217', 'subgroup_hash': 217, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.89', 'subgroup_hash': 89, 'subgroup_order': 64, 'subgroup_tex': '(C_2^2\\times C_8):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.211', 'subgroup_hash': 211, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.99', 'subgroup_hash': 99, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.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': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.212', 'subgroup_hash': 212, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.83', 'subgroup_hash': 83, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.100', 'subgroup_hash': 100, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.86', 'subgroup_hash': 86, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.93', 'subgroup_hash': 93, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.93', 'subgroup_hash': 93, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.110', 'subgroup_hash': 110, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.4.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.22', 'subgroup_hash': 22, 'subgroup_order': 64, 'subgroup_tex': 'C_4.C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.254', 'subgroup_hash': 254, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.253', 'subgroup_hash': 253, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.251', 'subgroup_hash': 251, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.130', 'subgroup_hash': 130, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.130', 'subgroup_hash': 130, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.129', 'subgroup_hash': 129, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bp1.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: 26057697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.177', 'subgroup_hash': 177, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.133', 'subgroup_hash': 133, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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: 26057741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.176', 'subgroup_hash': 176, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.178', 'subgroup_hash': 178, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bv1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bv1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bv1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bv1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bw1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bw1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bw1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bw1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.152', 'subgroup_hash': 152, 'subgroup_order': 64, 'subgroup_tex': 'C_8.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bx1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bx1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bx1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bx1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.258', 'subgroup_hash': 258, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.by1.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': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.by1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.by1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.by1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.by1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bz1.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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bz1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bz1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.bz1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.bz1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.134', 'subgroup_hash': 134, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ca1.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': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.ca1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ca1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.4.ca1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.ca1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.173', 'subgroup_hash': 173, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.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': True, '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: 26057129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.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': True, '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: 26057130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 26057133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 26057134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 26057135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 26057136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u1.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': True, '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: 26057137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.v1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.d1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.w1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.w1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.d1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1.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': True, '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: 26057147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1.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': True, '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: 26057148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1.c1', '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': True, '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: 26057149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.8.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1.d1', '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': True, '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: 26057150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 26057173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.39', 'subgroup_hash': 39, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.9', 'subgroup_hash': 9, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cd1.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: 26057191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ce1.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: 26057193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ck1.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: 26057201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cr1.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: 26057210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cw1.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cy1.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.cz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.cz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.df1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.df1.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: 26057236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057240
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.di1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.di1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.do1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.do1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.38', 'subgroup_hash': 38, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ds1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ds1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.du1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dy1.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.dz1.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': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ea1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ea1.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: 26057281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ec1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ec1.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: 26057285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ed1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ed1.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: 26057288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ee1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ee1.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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ef1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ef1.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: 26057292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eg1.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': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.eh1.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': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.e1', 'outer_equivalence': False, 'perfect': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.f1', 'outer_equivalence': False, 'perfect': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.g1', 'outer_equivalence': False, 'perfect': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ei1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ei1.h1', 'outer_equivalence': False, 'perfect': False, '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': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.a1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.e1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.f1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.g1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ej1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ej1.h1', 'outer_equivalence': False, 'perfect': False, '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': '32.42', 'subgroup_hash': 42, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.a1', 'outer_equivalence': False, 'perfect': False, '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: 26057315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.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: 26057316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.e1', 'outer_equivalence': False, 'perfect': False, '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: 26057320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.f1', 'outer_equivalence': False, 'perfect': False, '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: 26057321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.g1', 'outer_equivalence': False, 'perfect': False, '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: 26057322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.ek1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ek1.h1', 'outer_equivalence': False, 'perfect': False, '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: 26057323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.8.el1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.el1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 291, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'U1', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 292, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 293, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 294, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 295, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 296, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 297, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.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: 26057339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 298, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 299, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.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: 26057343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 300, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.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: 26057344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 301, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.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: 26057345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.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: 26057347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 305, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 307, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.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: 26057351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 308, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 309, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 310, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 311, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 312, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 313, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 314, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.q1.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: 26057359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 315, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.q1.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: 26057360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 316, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.r1.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: 26057361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 317, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.r1.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: 26057362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 318, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.s1.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: 26057363
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 319, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.s1.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 320, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.t1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 321, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.16.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.t1.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': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26057371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26057372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 26057379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, '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: 26057391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057406
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1.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: 26057412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cf1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cf1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cg1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.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: 26057442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cy1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cy1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cz1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.cz1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.df1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.df1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.df1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dr1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dr1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ds1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ds1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ds1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.du1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.du1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.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: 26057491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dw1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dw1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx1.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: 26057495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.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: 26057498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dy1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dy1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.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: 26057502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dz1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.dz1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ea1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ea1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eb1.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: 26057511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ec1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ec1.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: 26057513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ed1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ed1.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: 26057515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ef1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ef1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eg1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eh1.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: 26057524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ei1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ei1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ei1.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: 26057526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ej1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ej1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ej1.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: 26057528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ek1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ek1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ek1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.el1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.el1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.el1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.em1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.em1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.em1.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: 26057537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.en1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.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: 26057539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eo1.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: 26057542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ep1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ep1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ep1.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: 26057544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eq1.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': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.er1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.er1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.er1.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: 26057548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.es1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.es1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.es1.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: 26057550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.es1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.es1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.es1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.es1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.et1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.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: 26057555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.et1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.et1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.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: 26057559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eu1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.eu1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ev1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.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: 26057565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ev1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ev1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ew1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.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: 26057569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ew1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ew1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ex1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ex1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ex1.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: 26057573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ey1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ey1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ey1.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: 26057576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ez1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.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: 26057578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ez1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ez1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fa1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fa1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fa1.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: 26057582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fb1.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: 26057584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fc1.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: 26057587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fd1.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: 26057589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 26057591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fe1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fe1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fe1.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: 26057593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ff1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.ff1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ff1.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: 26057595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, '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: 26057596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.16.fg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 532, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 533, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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: 26057602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 534, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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: 26057603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 535, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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': '32.46', '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: 26057604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 536, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 537, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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': '32.46', '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: 26057606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 8, 'counter': 538, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.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': '32.46', '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: 26057607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 539, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 540, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 541, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057611
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 542, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057612
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 543, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057613
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 544, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 545, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 546, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.32.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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: 26057623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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: 26057624
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057634
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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: 26057637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 26057654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 26057658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 26057662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.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: 26057669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bq1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bq1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 26057680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bu1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bu1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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: 26057687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bx1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bx1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.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: 26057695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1.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: 26057700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1.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: 26057702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.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: 26057713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057714
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 635, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 636, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.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: 26057716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.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: 26057720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057721
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 641, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057722
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 642, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ct1.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: 26057723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057727
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 647, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 648, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.cy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cy1.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: 26057729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057732
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 651, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057733
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 652, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.32.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 26057738
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057739
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.de1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.de1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057740
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.df1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.df1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057747
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 26057749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.di1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.di1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.e1', 'outer_equivalence': False, 'perfect': False, '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: 26057757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.f1', 'outer_equivalence': False, 'perfect': False, '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: 26057758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.g1', 'outer_equivalence': False, 'perfect': False, '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: 26057759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.32.dj1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.h1', 'outer_equivalence': False, 'perfect': False, '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: 26057760
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 677, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 678, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.64.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': '64.216', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 216, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 679, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18790.64.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': '64.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057764
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 680, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 681, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 26057766
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 682, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 26057767
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 683, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.211', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 211, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.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: 26057771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.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: 26057772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057776
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 691, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.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: 26057777
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 692, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057778
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 693, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057779
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 694, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057780
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 695, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.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: 26057781
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 696, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.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: 26057782
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 697, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.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: 26057783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057791
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057792
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057793
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057798
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 710, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057799
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 711, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057802
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057803
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bb1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057806
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057809
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.bc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057810
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.64.bc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 26057811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.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': 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: 26057813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.18790.64.bd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 26057815
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 726, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.128.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': '128.1165', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1165, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_4^2', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 727, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.128.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': '128.2023', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2023, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 728, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.18790.128.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2023', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2023, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057820
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.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: 26057821
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.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: 26057822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 26057823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 733, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057824
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057825
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057826
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 26057827
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.18790.128.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.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': 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: 26057828
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.18790', 'ambient_counter': 18790, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 738, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.18790.256.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': '256.18790', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18790, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_4^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 26057119
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '2.l1.a1', '2.m1.a1', '2.n1.a1', '2.o1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3939, 4936, 6814, 4896, 3949, 4951, 6805, 4925], 'generators': [1, 2, 4, 32], 'label': '256.18790.1.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.j1.a1', '2.k1.a1', '2.h1.a1', '2.i1.a1', '2.n1.a1', '2.o1.a1', '2.l1.a1', '2.m1.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: 26057120
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': ['128.i1.a1', '128.h1.a1', '128.h1.b1', '128.e1.a1', '128.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.k1.a1', '4.m1.a1', '4.o1.a1', '4.r1.a1', '4.bc1.a1', '4.bh1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4183, 7563, 6596, 4896, 4193, 7539, 6587, 4925], 'generators': [2, 4, 32], 'label': '256.18790.2.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.k1.a1', '4.m1.a1', '4.o1.a1', '4.r1.a1', '4.bc1.a1', '4.bh1.a1'], '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: 26057121
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.l1.a1', '4.p1.a1', '4.v1.a1', '4.y1.a1', '4.bb1.a1', '4.bg1.a1'], 'contains': ['16.a1.a1', '16.bc1.a1', '16.bw1.a1', '16.ca1.a1', '16.cr1.a1', '16.cv1.a1', '16.dk1.a1', '16.do1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3728, 3183, 7974, 5539, 3737, 3193, 7964, 5594], 'generators': [35, 216, 16, 64], 'label': '256.18790.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.f1.a1', '4.l1.a1', '4.v1.a1', '4.p1.a1', '4.y1.a1', '4.bb1.a1', '4.bg1.a1'], 'normal_contains': ['16.a1.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: 26057122
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.h1.a1', '4.u1.a1', '4.y1.a1', '4.bc1.a1', '4.be1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.h1.a1', '16.m1.a1', '16.m1.b1', '16.r1.a1', '16.r1.b1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7061, 2472, 4582, 5297, 7078, 2479, 4577, 5350], 'generators': [32, 216, 16], 'label': '256.18790.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.g1.a1', '4.h1.a1', '4.u1.a1', '4.y1.a1', '4.bc1.a1', '4.be1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.h1.a1', '16.m1.b1', '16.m1.a1', '16.r1.b1', '16.r1.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: 26057123
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.m1.a1', '4.r1.a1', '4.v1.a1', '4.x1.a1', '4.bc1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.k1.b1', '16.cw1.a1', '16.dl1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2092, 7327, 6670, 4281, 2097, 7349, 6662, 4307], 'generators': [36, 16, 64], 'label': '256.18790.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.e1.a1', '4.m1.a1', '4.v1.a1', '4.r1.a1', '4.x1.a1', '4.bc1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1', '16.k1.b1', '16.k1.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: 26057124
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.l1.a1', '4.n1.a1', '4.w1.a1', '4.be1.a1', '4.bf1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.t1.a1', '16.t1.b1', '16.bx1.a1', '16.cx1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4144, 5762, 8347, 4017, 4154, 5779, 8336, 4041], 'generators': [33, 216, 64], 'label': '256.18790.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.d1.a1', '4.l1.a1', '4.w1.a1', '4.n1.a1', '4.be1.a1', '4.bf1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1', '16.t1.a1', '16.t1.b1'], '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: 26057125
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.i1.a1', '4.q1.a1', '4.z1.a1', '4.ba1.a1', '4.bg1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '16.n1.b1', '16.by1.a1', '16.dm1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7241, 3448, 4252, 3489, 7258, 3458, 4246, 3510], 'generators': [5, 216, 16], 'label': '256.18790.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.g1.a1', '4.i1.a1', '4.q1.a1', '4.z1.a1', '4.ba1.a1', '4.bg1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1', '16.n1.b1', '16.n1.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: 26057126
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.a1', '4.r1.a1', '4.t1.a1', '4.z1.a1', '4.bf1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.cb1.a1', '16.cs1.a1', '16.dp1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4268, 4911, 5850, 3180, 4279, 4926, 5843, 3199], 'generators': [6, 16, 64], 'label': '256.18790.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.f1.a1', '4.k1.a1', '4.t1.a1', '4.r1.a1', '4.z1.a1', '4.bf1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1'], '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: 26057127
    {'ambient': '256.18790', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.m1.a1', '4.o1.a1', '4.w1.a1', '4.bd1.a1', '4.bg1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.cc1.a1', '16.ct1.a1', '16.dq1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3421, 5221, 6605, 4790, 3429, 5236, 6597, 4819], 'generators': [38, 16, 64], 'label': '256.18790.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.c1.a1', '4.m1.a1', '4.w1.a1', '4.o1.a1', '4.bd1.a1', '4.bg1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1'], '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: 26057128
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1', '32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.k1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [246, 7843, 5966, 2578, 247, 7866, 5958, 2594], 'generators': [1, 36], 'label': '256.18790.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.a1', '16.k1.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: 26057129
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bn1.b1', '4.bo1.b1'], 'contains': ['16.b1.a1', '16.j1.b1', '16.k1.b1'], 'core': '8.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [246, 7843, 5903, 2834, 247, 7866, 5896, 2851], 'generators': [65, 100], 'label': '256.18790.8.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.b1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.b1', '16.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057130
    {'ambient': '256.18790', '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.c1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bj1.a1', '4.bq1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.h1.a1', '16.ek1.a1', '16.ek1.b1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8112, 1420, 3855, 8185, 8132, 1425, 3851, 8255], 'generators': [2, 248, 16], 'label': '256.18790.8.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.h1.a1'], 'normalizer': '1.a1.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: 26057131
    {'ambient': '256.18790', '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.g1.a1', '128.e1.a1', '128.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.s1.a1', '4.t1.a1', '4.z1.a1', '4.ba1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3362, 6205, 8291, 3742, 3371, 6144, 8317, 3764], 'generators': [1, 2, 4], 'label': '256.18790.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.j1.a1', '4.k1.a1', '4.s1.a1', '4.t1.a1', '4.z1.a1', '4.ba1.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: 26057132
    {'ambient': '256.18790', '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': '16.i1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bk1.a1', '4.br1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1', '16.em1.a1', '16.em1.b1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8012, 1900, 3972, 7936, 8032, 1906, 3967, 8005], 'generators': [2, 32, 16], 'label': '256.18790.8.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1'], 'normalizer': '1.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: 26057133
    {'ambient': '256.18790', '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': '16.b1.a1', 'complements': ['32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1', '32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bl1.a1', '4.bt1.a1'], 'contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1', '16.er1.a1', '16.er1.b1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7797, 2208, 3644, 8663, 7815, 2215, 3640, 8736], 'generators': [218, 32, 16], 'label': '256.18790.8.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.d1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.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: 26057134
    {'ambient': '256.18790', '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.c1.a1', 'complements': ['32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1', '32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bm1.a1', '4.bu1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.h1.a1', '16.fc1.a1', '16.fc1.b1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7905, 1631, 3907, 8394, 7924, 1636, 3902, 8466], 'generators': [218, 248, 16], 'label': '256.18790.8.t1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.f1.a1', '16.e1.a1', '16.h1.a1'], 'normalizer': '1.a1.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: 26057135
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bp1.a1', '4.bs1.a1'], 'contains': ['16.i1.a1', '16.j1.a1', '16.k1.b1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [298, 7715, 5934, 2706, 299, 7737, 5927, 2722], 'generators': [1, 100], 'label': '256.18790.8.u1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.i1.a1', '16.j1.a1', '16.k1.b1'], 'normalizer': '1.a1.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: 26057136
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1', '32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bp1.b1', '4.bs1.b1'], 'contains': ['16.i1.a1', '16.j1.b1', '16.k1.a1'], 'core': '8.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [298, 7715, 5997, 2961, 299, 7737, 5989, 2980], 'generators': [65, 36], 'label': '256.18790.8.u1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.u1.b1', 'normal_contained_in': ['4.e1.a1'], 'normal_contains': ['16.i1.a1', '16.j1.b1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057137
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1', '32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bv1.a1', '4.bw1.a1'], 'contains': ['16.l1.a1', '16.m1.a1', '16.n1.a1', '16.dz1.a1', '16.ea1.b1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8579, 2672, 3483, 1339, 8599, 2681, 3480, 1348], 'generators': [5, 32, 216], 'label': '256.18790.8.v1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.l1.a1', '16.m1.a1', '16.n1.a1'], 'normalizer': '1.a1.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: 26057138
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1', '32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bv1.b1', '4.bw1.b1'], 'contains': ['16.l1.a1', '16.m1.b1', '16.n1.b1', '16.dz1.b1', '16.ea1.a1'], 'core': '8.v1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8579, 2672, 3439, 1157, 8599, 2681, 3435, 1164], 'generators': [21, 48, 216], 'label': '256.18790.8.v1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.v1.b1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.l1.a1', '16.m1.b1', '16.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057139
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.a1', '32.dj1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.c1', '32.dj1.d1', '32.dj1.g1', '32.dj1.h1', '32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bv1.c1', '4.bw1.c1'], 'contains': ['16.l1.b1', '16.m1.a1', '16.n1.b1', '16.dz1.c1', '16.ea1.d1'], 'core': '8.v1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8579, 2672, 3395, 793, 8599, 2681, 3391, 798], 'generators': [21, 32, 216], 'label': '256.18790.8.v1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.v1.c1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.l1.b1', '16.m1.a1', '16.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.v1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057140
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.dj1.e1', '32.dj1.f1', '32.dj1.a1', '32.dj1.b1', '32.dj1.g1', '32.dj1.h1', '32.dj1.c1', '32.dj1.d1', '32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bv1.d1', '4.bw1.d1'], 'contains': ['16.l1.b1', '16.m1.b1', '16.n1.a1', '16.dz1.d1', '16.ea1.c1'], 'core': '8.v1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8579, 2672, 3529, 975, 8599, 2681, 3524, 981], 'generators': [5, 48, 216], 'label': '256.18790.8.v1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.v1.d1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.l1.b1', '16.m1.b1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.v1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057141
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.di1.b1', '32.di1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.by1.a1', '4.bz1.a1'], 'contains': ['16.o1.a1', '16.s1.a1', '16.t1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3526, 7543, 8148, 1769, 3534, 7565, 8138, 1780], 'generators': [33, 4], 'label': '256.18790.8.w1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.w1.a1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.o1.a1', '16.s1.a1', '16.t1.a1'], 'normalizer': '1.a1.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: 26057142
    {'ambient': '256.18790', '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.g1.a1', '128.i1.a1', '128.e1.a1', '128.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.l1.a1', '4.m1.a1', '4.v1.a1', '4.w1.a1', '4.bg1.a1', '4.bi1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4311, 4371, 6814, 5822, 4321, 4385, 6805, 5836], 'generators': [33, 2, 36], 'label': '256.18790.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.l1.a1', '4.m1.a1', '4.v1.a1', '4.w1.a1', '4.bg1.a1', '4.bi1.a1'], '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: 26057143
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.by1.b1', '4.bz1.b1'], 'contains': ['16.o1.a1', '16.s1.b1', '16.t1.b1'], 'core': '8.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3526, 7543, 8552, 2194, 3534, 7565, 8542, 2208], 'generators': [97, 68], 'label': '256.18790.8.w1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.w1.b1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.o1.a1', '16.s1.b1', '16.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057144
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.by1.c1', '4.bz1.c1'], 'contains': ['16.o1.b1', '16.s1.a1', '16.t1.b1'], 'core': '8.w1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3526, 7543, 8411, 1982, 3534, 7565, 8400, 1994], 'generators': [97, 4], 'label': '256.18790.8.w1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.w1.c1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.o1.b1', '16.s1.a1', '16.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.w1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057145
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['32.di1.b1', '32.di1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.by1.d1', '4.bz1.d1'], 'contains': ['16.o1.b1', '16.s1.b1', '16.t1.a1'], 'core': '8.w1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3526, 7543, 8283, 2408, 3534, 7565, 8272, 2422], 'generators': [33, 68], 'label': '256.18790.8.w1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.w1.d1', 'normal_contained_in': ['4.d1.a1'], 'normal_contains': ['16.o1.b1', '16.s1.b1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.w1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057146
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bx1.a1', '4.ca1.a1'], 'contains': ['16.p1.a1', '16.q1.a1', '16.r1.a1', '16.eu1.a1', '16.ev1.a1'], 'core': '8.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7610, 2919, 3795, 6707, 7628, 2927, 3790, 6768], 'generators': [7, 32, 200], 'label': '256.18790.8.x1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': ['4.u1.a1'], 'normal_contains': ['16.p1.a1', '16.q1.a1', '16.r1.a1'], 'normalizer': '1.a1.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: 26057147
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bx1.b1', '4.ca1.b1'], 'contains': ['16.p1.a1', '16.q1.b1', '16.r1.b1', '16.eu1.b1', '16.ev1.b1'], 'core': '8.x1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7610, 2919, 4047, 7322, 7628, 2927, 4042, 7387], 'generators': [7, 48, 200], 'label': '256.18790.8.x1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.x1.b1', 'normal_contained_in': ['4.u1.a1'], 'normal_contains': ['16.p1.a1', '16.q1.b1', '16.r1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057148
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bx1.c1', '4.ca1.c1'], 'contains': ['16.p1.b1', '16.q1.a1', '16.r1.b1', '16.eu1.c1', '16.ev1.c1'], 'core': '8.x1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7610, 2919, 4122, 7629, 7628, 2927, 4117, 7696], 'generators': [23, 48, 200], 'label': '256.18790.8.x1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.x1.c1', 'normal_contained_in': ['4.u1.a1'], 'normal_contains': ['16.p1.b1', '16.q1.a1', '16.r1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.x1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057149
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['32.di1.a1', '32.di1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bx1.d1', '4.ca1.d1'], 'contains': ['16.p1.b1', '16.q1.b1', '16.r1.a1', '16.eu1.d1', '16.ev1.d1'], 'core': '8.x1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7610, 2919, 3720, 7014, 7628, 2927, 3715, 7078], 'generators': [23, 32, 200], 'label': '256.18790.8.x1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.x1.d1', 'normal_contained_in': ['4.u1.a1'], 'normal_contains': ['16.p1.b1', '16.q1.b1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.x1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.x1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057150
    {'ambient': '256.18790', '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.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.u1.a1', '16.v1.a1', '16.bb1.a1', '16.bd1.a1', '16.bh1.a1', '16.bk1.a1', '16.cd1.a1', '16.cf1.a1', '16.cf1.a2', '16.cf1.b1', '16.cf1.b2', '16.cy1.a1', '16.cy1.b1', '16.cy1.c1', '16.cy1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6195, -1, 4786, -1, 6210, -1, 4780, -1], 'generators': [37, 2, 24, 16], 'label': '256.18790.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '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}
  • id: 26057151
    {'ambient': '256.18790', '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.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.u1.a1', '16.w1.a1', '16.x1.a1', '16.be1.a1', '16.bf1.a1', '16.bl1.a1', '16.bo1.a1', '16.cg1.a1', '16.cg1.a2', '16.cg1.b1', '16.cg1.b2', '16.cz1.a1', '16.cz1.b1', '16.cz1.c1', '16.cz1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2469, -1, 214, -1, 2474, -1, 214, -1], 'generators': [37, 34, 24, 16], 'label': '256.18790.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.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: 26057152
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.v1.a1', '16.y1.a1', '16.ba1.a1', '16.bi1.a1', '16.bi1.b1', '16.br1.a1', '16.br1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [436, -1, 9782, -1, 437, -1, 9769, -1], 'generators': [1, 2, 24], 'label': '256.18790.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.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: 26057153
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '2.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.e1.a1', '128.e1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.q1.a1', '4.r1.a1', '4.x1.a1', '4.z1.a1', '4.bf1.a1', '4.bi1.a1'], 'core': '2.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4055, 6677, 6673, 4027, 4065, 6611, 6665, 4051], 'generators': [33, 34, 36], 'label': '256.18790.2.l1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.l1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.q1.a1', '4.r1.a1', '4.x1.a1', '4.z1.a1', '4.bf1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057154
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1'], 'contains': ['16.w1.a1', '16.ba1.a1', '16.bc1.a1', '16.bn1.a1', '16.bn1.b1', '16.ce1.a1', '16.ce1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [50, -1, 9446, -1, 50, -1, 9434, -1], 'generators': [1, 34, 24], 'label': '256.18790.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '8.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: 26057155
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1'], 'contains': ['16.x1.a1', '16.y1.a1', '16.z1.a1', '16.df1.a1', '16.df1.b1', '16.df1.c1', '16.df1.d1', '16.fg1.a1', '16.fg1.b1', '16.fg1.c1', '16.fg1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [990, -1, 9989, -1, 993, -1, 9976, -1], 'generators': [3, 4, 16, 128], 'label': '256.18790.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.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: 26057156
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1'], 'contains': ['16.z1.a1', '16.bb1.a1', '16.bc1.a1', '16.dr1.a1', '16.dr1.b1', '16.dr1.c1', '16.dr1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1145, -1, 9934, -1, 1148, -1, 9921, -1], 'generators': [35, 4, 16], 'label': '256.18790.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '8.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: 26057157
    {'ambient': '256.18790', '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.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.c1.a1', '16.bd1.a1', '16.bg1.a1', '16.bk1.a1', '16.bv1.a1', '16.ds1.a1', '16.ds1.b1', '16.ds1.c1', '16.ds1.d1', '16.dt1.a1', '16.dt1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7501, -1, 4432, -1, 7519, -1, 4427, -1], 'generators': [37, 2, 16, 64], 'label': '256.18790.8.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: 26057158
    {'ambient': '256.18790', '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': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.d1.a1', '16.be1.a1', '16.bg1.a1', '16.bl1.a1', '16.bp1.a1', '16.du1.a1', '16.du1.b1', '16.du1.c1', '16.du1.d1', '16.dv1.a1', '16.dv1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6485, -1, 307, -1, 6500, -1, 306, -1], 'generators': [37, 250, 16, 64], 'label': '256.18790.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.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: 26057159
    {'ambient': '256.18790', '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': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.e1.a1', '16.bf1.a1', '16.bg1.a1', '16.bo1.a1', '16.bp1.a1', '16.dw1.a1', '16.dw1.b1', '16.dw1.c1', '16.dw1.d1', '16.dx1.a1', '16.dx1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6575, -1, 610, -1, 6591, -1, 610, -1], 'generators': [37, 34, 16, 64], 'label': '256.18790.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.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: 26057160
    {'ambient': '256.18790', '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.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.f1.a1', '16.bg1.a1', '16.bh1.a1', '16.bv1.a1', '16.cd1.a1', '16.dy1.a1', '16.dy1.b1', '16.dy1.c1', '16.dy1.d1', '16.eb1.a1', '16.eb1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7348, -1, 4187, -1, 7365, -1, 4181, -1], 'generators': [37, 218, 16, 64], 'label': '256.18790.8.bh1.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.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: 26057161
    {'ambient': '256.18790', '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': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.g1.a1', '16.bg1.a1', '16.by1.a1', '16.dz1.a1', '16.dz1.b1', '16.dz1.c1', '16.dz1.d1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9122, -1, 2151, -1, 9144, -1, 2149, -1], 'generators': [5, 32, 16], 'label': '256.18790.8.bi1.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.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: 26057162
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.h1.a1', '16.bg1.a1', '16.by1.a1', '16.ea1.a1', '16.ea1.b1', '16.ea1.c1', '16.ea1.d1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9301, -1, 2404, -1, 9324, -1, 2400, -1], 'generators': [5, 248, 16], 'label': '256.18790.8.bj1.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.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: 26057163
    {'ambient': '256.18790', '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.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bn1.a1', '4.bn1.b1'], 'contains': ['16.b1.a1', '16.bd1.a1', '16.bh1.a1', '16.bj1.a1', '16.bz1.a1', '16.ec1.a1', '16.ec1.b1', '16.ed1.a1', '16.ed1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5141, -1, 4692, -1, 5153, -1, 4686, -1], 'generators': [37, 2, 216, 16], 'label': '256.18790.8.bk1.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.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: 26057164
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '2.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.i1.a1', '128.e1.a1', '128.e1.b1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.p1.a1', '4.q1.a1', '4.ba1.a1', '4.bb1.a1', '4.bd1.a1', '4.bg1.a1'], 'core': '2.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3248, 3736, 7048, 6128, 3256, 3747, 7037, 6211], 'generators': [1, 34, 4], 'label': '256.18790.2.m1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.m1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.o1.a1', '4.p1.a1', '4.q1.a1', '4.ba1.a1', '4.bb1.a1', '4.bd1.a1', '4.bg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057165
    {'ambient': '256.18790', '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': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bo1.a1', '4.bo1.b1'], 'contains': ['16.b1.a1', '16.be1.a1', '16.bf1.a1', '16.bm1.a1', '16.bq1.a1', '16.ee1.a1', '16.ee1.b1', '16.ef1.a1', '16.ef1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1288, -1, 122, -1, 1291, -1, 122, -1], 'generators': [37, 34, 216, 16], 'label': '256.18790.8.bl1.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.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: 26057166
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bn1.a1', '4.bn1.b1'], 'contains': ['16.b1.a1', '16.bt1.a1', '16.cc1.a1', '16.eg1.a1', '16.eg1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1463, -1, 6036, -1, 1467, -1, 6028, -1], 'generators': [37, 38, 16], 'label': '256.18790.8.bm1.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.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: 26057167
    {'ambient': '256.18790', '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.f1.a1', '4.bo1.a1', '4.bo1.b1'], 'contains': ['16.b1.a1', '16.ca1.a1', '16.cb1.a1', '16.eh1.a1', '16.eh1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2574, -1, 5337, -1, 2581, -1, 5331, -1], 'generators': [37, 6, 16], 'label': '256.18790.8.bn1.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.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: 26057168
    {'ambient': '256.18790', '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.j1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.j1.a1', '16.bi1.a1', '16.bj1.a1', '16.br1.a1', '16.bt1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 8710, -1, 356, -1, 8699, -1], 'generators': [1, 2, 216], 'label': '256.18790.8.bo1.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.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: 26057169
    {'ambient': '256.18790', '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.j1.a1', '4.bn1.b1', '4.bp1.b1'], 'contains': ['16.j1.b1', '16.bi1.b1', '16.bj1.a1', '16.br1.b1', '16.bt1.a1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [356, -1, 8748, -1, 356, -1, 8737, -1], 'generators': [65, 2, 216], 'label': '256.18790.8.bo1.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.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: 26057170
    {'ambient': '256.18790', '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.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bp1.a1', '4.bp1.b1'], 'contains': ['16.i1.a1', '16.bj1.a1', '16.bk1.a1', '16.bz1.a1', '16.cd1.a1', '16.ei1.a1', '16.ei1.b1', '16.ej1.a1', '16.ej1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5232, -1, 4981, -1, 5245, -1, 4975, -1], 'generators': [101, 2, 216, 16], 'label': '256.18790.8.bp1.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.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: 26057171
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bn1.a1', '4.bp1.b1'], 'contains': ['16.k1.a1', '16.bj1.a1', '16.cc1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1067, -1, 6492, -1, 1069, -1, 6484, -1], 'generators': [2, 36], 'label': '256.18790.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 26057172
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bn1.b1', '4.bp1.a1'], 'contains': ['16.k1.b1', '16.bj1.a1', '16.cc1.a1'], 'core': '16.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1067, -1, 6154, -1, 1069, -1, 6146, -1], 'generators': [2, 100], 'label': '256.18790.8.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057173
    {'ambient': '256.18790', '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.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.c1.a1', '16.bp1.a1', '16.by1.a1', '16.el1.a1', '16.el1.b1', '16.el1.c1', '16.el1.d1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9402, -1, 1949, -1, 9425, -1, 1946, -1], 'generators': [5, 2, 16], 'label': '256.18790.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.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: 26057174
    {'ambient': '256.18790', '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.j1.a1', '4.bq1.a1', '4.br1.a1'], 'contains': ['16.c1.a1', '16.bi1.a1', '16.bi1.b1', '16.bs1.a1', '16.bu1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4605, -1, 9612, -1, 4615, -1, 9600, -1], 'generators': [1, 2, 64], 'label': '256.18790.8.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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: 26057175
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '2.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': ['128.f1.a1', '128.g1.a1', '128.e1.a1', '128.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.s1.a1', '4.u1.a1', '4.v1.a1', '4.x1.a1', '4.y1.a1', '4.bb1.a1', '4.bc1.a1', '4.ca1.a1', '4.ca1.b1', '4.ca1.c1', '4.ca1.d1'], 'core': '2.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3490, 4053, 7196, 6533, 3499, 4066, 7118, 6573], 'generators': [3, 4, 32, 16], 'label': '256.18790.2.n1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.n1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.s1.a1', '4.u1.a1', '4.v1.a1', '4.x1.a1', '4.y1.a1', '4.bb1.a1', '4.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057176
    {'ambient': '256.18790', '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.l1.a1', '4.bq1.a1', '4.br1.a1'], 'contains': ['16.c1.a1', '16.bw1.a1', '16.bx1.a1', '16.en1.a1', '16.en1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6086, -1, 9312, -1, 6101, -1, 9301, -1], 'generators': [33, 2, 64], 'label': '256.18790.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.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: 26057177
    {'ambient': '256.18790', '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': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bs1.a1', '4.bs1.b1'], 'contains': ['16.i1.a1', '16.bl1.a1', '16.bm1.a1', '16.bo1.a1', '16.bq1.a1', '16.eo1.a1', '16.eo1.b1', '16.ep1.a1', '16.ep1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1379, -1, 477, -1, 1382, -1, 476, -1], 'generators': [101, 34, 216, 16], 'label': '256.18790.8.bu1.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.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: 26057178
    {'ambient': '256.18790', '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.p1.a1', '4.bo1.a1', '4.bs1.a1'], 'contains': ['16.j1.a1', '16.bm1.a1', '16.bn1.a1', '16.ca1.a1', '16.ce1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [138, -1, 7739, -1, 138, -1, 7729, -1], 'generators': [1, 34, 216], 'label': '256.18790.8.bv1.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.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: 26057179
    {'ambient': '256.18790', '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.p1.a1', '4.bo1.b1', '4.bs1.b1'], 'contains': ['16.j1.b1', '16.bm1.a1', '16.bn1.b1', '16.ca1.a1', '16.ce1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [138, -1, 7777, -1, 138, -1, 7768, -1], 'generators': [65, 34, 216], 'label': '256.18790.8.bv1.b1', '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.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: 26057180
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bo1.a1', '4.bs1.b1'], 'contains': ['16.k1.a1', '16.bm1.a1', '16.cb1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [516, -1, 5450, -1, 518, -1, 5443, -1], 'generators': [34, 36], 'label': '256.18790.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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: 26057181
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bo1.b1', '4.bs1.a1'], 'contains': ['16.k1.b1', '16.bm1.a1', '16.cb1.a1'], 'core': '16.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [516, -1, 5281, -1, 518, -1, 5274, -1], 'generators': [34, 100], 'label': '256.18790.8.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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: 26057182
    {'ambient': '256.18790', '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.bq1.a1', '4.bt1.a1'], 'contains': ['16.d1.a1', '16.bs1.a1', '16.bx1.a1', '16.eq1.a1', '16.eq1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4669, -1, 8971, -1, 4680, -1, 8959, -1], 'generators': [33, 250, 64], 'label': '256.18790.8.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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: 26057183
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.bq1.a1', '4.bt1.a1'], 'contains': ['16.d1.a1', '16.bn1.a1', '16.bn1.b1', '16.bu1.a1', '16.bw1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4501, -1, 9366, -1, 4512, -1, 9354, -1], 'generators': [1, 250, 64], 'label': '256.18790.8.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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: 26057184
    {'ambient': '256.18790', '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.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.d1.a1', '16.bv1.a1', '16.by1.a1', '16.es1.a1', '16.es1.b1', '16.es1.c1', '16.es1.d1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8677, -1, 1769, -1, 8698, -1, 1767, -1], 'generators': [5, 250, 16], 'label': '256.18790.8.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 26057185
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.f1.a1', '16.bp1.a1', '16.by1.a1', '16.et1.a1', '16.et1.b1', '16.et1.c1', '16.et1.d1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8801, -1, 1888, -1, 8822, -1, 1886, -1], 'generators': [5, 218, 16], 'label': '256.18790.8.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057186
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '2.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.f1.a1', '128.i1.a1', '128.e1.a1', '128.e1.b1', '128.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.t1.a1', '4.u1.a1', '4.w1.a1', '4.bd1.a1', '4.be1.a1', '4.bf1.a1', '4.bh1.a1'], 'core': '2.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3939, 4936, 6744, 5215, 3949, 4951, 6735, 5247], 'generators': [1, 6, 32], 'label': '256.18790.2.o1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.o1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.t1.a1', '4.u1.a1', '4.w1.a1', '4.bd1.a1', '4.be1.a1', '4.bf1.a1', '4.bh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057187
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.g1.a1', '16.bp1.a1', '16.bv1.a1', '16.eu1.a1', '16.eu1.b1', '16.eu1.c1', '16.eu1.d1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8212, -1, 2977, -1, 8232, -1, 2973, -1], 'generators': [7, 32, 16], 'label': '256.18790.8.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057188
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cc1', '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.u1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.h1.a1', '16.bp1.a1', '16.bv1.a1', '16.ev1.a1', '16.ev1.b1', '16.ev1.c1', '16.ev1.d1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8924, -1, 3153, -1, 8946, -1, 3149, -1], 'generators': [7, 248, 16], 'label': '256.18790.8.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057189
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cd1', '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.t1.a1', '4.bo1.a1', '4.bs1.a1'], 'contains': ['16.j1.a1', '16.bq1.a1', '16.cb1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [195, -1, 5712, -1, 196, -1, 5705, -1], 'generators': [1, 6], 'label': '256.18790.8.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057190
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cd1', '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.t1.a1', '4.bo1.b1', '4.bs1.b1'], 'contains': ['16.j1.b1', '16.bq1.a1', '16.cb1.a1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [195, -1, 5743, -1, 196, -1, 5736, -1], 'generators': [65, 6], 'label': '256.18790.8.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.cd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057191
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ce1', '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.v1.a1', '4.bo1.a1', '4.bs1.b1'], 'contains': ['16.k1.a1', '16.bq1.a1', '16.ca1.a1', '16.ew1.a1', '16.ew1.c1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [610, -1, 6285, -1, 611, -1, 6277, -1], 'generators': [35, 36, 16], 'label': '256.18790.8.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057192
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ce1', '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.v1.a1', '4.bo1.b1', '4.bs1.a1'], 'contains': ['16.k1.b1', '16.bq1.a1', '16.ca1.a1', '16.ew1.b1', '16.ew1.d1'], 'core': '16.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [610, -1, 6210, -1, 611, -1, 6202, -1], 'generators': [35, 100, 16], 'label': '256.18790.8.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.ce1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057193
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cf1', '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.bt1.a1', '4.bu1.a1'], 'contains': ['16.f1.a1', '16.br1.a1', '16.br1.b1', '16.bs1.a1', '16.bu1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4553, -1, 9581, -1, 4564, -1, 9568, -1], 'generators': [1, 218, 64], 'label': '256.18790.8.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057194
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cg1', '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.br1.a1', '4.bu1.a1'], 'contains': ['16.e1.a1', '16.bs1.a1', '16.bx1.a1', '16.fa1.a1', '16.fa1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5033, -1, 9032, -1, 5045, -1, 9020, -1], 'generators': [33, 34, 64], 'label': '256.18790.8.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057195
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ch1', '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.y1.a1', '4.br1.a1', '4.bt1.a1'], 'contains': ['16.g1.a1', '16.bs1.a1', '16.bw1.a1', '16.ex1.a1', '16.ex1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5747, -1, 7411, -1, 5761, -1, 7402, -1], 'generators': [3, 32, 16], 'label': '256.18790.8.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057196
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ci1', '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.y1.a1', '4.bq1.a1', '4.bu1.a1'], 'contains': ['16.h1.a1', '16.bs1.a1', '16.bw1.a1', '16.ey1.a1', '16.ey1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5870, -1, 7486, -1, 5885, -1, 7477, -1], 'generators': [3, 248, 16], 'label': '256.18790.8.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057197
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.h1.a1', '8.y1.a1', '8.be1.a1', '8.bh1.a1', '8.bk1.a1', '8.bp1.a1', '8.cs1.a1', '8.cs1.b1', '8.ct1.a1', '8.dk1.a1', '8.dk1.b1', '8.dl1.a1', '8.dl1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6273, 5454, 4715, 7752, 6288, 5470, 4709, 7799], 'generators': [37, 2, 216, 64, 16], 'label': '256.18790.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.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: 26057198
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cj1', '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.c1.a1', '4.bp1.a1', '4.bp1.b1'], 'contains': ['16.i1.a1', '16.bt1.a1', '16.cc1.a1', '16.fb1.a1', '16.fb1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1564, -1, 6096, -1, 1567, -1, 6089, -1], 'generators': [101, 38, 16], 'label': '256.18790.8.cj1.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.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057199
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ck1', '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.x1.a1', '4.bn1.a1', '4.bp1.b1'], 'contains': ['16.k1.a1', '16.bt1.a1', '16.bz1.a1', '16.ez1.a1', '16.ez1.c1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [785, -1, 7111, -1, 787, -1, 7102, -1], 'generators': [3, 36, 16], 'label': '256.18790.8.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057200
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ck1', '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.x1.a1', '4.bn1.b1', '4.bp1.a1'], 'contains': ['16.k1.b1', '16.bt1.a1', '16.bz1.a1', '16.ez1.b1', '16.ez1.d1'], 'core': '16.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [785, -1, 7036, -1, 787, -1, 7027, -1], 'generators': [3, 100, 16], 'label': '256.18790.8.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.ck1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057201
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cl1', '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.p1.a1', '4.br1.a1', '4.bu1.a1'], 'contains': ['16.e1.a1', '16.bu1.a1', '16.bw1.a1', '16.ce1.a1', '16.ce1.b1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4732, -1, 9398, -1, 4744, -1, 9385, -1], 'generators': [1, 34, 64], 'label': '256.18790.8.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057202
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.br1.a1', '4.bt1.a1'], 'contains': ['16.g1.a1', '16.bu1.a1', '16.bx1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5548, -1, 9092, -1, 5561, -1, 9081, -1], 'generators': [1, 32], 'label': '256.18790.8.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057203
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.bq1.a1', '4.bu1.a1'], 'contains': ['16.h1.a1', '16.bu1.a1', '16.bx1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5635, -1, 9145, -1, 5649, -1, 9134, -1], 'generators': [1, 248], 'label': '256.18790.8.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057204
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.e1.a1', '16.bv1.a1', '16.by1.a1', '16.fd1.a1', '16.fd1.b1', '16.fd1.c1', '16.fd1.d1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9032, -1, 2207, -1, 9054, -1, 2203, -1], 'generators': [5, 34, 16], 'label': '256.18790.8.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.co1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.co1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057205
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cp1', '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.bt1.a1', '4.bu1.a1'], 'contains': ['16.f1.a1', '16.bw1.a1', '16.bx1.a1', '16.fe1.a1', '16.fe1.b1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5979, -1, 9204, -1, 5993, -1, 9192, -1], 'generators': [33, 218, 64], 'label': '256.18790.8.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.cp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057206
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cq1', '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.f1.a1', '4.bs1.a1', '4.bs1.b1'], 'contains': ['16.i1.a1', '16.ca1.a1', '16.cb1.a1', '16.ff1.a1', '16.ff1.b1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2683, -1, 5403, -1, 2689, -1, 5396, -1], 'generators': [101, 6, 16], 'label': '256.18790.8.cq1.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.cq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057207
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cr1', '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.bd1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.j1.a1', '16.bz1.a1', '16.cc1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [698, -1, 6426, -1, 699, -1, 6418, -1], 'generators': [1, 38], 'label': '256.18790.8.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.cr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057208
    {'ambient': '256.18790', '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': '64.a1.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.d1.a1', '8.z1.a1', '8.bf1.a1', '8.bg1.a1', '8.bl1.a1', '8.bu1.a1', '8.cu1.a1', '8.cu1.b1', '8.cv1.a1', '8.dm1.a1', '8.dm1.b1', '8.dn1.a1', '8.dn1.b1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3717, 3193, 501, 8625, 3726, 3203, 500, 8678], 'generators': [37, 34, 216, 64, 16], 'label': '256.18790.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.c1.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: 26057209
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cr1', '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.bd1.a1', '4.bn1.b1', '4.bp1.b1'], 'contains': ['16.j1.b1', '16.bz1.a1', '16.cc1.a1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [698, -1, 6457, -1, 699, -1, 6449, -1], 'generators': [65, 38], 'label': '256.18790.8.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.cr1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cr1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057284
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ec1', '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.x1.a1', '4.ca1.b1', '4.ca1.d1'], 'contains': ['16.q1.b1', '16.dh1.a1', '16.dl1.a1', '16.ez1.c1', '16.ez1.d1'], 'core': '16.q1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1934, -1, 7336, -1, 1939, -1, 7327, -1], 'generators': [19, 36, 64], 'label': '256.18790.8.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ec1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ec1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057210
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cs1', '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.a1.a1', '4.bv1.a1', '4.bv1.b1'], 'contains': ['16.l1.a1', '16.cf1.a1', '16.cf1.a2', '16.ci1.a1', '16.cq1.a1', '16.ds1.a1', '16.ds1.b1', '16.dy1.a1', '16.dy1.b1', '16.ed1.a1', '16.ej1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7703, -1, 4308, -1, 7722, -1, 4303, -1], 'generators': [37, 2, 216, 64], 'label': '256.18790.8.cs1.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.cs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057211
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cs1', '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.a1.a1', '4.bv1.c1', '4.bv1.d1'], 'contains': ['16.l1.b1', '16.cf1.b1', '16.cf1.b2', '16.ci1.a1', '16.cq1.a1', '16.ds1.c1', '16.ds1.d1', '16.dy1.c1', '16.dy1.d1', '16.ed1.b1', '16.ej1.b1'], 'core': '16.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7703, -1, 4347, -1, 7722, -1, 4341, -1], 'generators': [53, 2, 216, 64], 'label': '256.18790.8.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057212
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ct1', '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.a1.a1'], 'contains': ['16.cf1.a1', '16.cf1.a2', '16.cf1.b1', '16.cf1.b2', '16.ch1.a1', '16.cj1.a1', '16.cu1.a1', '16.dt1.a1', '16.dt1.b1', '16.eb1.a1', '16.eb1.b1', '16.ec1.a1', '16.ec1.b1', '16.ei1.a1', '16.ei1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6273, -1, 4739, -1, 6288, -1, 4733, -1], 'generators': [37, 2, 24, 80], 'label': '256.18790.8.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.ct1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ct1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057213
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cu1', '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.b1.a1', '4.bv1.a1', '4.bv1.b1'], 'contains': ['16.l1.a1', '16.cg1.a1', '16.cg1.a2', '16.ck1.a1', '16.cm1.a1', '16.du1.a1', '16.du1.b1', '16.dw1.a1', '16.dw1.b1', '16.ef1.a1', '16.ep1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6654, -1, 260, -1, 6670, -1, 260, -1], 'generators': [37, 34, 216, 64], 'label': '256.18790.8.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057214
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cu1', '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.b1.a1', '4.bv1.c1', '4.bv1.d1'], 'contains': ['16.l1.b1', '16.cg1.b1', '16.cg1.b2', '16.ck1.a1', '16.cm1.a1', '16.du1.c1', '16.du1.d1', '16.dw1.c1', '16.dw1.d1', '16.ef1.b1', '16.ep1.b1'], 'core': '16.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6654, -1, 429, -1, 6670, -1, 429, -1], 'generators': [53, 34, 216, 64], 'label': '256.18790.8.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057215
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cv1', '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.b1.a1'], 'contains': ['16.cg1.a1', '16.cg1.a2', '16.cg1.b1', '16.cg1.b2', '16.ch1.a1', '16.cl1.a1', '16.cn1.a1', '16.dv1.a1', '16.dv1.b1', '16.dx1.a1', '16.dx1.b1', '16.ee1.a1', '16.ee1.b1', '16.eo1.a1', '16.eo1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2899, -1, 168, -1, 2907, -1, 168, -1], 'generators': [37, 34, 24, 80], 'label': '256.18790.8.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.cv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057216
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cw1', '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.c1.a1', '4.bw1.a1', '4.bw1.b1'], 'contains': ['16.l1.a1', '16.co1.a1', '16.ct1.a1', '16.eg1.a1', '16.fb1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 5563, -1, 4802, -1, 5556, -1], 'generators': [37, 38, 64], 'label': '256.18790.8.cw1.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.cw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057217
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cw1', '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.c1.a1', '4.bw1.c1', '4.bw1.d1'], 'contains': ['16.l1.b1', '16.co1.a1', '16.ct1.a1', '16.eg1.b1', '16.fb1.b1'], 'core': '16.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 5602, -1, 4802, -1, 5595, -1], 'generators': [53, 38, 64], 'label': '256.18790.8.cw1.b1', '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.cw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057218
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cx1', '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.f1.a1', '4.bw1.a1', '4.bw1.b1'], 'contains': ['16.l1.a1', '16.cr1.a1', '16.cs1.a1', '16.eh1.a1', '16.ff1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6404, -1, 5151, -1, 6419, -1, 5145, -1], 'generators': [37, 6, 64], 'label': '256.18790.8.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.cx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057219
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.o1.a1', '8.bm1.a1', '8.cj1.a1', '8.cw1.a1', '8.cw1.b1', '8.do1.a1', '8.do1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3391, 8268, 6145, 2671, 3399, 8293, 6137, 2687], 'generators': [37, 38, 16, 64], 'label': '256.18790.4.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.e1.a1', '8.o1.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: 26057220
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cx1', '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.f1.a1', '4.bw1.c1', '4.bw1.d1'], 'contains': ['16.l1.b1', '16.cr1.a1', '16.cs1.a1', '16.eh1.b1', '16.ff1.b1'], 'core': '16.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6404, -1, 5240, -1, 6419, -1, 5233, -1], 'generators': [53, 6, 64], 'label': '256.18790.8.cx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.cx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057221
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cy1', '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.h1.a1', '4.bv1.a1', '4.bv1.c1'], 'contains': ['16.m1.a1', '16.ci1.a1', '16.ck1.a1', '16.ek1.b1', '16.em1.a1', '16.er1.a1', '16.fc1.b1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9768, -1, 2578, -1, 9791, -1, 2574, -1], 'generators': [2, 32, 216], 'label': '256.18790.8.cy1.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.cy1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cy1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057222
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cy1', '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.h1.a1', '4.bv1.b1', '4.bv1.d1'], 'contains': ['16.m1.b1', '16.ci1.a1', '16.ck1.a1', '16.ek1.a1', '16.em1.b1', '16.er1.b1', '16.fc1.a1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9768, -1, 3250, -1, 9791, -1, 3246, -1], 'generators': [2, 48, 216], 'label': '256.18790.8.cy1.b1', '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.cy1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cy1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057223
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cz1', '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.bv1.a1', '4.bv1.d1'], 'contains': ['16.n1.a1', '16.ci1.a1', '16.cm1.a1', '16.el1.a1', '16.el1.c1', '16.et1.a1', '16.et1.c1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9535, -1, 3095, -1, 9558, -1, 3092, -1], 'generators': [5, 2, 216], 'label': '256.18790.8.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057224
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.cz1', '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.bv1.b1', '4.bv1.c1'], 'contains': ['16.n1.b1', '16.ci1.a1', '16.cm1.a1', '16.el1.b1', '16.el1.d1', '16.et1.b1', '16.et1.d1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9535, -1, 1236, -1, 9558, -1, 1234, -1], 'generators': [21, 2, 216], 'label': '256.18790.8.cz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.cz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057225
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.da1', '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'], 'contains': ['16.cj1.a1', '16.cv1.a1', '16.cx1.a1', '16.en1.a1', '16.en1.b1', '16.fe1.a1', '16.fe1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5401, -1, 9253, -1, 5414, -1, 9242, -1], 'generators': [33, 2, 24], 'label': '256.18790.8.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.da1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.da1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057226
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.db1', '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'], 'contains': ['16.cl1.a1', '16.cp1.a1', '16.cx1.a1', '16.eq1.a1', '16.eq1.b1', '16.fa1.a1', '16.fa1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3600, -1, 8841, -1, 3609, -1, 8829, -1], 'generators': [33, 34, 24], 'label': '256.18790.8.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '8.db1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.db1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057227
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dc1', '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.bv1.a1', '4.bv1.d1'], 'contains': ['16.n1.a1', '16.ck1.a1', '16.cq1.a1', '16.es1.a1', '16.es1.c1', '16.fd1.a1', '16.fd1.c1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8506, -1, 2256, -1, 8526, -1, 2253, -1], 'generators': [5, 34, 216], 'label': '256.18790.8.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057228
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dc1', '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.bv1.b1', '4.bv1.c1'], 'contains': ['16.n1.b1', '16.ck1.a1', '16.cq1.a1', '16.es1.b1', '16.es1.d1', '16.fd1.b1', '16.fd1.d1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8506, -1, 736, -1, 8526, -1, 735, -1], 'generators': [21, 34, 216], 'label': '256.18790.8.dc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057229
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dd1', '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.u1.a1', '4.bv1.a1', '4.bv1.c1'], 'contains': ['16.m1.a1', '16.cm1.a1', '16.cq1.a1', '16.eu1.a1', '16.eu1.d1', '16.ev1.b1', '16.ev1.c1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8408, -1, 2631, -1, 8428, -1, 2627, -1], 'generators': [7, 32, 216], 'label': '256.18790.8.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057230
    {'ambient': '256.18790', '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': ['128.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1', '4.h1.a1', '4.i1.a1', '4.q1.a1', '4.u1.a1', '4.bj1.a1', '4.bk1.a1', '4.bl1.a1', '4.bm1.a1', '4.bv1.a1', '4.bv1.b1', '4.bv1.c1', '4.bv1.d1', '4.bx1.a1', '4.bx1.b1', '4.bx1.c1', '4.bx1.d1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7866, 2423, 2483, 8494, 7884, 2430, 2480, 8546], 'generators': [5, 2, 32, 16, 216], 'label': '256.18790.2.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.i1.a1', '4.h1.a1', '4.u1.a1', '4.q1.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: 26057231
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.l1.a1', '8.w1.a1', '8.w1.b1', '8.w1.c1', '8.w1.d1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3939, 9651, 8148, 498, 3948, 9680, 8138, 501], 'generators': [33, 4, 64], 'label': '256.18790.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.f1.a1', '8.l1.a1', '8.w1.d1', '8.w1.c1', '8.w1.b1', '8.w1.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: 26057232
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dd1', '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.u1.a1', '4.bv1.b1', '4.bv1.d1'], 'contains': ['16.m1.b1', '16.cm1.a1', '16.cq1.a1', '16.eu1.b1', '16.eu1.c1', '16.ev1.a1', '16.ev1.d1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8408, -1, 3304, -1, 8428, -1, 3299, -1], 'generators': [7, 48, 216], 'label': '256.18790.8.dd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057233
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.de1', '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.v1.a1'], 'contains': ['16.cn1.a1', '16.cv1.a1', '16.cw1.a1', '16.ew1.a1', '16.ew1.b1', '16.ew1.c1', '16.ew1.d1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1687, -1, 6961, -1, 1691, -1, 6952, -1], 'generators': [35, 36, 80], 'label': '256.18790.8.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '8.de1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.de1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057234
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.df1', '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.y1.a1', '4.bw1.a1', '4.bw1.c1'], 'contains': ['16.m1.a1', '16.co1.a1', '16.cr1.a1', '16.ex1.a1', '16.ey1.b1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6747, -1, 5507, -1, 6763, -1, 5500, -1], 'generators': [3, 32, 216], 'label': '256.18790.8.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.df1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.df1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057235
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.df1', '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.y1.a1', '4.bw1.b1', '4.bw1.d1'], 'contains': ['16.m1.b1', '16.co1.a1', '16.cr1.a1', '16.ex1.b1', '16.ey1.a1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6747, -1, 5659, -1, 6763, -1, 5651, -1], 'generators': [3, 48, 216], 'label': '256.18790.8.df1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.df1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.df1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057236
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dg1', '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.z1.a1', '4.bw1.a1', '4.bw1.d1'], 'contains': ['16.n1.a1', '16.co1.a1', '16.cs1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6934, -1, 5110, -1, 6950, -1, 5104, -1], 'generators': [5, 6], 'label': '256.18790.8.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.dg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057237
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dg1', '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.z1.a1', '4.bw1.b1', '4.bw1.c1'], 'contains': ['16.n1.b1', '16.co1.a1', '16.cs1.a1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6934, -1, 5028, -1, 6950, -1, 5021, -1], 'generators': [21, 6], 'label': '256.18790.8.dg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.dg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057238
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dh1', '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.x1.a1'], 'contains': ['16.cp1.a1', '16.cu1.a1', '16.cw1.a1', '16.ez1.a1', '16.ez1.b1', '16.ez1.c1', '16.ez1.d1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2197, -1, 7561, -1, 2203, -1, 7551, -1], 'generators': [3, 36, 80], 'label': '256.18790.8.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '8.dh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057239
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.di1', '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.bg1.a1', '4.bw1.a1', '4.bw1.d1'], 'contains': ['16.n1.a1', '16.cr1.a1', '16.ct1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7142, -1, 5196, -1, 7159, -1, 5189, -1], 'generators': [5, 38], 'label': '256.18790.8.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.di1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057240
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.di1', '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.bg1.a1', '4.bw1.b1', '4.bw1.c1'], 'contains': ['16.n1.b1', '16.cr1.a1', '16.ct1.a1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7142, -1, 5069, -1, 7159, -1, 5063, -1], 'generators': [21, 38], 'label': '256.18790.8.di1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.di1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057241
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dj1', '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.bh1.a1', '4.bw1.a1', '4.bw1.c1'], 'contains': ['16.m1.a1', '16.cs1.a1', '16.ct1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6991, -1, 4831, -1, 7008, -1, 4825, -1], 'generators': [6, 32], 'label': '256.18790.8.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.dj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057242
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.k1.a1', '8.p1.a1', '8.p1.b1', '8.u1.a1', '8.u1.b1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [944, 9897, 6076, 743, 946, 9926, 6069, 748], 'generators': [1, 36, 64], 'label': '256.18790.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.g1.a1', '8.k1.a1', '8.p1.a1', '8.p1.b1', '8.u1.a1', '8.u1.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: 26057243
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dj1', '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.bh1.a1', '4.bw1.b1', '4.bw1.d1'], 'contains': ['16.m1.b1', '16.cs1.a1', '16.ct1.a1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6991, -1, 4862, -1, 7008, -1, 4856, -1], 'generators': [6, 48], 'label': '256.18790.8.dj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.dj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057244
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dk1', '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.a1.a1', '4.bx1.a1', '4.bx1.c1'], 'contains': ['16.q1.a1', '16.cy1.a1', '16.cy1.c1', '16.da1.a1', '16.db1.a1', '16.ds1.a1', '16.ds1.c1', '16.dy1.a1', '16.dy1.c1', '16.ec1.a1', '16.ei1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7423, -1, 4480, -1, 7441, -1, 4474, -1], 'generators': [53, 2, 200, 64], 'label': '256.18790.8.dk1.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.dk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057245
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dk1', '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.a1.a1', '4.bx1.b1', '4.bx1.d1'], 'contains': ['16.q1.b1', '16.cy1.b1', '16.cy1.d1', '16.da1.a1', '16.db1.a1', '16.ds1.b1', '16.ds1.d1', '16.dy1.b1', '16.dy1.d1', '16.ec1.b1', '16.ei1.b1'], 'core': '16.q1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7423, -1, 4385, -1, 7441, -1, 4379, -1], 'generators': [37, 2, 200, 64], 'label': '256.18790.8.dk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dk1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dk1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057246
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dl1', '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.a1.a1', '4.by1.a1', '4.by1.b1'], 'contains': ['16.o1.a1', '16.cy1.a1', '16.cy1.b1', '16.dc1.a1', '16.dn1.a1', '16.dt1.a1', '16.eb1.a1', '16.ed1.a1', '16.ej1.b1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6336, -1, 4935, -1, 6352, -1, 4929, -1], 'generators': [37, 2, 216, 80], 'label': '256.18790.8.dl1.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.dl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057247
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dl1', '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.a1.a1', '4.by1.c1', '4.by1.d1'], 'contains': ['16.o1.b1', '16.cy1.c1', '16.cy1.d1', '16.dc1.a1', '16.dn1.a1', '16.dt1.b1', '16.eb1.b1', '16.ed1.b1', '16.ej1.a1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6336, -1, 4897, -1, 6352, -1, 4891, -1], 'generators': [101, 2, 216, 80], 'label': '256.18790.8.dl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.dl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057248
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dm1', '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.b1.a1', '4.bx1.a1', '4.bx1.b1'], 'contains': ['16.p1.a1', '16.cz1.a1', '16.cz1.c1', '16.da1.a1', '16.dd1.a1', '16.du1.a1', '16.du1.c1', '16.dw1.a1', '16.dw1.c1', '16.ee1.a1', '16.eo1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4939, -1, 563, -1, 4951, -1, 562, -1], 'generators': [53, 34, 200, 64], 'label': '256.18790.8.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057249
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dm1', '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.b1.a1', '4.bx1.c1', '4.bx1.d1'], 'contains': ['16.p1.b1', '16.cz1.b1', '16.cz1.d1', '16.da1.a1', '16.dd1.a1', '16.du1.b1', '16.du1.d1', '16.dw1.b1', '16.dw1.d1', '16.ee1.b1', '16.eo1.b1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4939, -1, 391, -1, 4951, -1, 391, -1], 'generators': [37, 34, 200, 64], 'label': '256.18790.8.dm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057250
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dn1', '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.b1.a1', '4.bz1.a1', '4.bz1.b1'], 'contains': ['16.o1.a1', '16.cz1.a1', '16.cz1.b1', '16.de1.a1', '16.dg1.a1', '16.dv1.a1', '16.dx1.a1', '16.ef1.a1', '16.ep1.b1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2963, -1, 525, -1, 2970, -1, 524, -1], 'generators': [37, 34, 216, 80], 'label': '256.18790.8.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057251
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dn1', '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.b1.a1', '4.bz1.c1', '4.bz1.d1'], 'contains': ['16.o1.b1', '16.cz1.c1', '16.cz1.d1', '16.de1.a1', '16.dg1.a1', '16.dv1.b1', '16.dx1.b1', '16.ef1.b1', '16.ep1.a1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2963, -1, 353, -1, 2970, -1, 352, -1], 'generators': [101, 34, 216, 80], 'label': '256.18790.8.dn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057252
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.do1', '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.c1.a1', '4.bz1.a1', '4.bz1.b1'], 'contains': ['16.o1.a1', '16.di1.a1', '16.dq1.a1', '16.eg1.a1', '16.fb1.b1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3026, -1, 6905, -1, 3033, -1, 6895, -1], 'generators': [37, 38, 80], 'label': '256.18790.8.do1.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.do1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.do1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057253
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.n1.a1', '8.bn1.a1', '8.cq1.a1', '8.cx1.a1', '8.cx1.b1', '8.dq1.a1', '8.dq1.b1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4251, 3850, 5671, 1003, 4261, 3861, 5664, 1009], 'generators': [37, 6, 16, 64], 'label': '256.18790.4.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.i1.a1', '8.n1.a1'], '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: 26057254
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.do1', '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.c1.a1', '4.bz1.c1', '4.bz1.d1'], 'contains': ['16.o1.b1', '16.di1.a1', '16.dq1.a1', '16.eg1.b1', '16.fb1.a1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3026, -1, 6865, -1, 3033, -1, 6857, -1], 'generators': [101, 38, 80], 'label': '256.18790.8.do1.b1', '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.do1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.do1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057255
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bx1.a1', '4.bx1.d1'], 'contains': ['16.r1.a1', '16.da1.a1', '16.dm1.a1', '16.dz1.a1', '16.dz1.c1', '16.ea1.a1', '16.ea1.c1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9203, -1, 2033, -1, 9224, -1, 2030, -1], 'generators': [5, 32, 200], 'label': '256.18790.8.dp1.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.dp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057256
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bx1.b1', '4.bx1.c1'], 'contains': ['16.r1.b1', '16.da1.a1', '16.dm1.a1', '16.dz1.b1', '16.dz1.d1', '16.ea1.b1', '16.ea1.d1'], 'core': '16.r1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9203, -1, 3212, -1, 9224, -1, 3208, -1], 'generators': [5, 48, 200], 'label': '256.18790.8.dp1.b1', '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.dp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057257
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dq1', '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.f1.a1', '4.by1.a1', '4.by1.b1'], 'contains': ['16.o1.a1', '16.do1.a1', '16.dp1.a1', '16.eh1.a1', '16.ff1.b1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4366, -1, 6388, -1, 4377, -1, 6380, -1], 'generators': [37, 6, 80], 'label': '256.18790.8.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.dq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057258
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dq1', '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.f1.a1', '4.by1.c1', '4.by1.d1'], 'contains': ['16.o1.b1', '16.do1.a1', '16.dp1.a1', '16.eh1.b1', '16.ff1.a1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4366, -1, 6345, -1, 4377, -1, 6336, -1], 'generators': [101, 6, 80], 'label': '256.18790.8.dq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.dq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057259
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dr1', '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.h1.a1', '4.bx1.a1', '4.bx1.d1'], 'contains': ['16.r1.a1', '16.db1.a1', '16.dd1.a1', '16.ek1.a1', '16.em1.a1', '16.er1.a1', '16.fc1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9717, -1, 2071, -1, 9740, -1, 2068, -1], 'generators': [2, 32, 200], 'label': '256.18790.8.dr1.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.dr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057260
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dr1', '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.h1.a1', '4.bx1.b1', '4.bx1.c1'], 'contains': ['16.r1.b1', '16.db1.a1', '16.dd1.a1', '16.ek1.b1', '16.em1.b1', '16.er1.b1', '16.fc1.b1'], 'core': '16.r1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9717, -1, 3357, -1, 9740, -1, 3353, -1], 'generators': [2, 48, 200], 'label': '256.18790.8.dr1.b1', '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.dr1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dr1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057261
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ds1', '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.bx1.a1', '4.bx1.b1'], 'contains': ['16.p1.a1', '16.db1.a1', '16.dm1.a1', '16.el1.a1', '16.el1.b1', '16.et1.a1', '16.et1.b1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9472, -1, 2806, -1, 9495, -1, 2803, -1], 'generators': [21, 2, 200], 'label': '256.18790.8.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ds1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ds1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057262
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ds1', '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.bx1.c1', '4.bx1.d1'], 'contains': ['16.p1.b1', '16.db1.a1', '16.dm1.a1', '16.el1.c1', '16.el1.d1', '16.et1.c1', '16.et1.d1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9472, -1, 2919, -1, 9495, -1, 2916, -1], 'generators': [5, 2, 200], 'label': '256.18790.8.ds1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ds1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ds1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057263
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dt1', '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.k1.a1', '4.by1.a1', '4.by1.c1'], 'contains': ['16.s1.a1', '16.dc1.a1', '16.dp1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4865, -1, 8501, -1, 4877, -1, 8490, -1], 'generators': [2, 4], 'label': '256.18790.8.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.dt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057264
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.m1.a1', '8.v1.a1', '8.v1.b1', '8.v1.c1', '8.v1.d1', '8.bi1.a1', '8.bj1.a1', '8.dp1.a1', '8.dp1.b1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7804, 396, 3461, 164, 7823, 398, 3457, 164], 'generators': [5, 32, 216, 16], 'label': '256.18790.4.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.j1.a1', '8.m1.a1', '8.v1.d1', '8.v1.c1', '8.v1.b1', '8.v1.a1'], '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: 26057265
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dt1', '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.k1.a1', '4.by1.b1', '4.by1.d1'], 'contains': ['16.s1.b1', '16.dc1.a1', '16.dp1.a1'], 'core': '16.s1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4865, -1, 8605, -1, 4877, -1, 8594, -1], 'generators': [2, 68], 'label': '256.18790.8.dt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.dt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057266
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.du1', '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.by1.a1', '4.by1.d1'], 'contains': ['16.t1.a1', '16.dc1.a1', '16.do1.a1', '16.en1.a1', '16.fe1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5473, -1, 8882, -1, 5486, -1, 8870, -1], 'generators': [33, 2, 216], 'label': '256.18790.8.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.du1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.du1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057267
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.du1', '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.by1.b1', '4.by1.c1'], 'contains': ['16.t1.b1', '16.dc1.a1', '16.do1.a1', '16.en1.b1', '16.fe1.b1'], 'core': '16.t1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5473, -1, 8925, -1, 5486, -1, 8914, -1], 'generators': [97, 2, 216], 'label': '256.18790.8.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.du1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.du1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057268
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dv1', '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.bz1.a1', '4.bz1.d1'], 'contains': ['16.t1.a1', '16.de1.a1', '16.di1.a1', '16.eq1.a1', '16.fa1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3327, -1, 8238, -1, 3335, -1, 8227, -1], 'generators': [33, 34, 216], 'label': '256.18790.8.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057269
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dv1', '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.bz1.b1', '4.bz1.c1'], 'contains': ['16.t1.b1', '16.de1.a1', '16.di1.a1', '16.eq1.b1', '16.fa1.b1'], 'core': '16.t1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3327, -1, 8456, -1, 3335, -1, 8445, -1], 'generators': [97, 34, 216], 'label': '256.18790.8.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057270
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dw1', '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.bx1.a1', '4.bx1.c1'], 'contains': ['16.q1.a1', '16.dd1.a1', '16.dm1.a1', '16.es1.a1', '16.es1.b1', '16.fd1.a1', '16.fd1.b1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8311, -1, 1829, -1, 8330, -1, 1826, -1], 'generators': [21, 34, 200], 'label': '256.18790.8.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057271
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dw1', '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.bx1.b1', '4.bx1.d1'], 'contains': ['16.q1.b1', '16.dd1.a1', '16.dm1.a1', '16.es1.c1', '16.es1.d1', '16.fd1.c1', '16.fd1.d1'], 'core': '16.q1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8311, -1, 1648, -1, 8330, -1, 1645, -1], 'generators': [5, 34, 200], 'label': '256.18790.8.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.dw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057272
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dx1', '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.o1.a1', '4.bz1.a1', '4.bz1.c1'], 'contains': ['16.s1.a1', '16.de1.a1', '16.dq1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3100, -1, 7870, -1, 3108, -1, 7859, -1], 'generators': [34, 4], 'label': '256.18790.8.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057273
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dx1', '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.o1.a1', '4.bz1.b1', '4.bz1.d1'], 'contains': ['16.s1.b1', '16.de1.a1', '16.dq1.a1'], 'core': '16.s1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3100, -1, 7921, -1, 3108, -1, 7911, -1], 'generators': [34, 68], 'label': '256.18790.8.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057274
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dy1', '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.s1.a1', '4.ca1.a1', '4.ca1.b1'], 'contains': ['16.p1.a1', '16.df1.a1', '16.df1.b1', '16.dh1.a1', '16.dj1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1217, -1, 9858, -1, 1221, -1, 9846, -1], 'generators': [3, 4, 64], 'label': '256.18790.8.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.dy1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dy1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057275
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.j1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1', '8.t1.a1', '8.cy1.a1', '8.cy1.b1', '8.dr1.a1', '8.dr1.b1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7686, 103, 3750, 9836, 7705, 104, 3746, 9896], 'generators': [2, 32, 216, 16], 'label': '256.18790.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.j1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1', '8.t1.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: 26057276
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dy1', '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.s1.a1', '4.ca1.c1', '4.ca1.d1'], 'contains': ['16.p1.b1', '16.df1.c1', '16.df1.d1', '16.dh1.a1', '16.dj1.a1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1217, -1, 9827, -1, 1221, -1, 9815, -1], 'generators': [19, 4, 64], 'label': '256.18790.8.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.dy1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dy1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057277
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dz1', '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.s1.a1', '4.bz1.a1', '4.bz1.c1'], 'contains': ['16.s1.a1', '16.df1.a1', '16.df1.c1', '16.dg1.a1', '16.di1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2022, -1, 9705, -1, 2027, -1, 9693, -1], 'generators': [3, 4, 80], 'label': '256.18790.8.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057278
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.dz1', '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.s1.a1', '4.bz1.b1', '4.bz1.d1'], 'contains': ['16.s1.b1', '16.df1.b1', '16.df1.d1', '16.dg1.a1', '16.di1.a1'], 'core': '16.s1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2022, -1, 9889, -1, 2027, -1, 9877, -1], 'generators': [3, 68, 80], 'label': '256.18790.8.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.dz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057279
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ea1', '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.v1.a1', '4.ca1.a1', '4.ca1.b1'], 'contains': ['16.p1.a1', '16.dk1.a1', '16.dl1.a1', '16.ew1.a1', '16.ew1.b1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1811, -1, 7260, -1, 1815, -1, 7252, -1], 'generators': [35, 36, 64], 'label': '256.18790.8.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ea1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ea1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057280
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ea1', '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.v1.a1', '4.ca1.c1', '4.ca1.d1'], 'contains': ['16.p1.b1', '16.dk1.a1', '16.dl1.a1', '16.ew1.c1', '16.ew1.d1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1811, -1, 7186, -1, 1815, -1, 7177, -1], 'generators': [51, 36, 64], 'label': '256.18790.8.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ea1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ea1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057281
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eb1', '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.w1.a1', '4.bz1.a1', '4.bz1.d1'], 'contains': ['16.t1.a1', '16.dg1.a1', '16.dq1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3264, -1, 8021, -1, 3272, -1, 8010, -1], 'generators': [33, 38], 'label': '256.18790.8.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.eb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057282
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eb1', '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.w1.a1', '4.bz1.b1', '4.bz1.c1'], 'contains': ['16.t1.b1', '16.dg1.a1', '16.dq1.a1'], 'core': '16.t1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3264, -1, 8059, -1, 3272, -1, 8048, -1], 'generators': [97, 38], 'label': '256.18790.8.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.eb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057283
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ec1', '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.x1.a1', '4.ca1.a1', '4.ca1.c1'], 'contains': ['16.q1.a1', '16.dh1.a1', '16.dl1.a1', '16.ez1.a1', '16.ez1.b1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1934, -1, 7683, -1, 1939, -1, 7673, -1], 'generators': [3, 36, 64], 'label': '256.18790.8.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ec1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ec1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057285
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ed1', '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.y1.a1', '4.ca1.a1', '4.ca1.d1'], 'contains': ['16.r1.a1', '16.dh1.a1', '16.dk1.a1', '16.ex1.a1', '16.ey1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3927, -1, 6735, -1, 3937, -1, 6726, -1], 'generators': [3, 32, 200], 'label': '256.18790.8.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ed1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ed1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057286
    {'ambient': '256.18790', '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.a1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.m1.a1', '8.br1.a1', '8.ca1.a1', '8.cz1.a1', '8.cz1.b1', '8.ds1.a1', '8.ds1.b1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7927, 2931, 3008, 8364, 7946, 2940, 3004, 8415], 'generators': [5, 2, 216, 16], 'label': '256.18790.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.m1.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: 26057287
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ed1', '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.y1.a1', '4.ca1.b1', '4.ca1.c1'], 'contains': ['16.r1.b1', '16.dh1.a1', '16.dk1.a1', '16.ex1.b1', '16.ey1.b1'], 'core': '16.r1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3927, -1, 6809, -1, 3937, -1, 6800, -1], 'generators': [3, 48, 200], 'label': '256.18790.8.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ed1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ed1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057288
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ee1', '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.bb1.a1', '4.ca1.a1', '4.ca1.c1'], 'contains': ['16.q1.a1', '16.dj1.a1', '16.dk1.a1', '16.dr1.a1', '16.dr1.c1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2842, -1, 9674, -1, 2849, -1, 9662, -1], 'generators': [35, 4, 64], 'label': '256.18790.8.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ee1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ee1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057289
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ee1', '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.bb1.a1', '4.ca1.b1', '4.ca1.d1'], 'contains': ['16.q1.b1', '16.dj1.a1', '16.dk1.a1', '16.dr1.b1', '16.dr1.d1'], 'core': '16.q1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2842, -1, 9643, -1, 2849, -1, 9631, -1], 'generators': [51, 4, 64], 'label': '256.18790.8.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ee1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ee1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057290
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.ca1.a1', '4.ca1.d1'], 'contains': ['16.r1.a1', '16.dj1.a1', '16.dl1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2298, -1, 7621, -1, 2303, -1, 7612, -1], 'generators': [4, 32], 'label': '256.18790.8.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ef1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ef1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057291
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.ca1.b1', '4.ca1.c1'], 'contains': ['16.r1.b1', '16.dj1.a1', '16.dl1.a1'], 'core': '16.r1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2298, -1, 7820, -1, 2303, -1, 7810, -1], 'generators': [4, 48], 'label': '256.18790.8.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '8.ef1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ef1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057292
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eg1', '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.bb1.a1', '4.by1.a1', '4.by1.c1'], 'contains': ['16.s1.a1', '16.dn1.a1', '16.do1.a1', '16.dr1.a1', '16.dr1.b1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3658, -1, 9496, -1, 3667, -1, 9484, -1], 'generators': [35, 4, 80], 'label': '256.18790.8.eg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.eg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057293
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eg1', '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.bb1.a1', '4.by1.b1', '4.by1.d1'], 'contains': ['16.s1.b1', '16.dn1.a1', '16.do1.a1', '16.dr1.c1', '16.dr1.d1'], 'core': '16.s1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3658, -1, 9737, -1, 3667, -1, 9724, -1], 'generators': [35, 68, 80], 'label': '256.18790.8.eg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.eg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057294
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eh1', '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.bf1.a1', '4.by1.a1', '4.by1.d1'], 'contains': ['16.t1.a1', '16.dn1.a1', '16.dp1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4439, -1, 8100, -1, 4450, -1, 8090, -1], 'generators': [33, 6], 'label': '256.18790.8.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.eh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057295
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.eh1', '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.bf1.a1', '4.by1.b1', '4.by1.c1'], 'contains': ['16.t1.b1', '16.dn1.a1', '16.dp1.a1'], 'core': '16.t1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4439, -1, 8196, -1, 4450, -1, 8186, -1], 'generators': [97, 6], 'label': '256.18790.8.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.eh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.eh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057296
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.b1', '4.bx1.a1'], 'contains': ['16.ds1.a1', '16.du1.a1', '16.ea1.a1', '16.ek1.a1', '16.el1.b1', '16.es1.b1', '16.ev1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 996, -1, 9973, -1, 995, -1], 'generators': [21, 2, 232], 'label': '256.18790.8.ei1.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': '8.ei1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057297
    {'ambient': '256.18790', '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': ['64.bd1.c1', '64.bd1.d1', '64.bd1.b1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.g1.a1', '8.ba1.a1', '8.bo1.a1', '8.bo1.b1', '8.bs1.a1', '8.cf1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2792, 6341, 9028, 6809, 2799, 6360, 9017, 6851], 'generators': [1, 2, 216, 64], 'label': '256.18790.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.b1.a1', '2.j1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.g1.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: 26057298
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.a1', '4.bx1.b1'], 'contains': ['16.ds1.b1', '16.du1.a1', '16.ea1.b1', '16.ek1.b1', '16.el1.a1', '16.es1.c1', '16.ev1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 2460, -1, 9973, -1, 2457, -1], 'generators': [221, 2, 248], 'label': '256.18790.8.ei1.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': '8.ei1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057299
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.a1', '4.bx1.c1'], 'contains': ['16.ds1.a1', '16.du1.b1', '16.ea1.b1', '16.ek1.b1', '16.el1.c1', '16.es1.a1', '16.ev1.c1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 2542, -1, 9973, -1, 2539, -1], 'generators': [5, 2, 248], 'label': '256.18790.8.ei1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057300
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.b1', '4.bx1.d1'], 'contains': ['16.ds1.b1', '16.du1.b1', '16.ea1.a1', '16.ek1.a1', '16.el1.d1', '16.es1.d1', '16.ev1.d1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 915, -1, 9973, -1, 913, -1], 'generators': [205, 2, 232], 'label': '256.18790.8.ei1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057301
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.d1', '4.bx1.a1'], 'contains': ['16.ds1.c1', '16.du1.c1', '16.ea1.c1', '16.ek1.a1', '16.el1.a1', '16.es1.a1', '16.ev1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 2106, -1, 9973, -1, 2103, -1], 'generators': [221, 2, 232], 'label': '256.18790.8.ei1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057302
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.c1', '4.bx1.b1'], 'contains': ['16.ds1.d1', '16.du1.c1', '16.ea1.d1', '16.ek1.b1', '16.el1.b1', '16.es1.d1', '16.ev1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 1079, -1, 9973, -1, 1077, -1], 'generators': [21, 2, 248], 'label': '256.18790.8.ei1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057303
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.c1', '4.bx1.c1'], 'contains': ['16.ds1.c1', '16.du1.d1', '16.ea1.d1', '16.ek1.b1', '16.el1.d1', '16.es1.b1', '16.ev1.c1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 1349, -1, 9973, -1, 1347, -1], 'generators': [205, 2, 248], 'label': '256.18790.8.ei1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057304
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ei1', '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.bj1.a1', '4.bv1.d1', '4.bx1.d1'], 'contains': ['16.ds1.d1', '16.du1.d1', '16.ea1.c1', '16.ek1.a1', '16.el1.c1', '16.es1.c1', '16.ev1.d1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9950, -1, 1992, -1, 9973, -1, 1989, -1], 'generators': [5, 2, 232], 'label': '256.18790.8.ei1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ei1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ei1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057305
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.a1', '4.bx1.a1'], 'contains': ['16.ds1.a1', '16.dw1.a1', '16.dz1.a1', '16.el1.a1', '16.em1.a1', '16.eu1.a1', '16.fd1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 1716, -1, 9916, -1, 1714, -1], 'generators': [221, 2, 32], 'label': '256.18790.8.ej1.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': '8.ej1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057306
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.b1', '4.bx1.b1'], 'contains': ['16.ds1.b1', '16.dw1.a1', '16.dz1.b1', '16.el1.b1', '16.em1.b1', '16.eu1.b1', '16.fd1.d1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 1610, -1, 9916, -1, 1608, -1], 'generators': [21, 2, 48], 'label': '256.18790.8.ej1.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': '8.ej1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057307
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.b1', '4.bx1.c1'], 'contains': ['16.ds1.a1', '16.dw1.b1', '16.dz1.b1', '16.el1.d1', '16.em1.b1', '16.eu1.c1', '16.fd1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 1685, -1, 9916, -1, 1683, -1], 'generators': [205, 2, 48], 'label': '256.18790.8.ej1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057308
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': ['64.bd1.a1', '64.bd1.b1', '64.bd1.c1', '64.bd1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.n1.a1', '8.dt1.a1', '8.dt1.b1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4526, 7384, 8365, 1598, 4538, 7406, 8354, 1608], 'generators': [2, 4, 64], 'label': '256.18790.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.c1.a1', '2.j1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.n1.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: 26057309
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.a1', '4.bx1.d1'], 'contains': ['16.ds1.b1', '16.dw1.b1', '16.dz1.a1', '16.el1.c1', '16.em1.a1', '16.eu1.d1', '16.fd1.c1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 1534, -1, 9916, -1, 1532, -1], 'generators': [5, 2, 32], 'label': '256.18790.8.ej1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057310
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.c1', '4.bx1.a1'], 'contains': ['16.ds1.c1', '16.dw1.c1', '16.dz1.c1', '16.el1.b1', '16.em1.a1', '16.eu1.a1', '16.fd1.b1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 880, -1, 9916, -1, 878, -1], 'generators': [21, 2, 32], 'label': '256.18790.8.ej1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057311
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.d1', '4.bx1.b1'], 'contains': ['16.ds1.d1', '16.dw1.c1', '16.dz1.d1', '16.el1.a1', '16.em1.b1', '16.eu1.b1', '16.fd1.c1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 3030, -1, 9916, -1, 3026, -1], 'generators': [221, 2, 48], 'label': '256.18790.8.ej1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057312
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.d1', '4.bx1.c1'], 'contains': ['16.ds1.c1', '16.dw1.d1', '16.dz1.d1', '16.el1.c1', '16.em1.b1', '16.eu1.c1', '16.fd1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 3061, -1, 9916, -1, 3057, -1], 'generators': [5, 2, 48], 'label': '256.18790.8.ej1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057313
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '4.bv1.c1', '4.bx1.d1'], 'contains': ['16.ds1.d1', '16.dw1.d1', '16.dz1.c1', '16.el1.d1', '16.em1.a1', '16.eu1.d1', '16.fd1.d1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9892, -1, 848, -1, 9916, -1, 847, -1], 'generators': [205, 2, 32], 'label': '256.18790.8.ej1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ej1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ej1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057314
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.a1', '4.bx1.a1'], 'contains': ['16.du1.a1', '16.dy1.a1', '16.dz1.a1', '16.er1.a1', '16.es1.a1', '16.et1.a1', '16.eu1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 1481, -1, 9652, -1, 1479, -1], 'generators': [5, 218, 32], 'label': '256.18790.8.ek1.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': '8.ek1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057315
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.b1', '4.bx1.b1'], 'contains': ['16.du1.a1', '16.dy1.b1', '16.dz1.b1', '16.er1.b1', '16.es1.d1', '16.et1.b1', '16.eu1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 1179, -1, 9652, -1, 1178, -1], 'generators': [205, 218, 48], 'label': '256.18790.8.ek1.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': '8.ek1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057316
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.b1', '4.bx1.c1'], 'contains': ['16.du1.b1', '16.dy1.a1', '16.dz1.b1', '16.er1.b1', '16.es1.b1', '16.et1.d1', '16.eu1.c1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 1405, -1, 9652, -1, 1404, -1], 'generators': [21, 218, 48], 'label': '256.18790.8.ek1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057317
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.a1', '4.bx1.d1'], 'contains': ['16.du1.b1', '16.dy1.b1', '16.dz1.a1', '16.er1.a1', '16.es1.c1', '16.et1.c1', '16.eu1.d1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 1293, -1, 9652, -1, 1291, -1], 'generators': [221, 218, 32], 'label': '256.18790.8.ek1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057318
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.c1', '4.bx1.a1'], 'contains': ['16.du1.c1', '16.dy1.c1', '16.dz1.c1', '16.er1.a1', '16.es1.b1', '16.et1.b1', '16.eu1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 795, -1, 9652, -1, 794, -1], 'generators': [205, 218, 32], 'label': '256.18790.8.ek1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057319
    {'ambient': '256.18790', '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': ['64.bd1.a1', '64.bd1.b1', '64.bd1.d1', '64.bd1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.l1.a1', '8.bt1.a1', '8.cp1.a1', '8.da1.a1', '8.du1.a1', '8.du1.b1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5022, 3500, 8776, 8058, 5034, 3510, 8765, 8107], 'generators': [33, 2, 216, 64], 'label': '256.18790.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.c1.a1', '2.k1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.l1.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: 26057320
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.d1', '4.bx1.b1'], 'contains': ['16.du1.c1', '16.dy1.d1', '16.dz1.d1', '16.er1.b1', '16.es1.c1', '16.et1.a1', '16.eu1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 2750, -1, 9652, -1, 2746, -1], 'generators': [5, 218, 48], 'label': '256.18790.8.ek1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057321
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.d1', '4.bx1.c1'], 'contains': ['16.du1.d1', '16.dy1.c1', '16.dz1.d1', '16.er1.b1', '16.es1.a1', '16.et1.c1', '16.eu1.c1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 2863, -1, 9652, -1, 2859, -1], 'generators': [221, 218, 48], 'label': '256.18790.8.ek1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057322
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '4.bv1.c1', '4.bx1.d1'], 'contains': ['16.du1.d1', '16.dy1.d1', '16.dz1.c1', '16.er1.a1', '16.es1.d1', '16.et1.d1', '16.eu1.d1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9628, -1, 677, -1, 9652, -1, 675, -1], 'generators': [21, 218, 32], 'label': '256.18790.8.ek1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.ek1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ek1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057323
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.b1', '4.bx1.a1'], 'contains': ['16.dw1.a1', '16.dy1.a1', '16.ea1.a1', '16.et1.b1', '16.ev1.a1', '16.fc1.a1', '16.fd1.b1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 1037, -1, 9854, -1, 1036, -1], 'generators': [205, 218, 232], 'label': '256.18790.8.el1.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': '8.el1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057324
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.a1', '4.bx1.b1'], 'contains': ['16.dw1.a1', '16.dy1.b1', '16.ea1.b1', '16.et1.a1', '16.ev1.b1', '16.fc1.b1', '16.fd1.c1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 2501, -1, 9854, -1, 2498, -1], 'generators': [5, 218, 248], 'label': '256.18790.8.el1.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': '8.el1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057325
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.a1', '4.bx1.c1'], 'contains': ['16.dw1.b1', '16.dy1.a1', '16.ea1.b1', '16.et1.c1', '16.ev1.c1', '16.fc1.b1', '16.fd1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 2690, -1, 9854, -1, 2687, -1], 'generators': [221, 218, 248], 'label': '256.18790.8.el1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057326
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.b1', '4.bx1.d1'], 'contains': ['16.dw1.b1', '16.dy1.b1', '16.ea1.a1', '16.et1.d1', '16.ev1.d1', '16.fc1.a1', '16.fd1.d1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 955, -1, 9854, -1, 954, -1], 'generators': [21, 218, 232], 'label': '256.18790.8.el1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057327
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.d1', '4.bx1.a1'], 'contains': ['16.dw1.c1', '16.dy1.c1', '16.ea1.c1', '16.et1.a1', '16.ev1.a1', '16.fc1.a1', '16.fd1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 2343, -1, 9854, -1, 2341, -1], 'generators': [5, 218, 232], 'label': '256.18790.8.el1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057328
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.c1', '4.bx1.b1'], 'contains': ['16.dw1.c1', '16.dy1.d1', '16.ea1.d1', '16.et1.b1', '16.ev1.b1', '16.fc1.b1', '16.fd1.d1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 1120, -1, 9854, -1, 1118, -1], 'generators': [205, 218, 248], 'label': '256.18790.8.el1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057329
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.c1', '4.bx1.c1'], 'contains': ['16.dw1.d1', '16.dy1.c1', '16.ea1.d1', '16.et1.d1', '16.ev1.c1', '16.fc1.b1', '16.fd1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 1572, -1, 9854, -1, 1570, -1], 'generators': [21, 218, 248], 'label': '256.18790.8.el1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057330
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': ['64.bd1.b1', '64.bd1.d1', '64.bd1.c1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.o1.a1', '8.bq1.a1', '8.bq1.b1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3165, 9059, 6596, 5717, 3172, 9086, 6587, 5752], 'generators': [2, 36, 64], 'label': '256.18790.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.b1.a1', '2.k1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.k1.a1', '8.o1.a1'], '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: 26057331
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '8.el1', '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.bm1.a1', '4.bv1.d1', '4.bx1.d1'], 'contains': ['16.dw1.d1', '16.dy1.d1', '16.ea1.c1', '16.et1.c1', '16.ev1.d1', '16.fc1.a1', '16.fd1.c1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9830, -1, 2300, -1, 9854, -1, 2297, -1], 'generators': [221, 218, 232], 'label': '256.18790.8.el1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.el1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.el1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057332
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4373, 4536, 6374, 4513, 4383, 4517, 6365, 4541], 'generators': [216, 16, 64], 'label': '256.18790.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.d1.a1', '8.c1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.o1.a1', '8.n1.a1'], 'normal_contains': ['32.a1.a1', '32.c1.a1', '32.b1.a1', '32.e1.a1', '32.d1.a1', '32.f1.a1', '32.g1.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: 26057333
    {'ambient': '256.18790', '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.s1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.p1.b1', '8.bk1.a1', '8.bl1.a1', '8.bm1.a1', '8.bn1.a1'], 'contains': ['32.c1.a1', '32.h1.a1', '32.h1.b1', '32.l1.a1', '32.br1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2713, 5492, 4142, 2190, 2718, 5508, 4137, 2203], 'generators': [37, 216, 16], 'label': '256.18790.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.p1.a1', '8.p1.b1'], 'normal_contains': ['32.c1.a1', '32.h1.b1', '32.h1.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: 26057334
    {'ambient': '256.18790', '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': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.q1.a1', '8.r1.a1', '8.be1.a1', '8.br1.a1', '8.bs1.a1', '8.bt1.a1'], 'contains': ['32.b1.a1', '32.m1.a1', '32.bv1.a1', '32.bw1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7587, 1824, 5588, 7150, 7605, 1829, 5581, 7447], 'generators': [2, 16, 64], 'label': '256.18790.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.b1.a1', '8.q1.a1', '8.r1.a1'], 'normal_contains': ['32.b1.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: 26057335
    {'ambient': '256.18790', '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': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.q1.a1', '8.s1.a1', '8.bf1.a1', '8.bx1.a1', '8.by1.a1', '8.bz1.a1'], 'contains': ['32.b1.a1', '32.n1.a1', '32.ca1.a1', '32.cb1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7141, 2206, 3074, 7937, 7157, 2212, 3071, 8238], 'generators': [250, 16, 64], 'label': '256.18790.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.c1.a1', '8.q1.a1', '8.s1.a1'], 'normal_contains': ['32.b1.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: 26057336
    {'ambient': '256.18790', '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': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.r1.a1', '8.t1.a1', '8.bg1.a1', '8.cg1.a1', '8.cl1.a1', '8.co1.a1'], 'contains': ['32.b1.a1', '32.s1.a1', '32.cl1.a1', '32.cu1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7217, 2014, 4220, 7464, 7234, 2021, 4215, 7763], 'generators': [34, 16, 64], 'label': '256.18790.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.c1.a1', '8.r1.a1', '8.t1.a1'], 'normal_contains': ['32.b1.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: 26057337
    {'ambient': '256.18790', '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': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.s1.a1', '8.t1.a1', '8.bh1.a1', '8.ca1.a1', '8.cf1.a1', '8.cp1.a1'], 'contains': ['32.b1.a1', '32.t1.a1', '32.cm1.a1', '32.cv1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7434, 2397, 5448, 7716, 7451, 2404, 5441, 8016], 'generators': [218, 16, 64], 'label': '256.18790.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.b1.a1', '8.s1.a1', '8.t1.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: 26057338
    {'ambient': '256.18790', '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': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.r1.a1', '8.s1.a1', '8.bi1.a1', '8.cb1.a1', '8.ch1.a1', '8.cm1.a1'], 'contains': ['32.b1.a1', '32.i1.a1', '32.i1.b1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7817, 2588, 4003, 6943, 7835, 2595, 3998, 7006], 'generators': [32, 16], 'label': '256.18790.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.j1.a1', '8.r1.a1', '8.s1.a1'], 'normal_contains': ['32.b1.a1', '32.i1.b1', '32.i1.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: 26057339
    {'ambient': '256.18790', '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.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.q1.a1', '8.t1.a1', '8.bj1.a1', '8.cc1.a1', '8.ci1.a1', '8.cn1.a1'], 'contains': ['32.b1.a1', '32.j1.a1', '32.j1.b1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8021, 1632, 4049, 6754, 8040, 1637, 4045, 6816], 'generators': [248, 16], 'label': '256.18790.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.j1.a1', '8.q1.a1', '8.t1.a1'], 'normal_contains': ['32.b1.a1', '32.j1.b1', '32.j1.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: 26057340
    {'ambient': '256.18790', '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': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.u1.a1', '8.u1.b1', '8.bp1.a1', '8.bu1.a1', '8.cj1.a1', '8.cq1.a1'], 'contains': ['32.c1.a1', '32.k1.a1', '32.k1.b1', '32.q1.a1', '32.cq1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3148, 5157, 5402, 2380, 3154, 5173, 5395, 2395], 'generators': [101, 216, 16], 'label': '256.18790.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.a1.a1', '8.u1.a1', '8.u1.b1'], 'normal_contains': ['32.c1.a1', '32.k1.a1', '32.k1.b1'], '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: 26057341
    {'ambient': '256.18790', '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': ['128.g1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.j1.a1', '4.m1.a1', '4.x1.a1', '4.bd1.a1', '4.bn1.a1', '4.bn1.b1', '4.bp1.a1', '4.bp1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2730, 8073, 6423, 5541, 2737, 8139, 6415, 5553], 'generators': [1, 2, 36, 64], 'label': '256.18790.2.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.e1.a1', '4.j1.a1', '4.m1.a1', '4.x1.a1', '4.bd1.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: 26057342
    {'ambient': '256.18790', '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.d1.a1', '2.h1.a1', '2.l1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.l1.a1', '8.bx1.a1', '8.cg1.a1', '8.db1.a1', '8.dv1.a1', '8.dv1.b1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4055, 6859, 8506, 4871, 4065, 6880, 8495, 4900], 'generators': [33, 34, 216, 64], 'label': '256.18790.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.l1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.l1.a1'], '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: 26057343
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.p1.a1', '8.u1.a1', '8.bo1.a1', '8.bv1.a1', '8.cd1.a1', '8.cr1.a1'], 'contains': ['32.c1.a1', '32.r1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [460, 7311, 7307, 3424, 460, 7414, 7297, 3445], 'generators': [1, 216], 'label': '256.18790.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.g1.a1', '8.p1.a1', '8.u1.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: 26057344
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.p1.b1', '8.u1.b1', '8.bo1.b1', '8.bv1.b1', '8.cd1.b1', '8.cr1.b1'], 'contains': ['32.c1.a1', '32.r1.b1'], 'core': '16.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [460, 7311, 7338, 3931, 460, 7414, 7328, 3955], 'generators': [65, 216], 'label': '256.18790.16.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': ['8.g1.a1', '8.p1.b1', '8.u1.b1'], '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: 26057345
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.p1.a1', '8.u1.b1', '8.bq1.a1', '8.bw1.a1', '8.ce1.a1', '8.ck1.a1'], 'contains': ['32.c1.a1', '32.ct1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [740, 7552, 6277, 3772, 741, 7655, 6269, 3795], 'generators': [36, 16], 'label': '256.18790.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.k1.a1', '8.p1.a1', '8.u1.b1'], 'normal_contains': ['32.c1.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: 26057346
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.p1.b1', '8.u1.a1', '8.bq1.b1', '8.bw1.b1', '8.ce1.b1', '8.ck1.b1'], 'contains': ['32.c1.a1', '32.ct1.b1'], 'core': '16.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [740, 7552, 6231, 3583, 741, 7655, 6223, 3605], 'generators': [100, 16], 'label': '256.18790.16.k1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.b1', 'normal_contained_in': ['8.k1.a1', '8.p1.b1', '8.u1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057347
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.v1.a1', '8.v1.b1', '8.cs1.a1', '8.cu1.a1', '8.cw1.a1', '8.cx1.a1'], 'contains': ['32.d1.a1', '32.h1.a1', '32.k1.a1', '32.w1.a1', '32.bo1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 4361, 3701, 1497, 6856, 4343, 3696, 1506], 'generators': [37, 216, 64], 'label': '256.18790.16.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': ['8.a1.a1', '8.v1.b1', '8.v1.a1'], 'normal_contains': ['32.d1.a1', '32.h1.a1', '32.k1.a1'], 'normalizer': '1.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: 26057348
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.v1.c1', '8.v1.d1', '8.cs1.b1', '8.cu1.b1', '8.cw1.b1', '8.cx1.b1'], 'contains': ['32.d1.a1', '32.h1.b1', '32.k1.b1', '32.w1.b1', '32.bo1.b1'], 'core': '16.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 4361, 3732, 1369, 6856, 4343, 3728, 1377], 'generators': [53, 216, 64], 'label': '256.18790.16.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.l1.b1', 'normal_contained_in': ['8.a1.a1', '8.v1.d1', '8.v1.c1'], 'normal_contains': ['32.d1.a1', '32.h1.b1', '32.k1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057349
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.v1.a1', '8.v1.c1', '8.cy1.a1', '8.dd1.a1', '8.df1.a1', '8.dj1.a1'], 'contains': ['32.d1.a1', '32.i1.a1', '32.j1.b1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8149, 2778, 3505, 2760, 8168, 2786, 3500, 2777], 'generators': [32, 216], 'label': '256.18790.16.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': ['8.j1.a1', '8.v1.c1', '8.v1.a1'], 'normal_contains': ['32.d1.a1', '32.i1.a1', '32.j1.b1'], 'normalizer': '1.a1.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: 26057350
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.v1.b1', '8.v1.d1', '8.cy1.b1', '8.dd1.b1', '8.df1.b1', '8.dj1.b1'], 'contains': ['32.d1.a1', '32.i1.b1', '32.j1.a1'], 'core': '16.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8149, 2778, 3584, 2571, 8168, 2786, 3580, 2587], 'generators': [48, 216], 'label': '256.18790.16.m1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.m1.b1', 'normal_contained_in': ['8.j1.a1', '8.v1.d1', '8.v1.b1'], 'normal_contains': ['32.d1.a1', '32.i1.b1', '32.j1.a1'], 'normalizer': '1.a1.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: 26057351
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.v1.a1', '8.v1.d1', '8.cz1.a1', '8.dc1.a1', '8.dg1.a1', '8.di1.a1'], 'contains': ['32.d1.a1', '32.cp1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8214, 3448, 3545, 1769, 8234, 3458, 3540, 1780], 'generators': [5, 216], 'label': '256.18790.16.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': ['8.m1.a1', '8.v1.d1', '8.v1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.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: 26057352
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.v1.b1', '8.v1.c1', '8.cz1.b1', '8.dc1.b1', '8.dg1.b1', '8.di1.b1'], 'contains': ['32.d1.a1', '32.cp1.b1'], 'core': '16.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8214, 3448, 3464, 1630, 8234, 3458, 3460, 1640], 'generators': [21, 216], 'label': '256.18790.16.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.n1.b1', 'normal_contained_in': ['8.m1.a1', '8.v1.c1', '8.v1.b1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057353
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.o1.a1', '8.dx1.a1', '8.dx1.b1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3600, 7702, 7124, 5420, 3610, 7725, 7115, 5454], 'generators': [34, 4, 64], 'label': '256.18790.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.o1.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: 26057354
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.w1.a1', '8.w1.b1', '8.dl1.a1', '8.dn1.a1', '8.do1.a1', '8.dq1.a1'], 'contains': ['32.g1.a1', '32.h1.a1', '32.k1.b1', '32.bd1.a1', '32.bp1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3947, 4960, 5123, 1902, 3956, 4943, 5117, 1914], 'generators': [37, 216, 80], 'label': '256.18790.16.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': ['8.a1.a1', '8.w1.b1', '8.w1.a1'], 'normal_contains': ['32.g1.a1', '32.h1.a1', '32.k1.b1'], 'normalizer': '1.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: 26057355
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.w1.c1', '8.w1.d1', '8.dl1.b1', '8.dn1.b1', '8.do1.b1', '8.dq1.b1'], 'contains': ['32.g1.a1', '32.h1.b1', '32.k1.a1', '32.bd1.b1', '32.bp1.b1'], 'core': '16.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3947, 4960, 4702, 2031, 3956, 4943, 4696, 2043], 'generators': [101, 216, 80], 'label': '256.18790.16.o1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': ['8.a1.a1', '8.w1.d1', '8.w1.c1'], 'normal_contains': ['32.g1.a1', '32.h1.b1', '32.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057356
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.x1.a1', '8.x1.b1', '8.dm1.a1', '8.ds1.a1', '8.dy1.a1', '8.ea1.a1'], 'contains': ['32.f1.a1', '32.bg1.a1', '32.cd1.a1', '32.ce1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3883, 3947, 4376, 5804, 3891, 3958, 4371, 5859], 'generators': [7, 200, 64], 'label': '256.18790.16.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': ['8.d1.a1', '8.x1.a1', '8.x1.b1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.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: 26057357
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.x1.c1', '8.x1.d1', '8.dm1.b1', '8.ds1.b1', '8.dy1.b1', '8.ea1.b1'], 'contains': ['32.f1.a1', '32.bg1.b1', '32.cd1.b1', '32.ce1.b1'], 'core': '16.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3883, 3947, 4330, 6185, 3891, 3958, 4324, 6243], 'generators': [23, 200, 64], 'label': '256.18790.16.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': ['8.d1.a1', '8.x1.c1', '8.x1.d1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057358
    {'ambient': '256.18790', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.x1.a1', '8.x1.c1', '8.dk1.a1', '8.dw1.a1', '8.ec1.a1', '8.ee1.a1'], 'contains': ['32.f1.a1', '32.bj1.a1', '32.cn1.a1', '32.cr1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5430, 4167, 5541, 6375, 5443, 4179, 5534, 6434], 'generators': [39, 200, 64], 'label': '256.18790.16.q1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': ['8.h1.a1', '8.x1.c1', '8.x1.a1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.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: 26057359
    {'ambient': '256.18790', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.x1.b1', '8.x1.d1', '8.dk1.b1', '8.dw1.b1', '8.ec1.b1', '8.ee1.b1'], 'contains': ['32.f1.a1', '32.bj1.b1', '32.cn1.b1', '32.cr1.b1'], 'core': '16.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5430, 4167, 5495, 5994, 5443, 4179, 5488, 6051], 'generators': [55, 200, 64], 'label': '256.18790.16.q1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.q1.b1', 'normal_contained_in': ['8.h1.a1', '8.x1.d1', '8.x1.b1'], 'normal_contains': ['32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057360
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.x1.a1', '8.x1.d1', '8.dp1.a1', '8.dr1.a1', '8.ed1.a1', '8.ef1.a1'], 'contains': ['32.f1.a1', '32.i1.a1', '32.j1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7510, 2967, 3957, 5612, 7528, 2976, 3952, 5668], 'generators': [32, 200], 'label': '256.18790.16.r1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': ['8.j1.a1', '8.x1.d1', '8.x1.a1'], 'normal_contains': ['32.f1.a1', '32.i1.a1', '32.j1.a1'], 'normalizer': '1.a1.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: 26057361
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.x1.b1', '8.x1.c1', '8.dp1.b1', '8.dr1.b1', '8.ed1.b1', '8.ef1.b1'], 'contains': ['32.f1.a1', '32.i1.b1', '32.j1.b1'], 'core': '16.r1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7510, 2967, 4096, 6565, 7528, 2976, 4091, 6626], 'generators': [48, 200], 'label': '256.18790.16.r1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.r1.b1', 'normal_contained_in': ['8.j1.a1', '8.x1.c1', '8.x1.b1'], 'normal_contains': ['32.f1.a1', '32.i1.b1', '32.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057362
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.w1.a1', '8.w1.c1', '8.dt1.a1', '8.dx1.a1', '8.dz1.a1', '8.eg1.a1'], 'contains': ['32.g1.a1', '32.bi1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3564, 7108, 8686, 2912, 3573, 7129, 8675, 2929], 'generators': [4, 80], 'label': '256.18790.16.s1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': ['8.f1.a1', '8.w1.c1', '8.w1.a1'], 'normal_contains': ['32.g1.a1'], 'normalizer': '1.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: 26057363
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.w1.b1', '8.w1.d1', '8.dt1.b1', '8.dx1.b1', '8.dz1.b1', '8.eg1.b1'], 'contains': ['32.g1.a1', '32.bi1.b1'], 'core': '16.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3564, 7108, 8714, 3304, 3573, 7129, 8703, 3324], 'generators': [68, 80], 'label': '256.18790.16.s1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.s1.b1', 'normal_contained_in': ['8.f1.a1', '8.w1.d1', '8.w1.b1'], 'normal_contains': ['32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057364
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.i1.a1', '8.bb1.a1', '8.bv1.a1', '8.bv1.b1', '8.by1.a1', '8.cl1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2117, 1742, 8639, 9244, 2122, 1746, 8628, 9300], 'generators': [1, 34, 216, 64], 'label': '256.18790.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.a1', '8.i1.a1'], '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: 26057365
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.w1.a1', '8.w1.d1', '8.du1.a1', '8.dv1.a1', '8.eb1.a1', '8.eh1.a1'], 'contains': ['32.g1.a1', '32.cy1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4224, 5325, 7926, 3038, 4234, 5341, 7915, 3057], 'generators': [33, 216], 'label': '256.18790.16.t1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': ['8.l1.a1', '8.w1.d1', '8.w1.a1'], 'normal_contains': ['32.g1.a1'], 'normalizer': '1.a1.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: 26057366
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.w1.b1', '8.w1.c1', '8.du1.b1', '8.dv1.b1', '8.eb1.b1', '8.eh1.b1'], 'contains': ['32.g1.a1', '32.cy1.b1'], 'core': '16.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4224, 5325, 7959, 3177, 4234, 5341, 7949, 3196], 'generators': [97, 216], 'label': '256.18790.16.t1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.t1.b1', 'normal_contained_in': ['8.l1.a1', '8.w1.c1', '8.w1.b1'], 'normal_contains': ['32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057367
    {'ambient': '256.18790', '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.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.y1.a1', '8.z1.a1'], 'contains': ['32.a1.a1', '32.l1.a1', '32.q1.a1', '32.w1.a1', '32.w1.b1', '32.bd1.a1', '32.bd1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3754, -1, 3662, -1, 3763, -1, 3657, -1], 'generators': [37, 24, 16], 'label': '256.18790.16.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.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: 26057368
    {'ambient': '256.18790', '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': '16.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.y1.a1', '8.ba1.a1'], 'contains': ['32.a1.a1', '32.m1.a1', '32.t1.a1', '32.x1.a1', '32.be1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5774, -1, 7239, -1, 5787, -1, 7230, -1], 'generators': [2, 24, 16], 'label': '256.18790.16.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.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: 26057369
    {'ambient': '256.18790', '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': '16.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.z1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.n1.a1', '32.s1.a1', '32.y1.a1', '32.bf1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1786, -1, 2982, -1, 1790, -1, 2978, -1], 'generators': [34, 24, 16], 'label': '256.18790.16.w1.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.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: 26057370
    {'ambient': '256.18790', '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': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.z1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.o1.a1', '32.z1.a1', '32.bg1.a1', '32.bg1.b1', '32.de1.a1', '32.de1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1724, -1, 7277, -1, 1728, -1, 7268, -1], 'generators': [7, 24, 16, 128], 'label': '256.18790.16.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.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: 26057371
    {'ambient': '256.18790', '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': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.ba1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.p1.a1', '32.ba1.a1', '32.bh1.a1', '32.df1.a1', '32.df1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [966, -1, 9185, -1, 968, -1, 9172, -1], 'generators': [3, 24, 16, 128], 'label': '256.18790.16.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.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: 26057372
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.bc1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '32.bi1.a1', '32.bi1.b1', '32.dg1.a1', '32.dg1.b1', '32.dg1.c1', '32.dg1.d1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [823, -1, 9457, -1, 824, -1, 9445, -1], 'generators': [4, 16, 128], 'label': '256.18790.16.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.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: 26057373
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.r1.a1', '32.r1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [287, -1, 8829, -1, 287, -1, 8817, -1], 'generators': [1, 24], 'label': '256.18790.16.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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: 26057374
    {'ambient': '256.18790', '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': '16.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.y1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '32.u1.a1', '32.bb1.a1', '32.bj1.a1', '32.bj1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4878, -1, 7078, -1, 4889, -1, 7069, -1], 'generators': [39, 24, 16], 'label': '256.18790.16.bb1.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.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: 26057375
    {'ambient': '256.18790', '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.a1.a1', '2.l1.a1', '2.m1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.m1.a1', '8.bz1.a1', '8.co1.a1', '8.dc1.a1', '8.dc1.b1', '8.dw1.a1', '8.dw1.b1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7351, 2055, 2604, 8931, 7478, 2061, 2600, 8985], 'generators': [5, 34, 216, 16], 'label': '256.18790.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.a1.a1', '2.l1.a1', '2.m1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.a1', '8.m1.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: 26057376
    {'ambient': '256.18790', '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': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.bb1.a1', '8.bd1.a1'], 'contains': ['32.a1.a1', '32.v1.a1', '32.bc1.a1', '32.bk1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1033, -1, 8783, -1, 1035, -1, 8771, -1], 'generators': [35, 24, 16], 'label': '256.18790.16.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.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: 26057377
    {'ambient': '256.18790', '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.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.be1.a1', '8.bk1.a1'], 'contains': ['32.l1.a1', '32.m1.a1', '32.u1.a1', '32.bl1.a1', '32.bl1.b1', '32.bl1.c1', '32.bl1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6071, -1, 4663, -1, 6085, -1, 4657, -1], 'generators': [37, 2, 16], 'label': '256.18790.16.bd1.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.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: 26057378
    {'ambient': '256.18790', '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.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bf1.a1', '8.bl1.a1'], 'contains': ['32.l1.a1', '32.n1.a1', '32.o1.a1', '32.bm1.a1', '32.bm1.b1', '32.bm1.c1', '32.bm1.d1', '32.dh1.a1', '32.dh1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1924, -1, 11, -1, 1928, -1, 11, -1], 'generators': [37, 250, 16, 128], 'label': '256.18790.16.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.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: 26057379
    {'ambient': '256.18790', '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': '16.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bg1.a1', '8.bl1.a1'], 'contains': ['32.l1.a1', '32.o1.a1', '32.s1.a1', '32.bn1.a1', '32.bn1.b1', '32.bn1.c1', '32.bn1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2189, -1, 280, -1, 2195, -1, 280, -1], 'generators': [37, 34, 16], 'label': '256.18790.16.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.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: 26057380
    {'ambient': '256.18790', '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': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.be1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1', '8.bi1.a1', '8.bj1.a1'], 'contains': ['32.b1.a1', '32.l1.a1', '32.q1.a1', '32.bo1.a1', '32.bo1.b1', '32.bp1.a1', '32.bp1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7352, -1, 3125, -1, 7368, -1, 3120, -1], 'generators': [37, 16, 64], 'label': '256.18790.16.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.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: 26057381
    {'ambient': '256.18790', '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': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.bh1.a1', '8.bk1.a1'], 'contains': ['32.l1.a1', '32.t1.a1', '32.u1.a1', '32.bq1.a1', '32.bq1.b1', '32.bq1.c1', '32.bq1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5912, -1, 4426, -1, 5926, -1, 4420, -1], 'generators': [37, 218, 16], 'label': '256.18790.16.bh1.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.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: 26057382
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.bo1.a1', '8.bs1.a1'], 'contains': ['32.m1.a1', '32.p1.a1', '32.r1.a1', '32.di1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [524, -1, 8947, -1, 525, -1, 8936, -1], 'generators': [1, 2, 128], 'label': '256.18790.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '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: 26057383
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.bo1.b1', '8.bs1.a1'], 'contains': ['32.m1.a1', '32.p1.a1', '32.r1.b1', '32.di1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [524, -1, 8994, -1, 525, -1, 8982, -1], 'generators': [65, 2, 128], 'label': '256.18790.16.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057384
    {'ambient': '256.18790', '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': '16.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.bk1.a1', '8.bo1.a1', '8.bo1.b1', '8.bp1.a1', '8.bq1.a1', '8.bq1.b1'], 'contains': ['32.c1.a1', '32.m1.a1', '32.t1.a1', '32.bs1.a1', '32.bt1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4965, -1, 6460, -1, 4977, -1, 6452, -1], 'generators': [2, 216, 16], 'label': '256.18790.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.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: 26057385
    {'ambient': '256.18790', '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': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.be1.a1', '8.bp1.a1'], 'contains': ['32.m1.a1', '32.q1.a1', '32.u1.a1', '32.bu1.a1', '32.bu1.b1', '32.bu1.c1', '32.bu1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6153, -1, 5305, -1, 6168, -1, 5299, -1], 'generators': [101, 2, 16], 'label': '256.18790.16.bk1.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.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: 26057386
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '8.n1.a1', '8.bw1.a1', '8.bw1.b1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3053, 7999, 5446, 2939, 3061, 8023, 5438, 2957], 'generators': [34, 36, 64], 'label': '256.18790.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'normal_contains': ['8.c1.a1', '8.k1.a1', '8.n1.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: 26057387
    {'ambient': '256.18790', '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': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bf1.a1', '8.bu1.a1'], 'contains': ['32.n1.a1', '32.o1.a1', '32.q1.a1', '32.bx1.a1', '32.bx1.b1', '32.bx1.c1', '32.bx1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2113, -1, 606, -1, 2118, -1, 605, -1], 'generators': [101, 250, 16], 'label': '256.18790.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.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: 26057388
    {'ambient': '256.18790', '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': '16.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.bl1.a1', '8.bu1.a1', '8.bv1.a1', '8.bv1.b1', '8.bw1.a1', '8.bw1.b1'], 'contains': ['32.c1.a1', '32.n1.a1', '32.s1.a1', '32.by1.a1', '32.bz1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1121, -1, 2900, -1, 1123, -1, 2896, -1], 'generators': [34, 216, 16], 'label': '256.18790.16.bm1.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.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: 26057389
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.bv1.a1', '8.by1.a1'], 'contains': ['32.n1.a1', '32.r1.a1', '32.v1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 8551, -1, 351, -1, 8541, -1], 'generators': [1, 250], 'label': '256.18790.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '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: 26057390
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.bv1.b1', '8.by1.a1'], 'contains': ['32.n1.a1', '32.r1.b1', '32.v1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 8622, -1, 351, -1, 8610, -1], 'generators': [65, 250], 'label': '256.18790.16.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057391
    {'ambient': '256.18790', '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': '16.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.bg1.a1', '8.bu1.a1'], 'contains': ['32.o1.a1', '32.q1.a1', '32.s1.a1', '32.cc1.a1', '32.cc1.b1', '32.cc1.c1', '32.cc1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2272, -1, 984, -1, 2277, -1, 983, -1], 'generators': [101, 34, 16], 'label': '256.18790.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.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: 26057392
    {'ambient': '256.18790', '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': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.bf1.a1', '8.bg1.a1', '8.br1.a1', '8.ca1.a1', '8.cb1.a1', '8.cc1.a1'], 'contains': ['32.b1.a1', '32.o1.a1', '32.cd1.a1', '32.cd1.b1', '32.cf1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7893, -1, 1777, -1, 7912, -1, 1775, -1], 'generators': [7, 16, 64], 'label': '256.18790.16.bp1.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.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: 26057393
    {'ambient': '256.18790', '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': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.bl1.a1', '8.bu1.a1', '8.cd1.a1', '8.cd1.b1', '8.ce1.a1', '8.ce1.b1'], 'contains': ['32.c1.a1', '32.o1.a1', '32.ce1.a1', '32.ce1.b1', '32.cg1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1203, -1, 3771, -1, 1205, -1, 3767, -1], 'generators': [7, 216, 16], 'label': '256.18790.16.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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: 26057394
    {'ambient': '256.18790', '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.ba1.a1', '8.bo1.a1', '8.cf1.a1'], 'contains': ['32.p1.a1', '32.r1.a1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [670, -1, 8867, -1, 671, -1, 8855, -1], 'generators': [1, 218], 'label': '256.18790.16.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '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: 26057395
    {'ambient': '256.18790', '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.ba1.a1', '8.bo1.b1', '8.cf1.a1'], 'contains': ['32.p1.a1', '32.r1.b1', '32.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [670, -1, 8905, -1, 671, -1, 8894, -1], 'generators': [65, 218], 'label': '256.18790.16.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', '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: 26057396
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.bs1.a1', '8.bx1.a1', '8.cf1.a1', '8.cg1.a1', '8.ch1.a1', '8.ci1.a1'], 'contains': ['32.b1.a1', '32.p1.a1', '32.ch1.a1', '32.cj1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4796, -1, 8382, -1, 4806, -1, 8371, -1], 'generators': [3, 16, 64], 'label': '256.18790.16.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', '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: 26057397
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.f1.a1', '8.bc1.a1', '8.dy1.a1', '8.dy1.b1', '8.dz1.a1', '8.dz1.b1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2419, 7108, 9546, 4623, 2425, 7129, 9533, 4651], 'generators': [3, 4, 16, 64], 'label': '256.18790.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.f1.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: 26057398
    {'ambient': '256.18790', '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.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.bm1.a1', '8.bo1.a1', '8.bo1.b1', '8.cj1.a1', '8.ck1.a1', '8.ck1.b1'], 'contains': ['32.c1.a1', '32.p1.a1', '32.ci1.a1', '32.ck1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1280, -1, 7377, -1, 1282, -1, 7367, -1], 'generators': [3, 216, 16], 'label': '256.18790.16.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 26057399
    {'ambient': '256.18790', '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': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.bs1.a1', '8.by1.a1', '8.cf1.a1', '8.cl1.a1', '8.cm1.a1', '8.cn1.a1'], 'contains': ['32.b1.a1', '32.r1.a1', '32.r1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4734, -1, 8742, -1, 4745, -1, 8730, -1], 'generators': [1, 64], 'label': '256.18790.16.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', '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: 26057400
    {'ambient': '256.18790', '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': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.be1.a1', '8.bh1.a1', '8.bz1.a1', '8.cb1.a1', '8.cc1.a1', '8.co1.a1'], 'contains': ['32.b1.a1', '32.u1.a1', '32.cn1.a1', '32.cn1.b1', '32.cw1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8282, -1, 3911, -1, 8301, -1, 3906, -1], 'generators': [39, 16, 64], 'label': '256.18790.16.bv1.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.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: 26057401
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.bw1', '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.i1.a1', '8.bt1.a1', '8.by1.a1', '8.ch1.a1', '8.ci1.a1', '8.cl1.a1', '8.cp1.a1'], 'contains': ['32.b1.a1', '32.v1.a1', '32.co1.a1', '32.cx1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5124, -1, 8289, -1, 5136, -1, 8278, -1], 'generators': [35, 16, 64], 'label': '256.18790.16.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057402
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.bt1.a1', '8.bx1.a1', '8.cg1.a1', '8.cm1.a1', '8.cn1.a1', '8.cp1.a1'], 'contains': ['32.b1.a1', '32.cy1.a1', '32.cy1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5354, -1, 8243, -1, 5366, -1, 8232, -1], 'generators': [33, 64], 'label': '256.18790.16.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057403
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.bi1.a1', '8.bj1.a1', '8.br1.a1', '8.bz1.a1', '8.ca1.a1', '8.co1.a1'], 'contains': ['32.b1.a1', '32.cp1.a1', '32.cp1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8648, -1, 2175, -1, 8669, -1, 2172, -1], 'generators': [5, 16], 'label': '256.18790.16.by1.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.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057404
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.bk1.a1', '8.bp1.a1', '8.ck1.a1', '8.ck1.b1', '8.cr1.a1', '8.cr1.b1'], 'contains': ['32.c1.a1', '32.u1.a1', '32.cr1.a1', '32.cr1.b1', '32.cz1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4290, -1, 5970, -1, 4300, -1, 5962, -1], 'generators': [39, 216, 16], 'label': '256.18790.16.bz1.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.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057405
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ca1', '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.i1.a1', '8.bn1.a1', '8.bv1.a1', '8.bv1.b1', '8.ce1.a1', '8.ce1.b1', '8.cq1.a1'], 'contains': ['32.c1.a1', '32.v1.a1', '32.cs1.a1', '32.da1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1863, -1, 6608, -1, 1867, -1, 6600, -1], 'generators': [35, 216, 16], 'label': '256.18790.16.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057406
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.bn1.a1', '8.bw1.a1', '8.bw1.b1', '8.cd1.a1', '8.cd1.b1', '8.cq1.a1'], 'contains': ['32.c1.a1', '32.db1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1986, -1, 5923, -1, 1989, -1, 5915, -1], 'generators': [6, 16], 'label': '256.18790.16.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057537
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.en1', '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.bt1.a1', '8.da1.a1', '8.du1.a1'], 'contains': ['32.bw1.a1', '32.cx1.a1', '32.cy1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5598, -1, 8483, -1, 5611, -1, 8471, -1], 'generators': [33, 2], 'label': '256.18790.16.en1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.en1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057407
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.bm1.a1', '8.bq1.a1', '8.bq1.b1', '8.cj1.a1', '8.cr1.a1', '8.cr1.b1'], 'contains': ['32.c1.a1', '32.dc1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1411, -1, 6324, -1, 1414, -1, 6315, -1], 'generators': [38, 16], 'label': '256.18790.16.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057408
    {'ambient': '256.18790', '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.e1.a1', '2.j1.a1', '2.o1.a1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.n1.a1', '8.cd1.a1', '8.cd1.b1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2006, 4439, 6022, 3742, 2011, 4453, 6014, 3764], 'generators': [1, 6, 64], 'label': '256.18790.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.a1', '2.o1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.n1.a1'], '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: 26057409
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cd1', '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.y1.a1', '8.bh1.a1', '8.bp1.a1'], 'contains': ['32.q1.a1', '32.t1.a1', '32.u1.a1', '32.dd1.a1', '32.dd1.b1', '32.dd1.c1', '32.dd1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5995, -1, 5054, -1, 6009, -1, 5047, -1], 'generators': [101, 218, 16], 'label': '256.18790.16.cd1.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.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057410
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ce1', '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.bb1.a1', '8.bv1.a1', '8.cl1.a1'], 'contains': ['32.r1.a1', '32.s1.a1', '32.v1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [408, -1, 8587, -1, 409, -1, 8576, -1], 'generators': [1, 34], 'label': '256.18790.16.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057411
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ce1', '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.bb1.a1', '8.bv1.b1', '8.cl1.a1'], 'contains': ['32.r1.b1', '32.s1.a1', '32.v1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [408, -1, 8657, -1, 409, -1, 8645, -1], 'generators': [65, 34], 'label': '256.18790.16.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.ce1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057412
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.cs1.a1', '8.ct1.a1'], 'contains': ['32.w1.a1', '32.x1.a1', '32.bb1.a1', '32.bl1.b1', '32.bq1.a1', '32.bu1.a1', '32.dd1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6969, -1, 4795, -1, 6985, -1, 4790, -1], 'generators': [37, 2, 24], 'label': '256.18790.16.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057413
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.cs1.a1', '8.ct1.a1'], 'contains': ['32.w1.a1', '32.x1.a1', '32.bb1.a1', '32.bl1.a1', '32.bq1.b1', '32.bu1.b1', '32.dd1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6969, -1, 4764, -1, 6985, -1, 4758, -1], 'generators': [101, 2, 24], 'label': '256.18790.16.cf1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057414
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.cs1.b1', '8.ct1.a1'], 'contains': ['32.w1.b1', '32.x1.a1', '32.bb1.a1', '32.bl1.c1', '32.bq1.d1', '32.bu1.d1', '32.dd1.c1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6969, -1, 4827, -1, 6985, -1, 4821, -1], 'generators': [53, 2, 24], 'label': '256.18790.16.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057415
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.cs1.b1', '8.ct1.a1'], 'contains': ['32.w1.b1', '32.x1.a1', '32.bb1.a1', '32.bl1.d1', '32.bq1.c1', '32.bu1.c1', '32.dd1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6969, -1, 4858, -1, 6985, -1, 4852, -1], 'generators': [117, 2, 24], 'label': '256.18790.16.cf1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cf1.b2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.b2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057416
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.cu1.a1', '8.cv1.a1'], 'contains': ['32.w1.a1', '32.y1.a1', '32.z1.a1', '32.bm1.b1', '32.bn1.a1', '32.bx1.a1', '32.cc1.c1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2789, -1, 327, -1, 2795, -1, 327, -1], 'generators': [101, 34, 24], 'label': '256.18790.16.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057417
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.cu1.a1', '8.cv1.a1'], 'contains': ['32.w1.a1', '32.y1.a1', '32.z1.a1', '32.bm1.a1', '32.bn1.b1', '32.bx1.c1', '32.cc1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2789, -1, 234, -1, 2795, -1, 234, -1], 'generators': [37, 34, 24], 'label': '256.18790.16.cg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cg1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057418
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.cu1.b1', '8.cv1.a1'], 'contains': ['32.w1.b1', '32.y1.a1', '32.z1.a1', '32.bm1.c1', '32.bn1.d1', '32.bx1.d1', '32.cc1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2789, -1, 466, -1, 2795, -1, 466, -1], 'generators': [117, 34, 24], 'label': '256.18790.16.cg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057419
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.n1.a1', '2.o1.a1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.j1.a1', '8.x1.a1', '8.x1.b1', '8.x1.c1', '8.x1.d1', '8.cb1.a1', '8.cc1.a1', '8.dd1.a1', '8.dd1.b1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7192, 1080, 3934, 9551, 7209, 1083, 3981, 9609], 'generators': [7, 32, 216, 16], 'label': '256.18790.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.a1.a1', '2.n1.a1', '2.o1.a1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.j1.a1', '8.x1.c1', '8.x1.d1', '8.x1.a1', '8.x1.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: 26057420
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.cu1.b1', '8.cv1.a1'], 'contains': ['32.w1.b1', '32.y1.a1', '32.z1.a1', '32.bm1.d1', '32.bn1.c1', '32.bx1.b1', '32.cc1.d1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2789, -1, 420, -1, 2795, -1, 420, -1], 'generators': [53, 34, 24], 'label': '256.18790.16.cg1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cg1.b2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.b2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057421
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.ct1.a1', '8.cv1.a1'], 'contains': ['32.e1.a1', '32.w1.a1', '32.w1.b1', '32.bp1.a1', '32.bp1.b1', '32.br1.a1', '32.cq1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4171, -1, 3623, -1, 4180, -1, 3618, -1], 'generators': [37, 24, 80], 'label': '256.18790.16.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057422
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ci1', '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': ['8.b1.a1', '8.cs1.a1', '8.cs1.b1', '8.cy1.a1', '8.cy1.b1', '8.cz1.a1', '8.cz1.b1'], 'contains': ['32.d1.a1', '32.x1.a1', '32.bt1.a1', '32.bv1.a1', '32.cm1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8478, -1, 4260, -1, 8498, -1, 4254, -1], 'generators': [2, 216, 64], 'label': '256.18790.16.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057423
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cj1', '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': ['8.b1.a1', '8.ct1.a1', '8.da1.a1'], 'contains': ['32.e1.a1', '32.x1.a1', '32.bs1.a1', '32.bw1.a1', '32.cv1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6352, -1, 6502, -1, 6367, -1, 6494, -1], 'generators': [2, 24, 80], 'label': '256.18790.16.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057424
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ck1', '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': ['8.c1.a1', '8.cu1.a1', '8.cu1.b1', '8.cy1.a1', '8.cy1.b1', '8.dc1.a1', '8.dc1.b1'], 'contains': ['32.d1.a1', '32.y1.a1', '32.bz1.a1', '32.ca1.a1', '32.cl1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7281, -1, 1404, -1, 7299, -1, 1402, -1], 'generators': [34, 216, 64], 'label': '256.18790.16.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057425
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cl1', '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': ['8.c1.a1', '8.cv1.a1', '8.db1.a1'], 'contains': ['32.e1.a1', '32.y1.a1', '32.by1.a1', '32.cb1.a1', '32.cu1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3818, -1, 2943, -1, 3827, -1, 2939, -1], 'generators': [34, 24, 80], 'label': '256.18790.16.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.cl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057426
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cm1', '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.d1.a1', '8.cu1.a1', '8.cu1.b1', '8.cz1.a1', '8.cz1.b1', '8.dd1.a1', '8.dd1.b1'], 'contains': ['32.d1.a1', '32.z1.a1', '32.cd1.a1', '32.cd1.b1', '32.cg1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6596, -1, 1731, -1, 6612, -1, 1729, -1], 'generators': [7, 216, 64], 'label': '256.18790.16.cm1.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.cm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057427
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cn1', '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.d1.a1', '8.cv1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.z1.a1', '32.ce1.a1', '32.ce1.b1', '32.cf1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2559, -1, 3818, -1, 2565, -1, 3813, -1], 'generators': [7, 24, 80], 'label': '256.18790.16.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.cn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057428
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.co1', '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.e1.a1', '8.cw1.a1', '8.cw1.b1', '8.df1.a1', '8.df1.b1', '8.dg1.a1', '8.dg1.b1'], 'contains': ['32.d1.a1', '32.ba1.a1', '32.ch1.a1', '32.ck1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5201, -1, 7128, -1, 5213, -1, 7118, -1], 'generators': [3, 216, 64], 'label': '256.18790.16.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.co1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057429
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cp1', '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.e1.a1', '8.db1.a1', '8.dh1.a1'], 'contains': ['32.e1.a1', '32.ba1.a1', '32.ci1.a1', '32.cj1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3224, -1, 8000, -1, 3231, -1, 7989, -1], 'generators': [3, 24, 80], 'label': '256.18790.16.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.cp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057430
    {'ambient': '256.18790', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.k1.a1', '8.ce1.a1', '8.ce1.b1', '8.de1.a1', '8.ea1.a1', '8.ea1.b1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2533, 2631, 6808, 7453, 2539, 2639, 6799, 7499], 'generators': [35, 36, 16, 64], 'label': '256.18790.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.a1', '8.k1.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: 26057431
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cq1', '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.h1.a1', '8.cs1.a1', '8.cs1.b1', '8.dc1.a1', '8.dc1.b1', '8.dd1.a1', '8.dd1.b1'], 'contains': ['32.d1.a1', '32.bb1.a1', '32.cn1.a1', '32.cn1.b1', '32.cz1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7740, -1, 3864, -1, 7758, -1, 3859, -1], 'generators': [39, 216, 64], 'label': '256.18790.16.cq1.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.cq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057432
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cr1', '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.i1.a1', '8.cx1.a1', '8.cx1.b1', '8.df1.a1', '8.df1.b1', '8.di1.a1', '8.di1.b1'], 'contains': ['32.d1.a1', '32.bc1.a1', '32.co1.a1', '32.da1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6725, -1, 5846, -1, 6741, -1, 5839, -1], 'generators': [35, 216, 64], 'label': '256.18790.16.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.cr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057433
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cs1', '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': ['8.n1.a1', '8.cx1.a1', '8.cx1.b1', '8.dg1.a1', '8.dg1.b1', '8.dj1.a1', '8.dj1.b1'], 'contains': ['32.d1.a1', '32.db1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7074, -1, 5629, -1, 7091, -1, 5621, -1], 'generators': [6, 64], 'label': '256.18790.16.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.cs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057434
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ct1', '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': ['8.o1.a1', '8.cw1.a1', '8.cw1.b1', '8.di1.a1', '8.di1.b1', '8.dj1.a1', '8.dj1.b1'], 'contains': ['32.d1.a1', '32.dc1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5840, -1, 5662, -1, 5854, -1, 5655, -1], 'generators': [38, 64], 'label': '256.18790.16.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ct1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057435
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cu1', '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.h1.a1', '8.ct1.a1', '8.dh1.a1'], 'contains': ['32.e1.a1', '32.bb1.a1', '32.cr1.a1', '32.cr1.b1', '32.cw1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5278, -1, 5703, -1, 5290, -1, 5695, -1], 'generators': [39, 24, 80], 'label': '256.18790.16.cu1.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.cu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057436
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cv1', '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.i1.a1', '8.da1.a1', '8.de1.a1'], 'contains': ['32.e1.a1', '32.bc1.a1', '32.cs1.a1', '32.cx1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4106, -1, 7516, -1, 4116, -1, 7507, -1], 'generators': [35, 24, 80], 'label': '256.18790.16.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '16.cv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057437
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.de1.a1', '8.dh1.a1'], 'contains': ['32.e1.a1', '32.ct1.a1', '32.ct1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1542, -1, 6722, -1, 1545, -1, 6713, -1], 'generators': [36, 80], 'label': '256.18790.16.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.cw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057438
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.da1.a1', '8.db1.a1'], 'contains': ['32.e1.a1', '32.cy1.a1', '32.cy1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4445, -1, 8155, -1, 4455, -1, 8145, -1], 'generators': [33, 24], 'label': '256.18790.16.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.cx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057439
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.dk1.a1', '8.dl1.a1'], 'contains': ['32.bd1.a1', '32.be1.a1', '32.bj1.a1', '32.bl1.a1', '32.bq1.a1', '32.bu1.c1', '32.dd1.c1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6532, -1, 5093, -1, 6547, -1, 5086, -1], 'generators': [117, 2, 8], 'label': '256.18790.16.cy1.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.cy1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057440
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.dk1.b1', '8.dl1.a1'], 'contains': ['32.bd1.a1', '32.be1.a1', '32.bj1.b1', '32.bl1.b1', '32.bq1.b1', '32.bu1.d1', '32.dd1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6532, -1, 4983, -1, 6547, -1, 4977, -1], 'generators': [37, 2, 8], 'label': '256.18790.16.cy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cy1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057441
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'contains': ['8.d1.a1', '8.l1.a1', '8.o1.a1', '8.eb1.a1', '8.eb1.b1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3822, 5192, 7194, 5131, 3831, 5207, 7185, 5163], 'generators': [33, 38, 64], 'label': '256.18790.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'normal_contains': ['8.d1.a1', '8.l1.a1', '8.o1.a1'], '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: 26057442
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.dk1.a1', '8.dl1.b1'], 'contains': ['32.bd1.b1', '32.be1.a1', '32.bj1.a1', '32.bl1.c1', '32.bq1.c1', '32.bu1.a1', '32.dd1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6532, -1, 4951, -1, 6547, -1, 4945, -1], 'generators': [53, 2, 8], 'label': '256.18790.16.cy1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cy1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057443
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.dk1.b1', '8.dl1.b1'], 'contains': ['32.bd1.b1', '32.be1.a1', '32.bj1.b1', '32.bl1.d1', '32.bq1.d1', '32.bu1.b1', '32.dd1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6532, -1, 4890, -1, 6547, -1, 4883, -1], 'generators': [101, 2, 8], 'label': '256.18790.16.cy1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cy1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057444
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dm1.a1', '8.dn1.a1'], 'contains': ['32.bd1.a1', '32.bf1.a1', '32.bg1.a1', '32.bm1.a1', '32.bn1.a1', '32.bx1.b1', '32.cc1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2636, -1, 934, -1, 2642, -1, 933, -1], 'generators': [117, 34, 8], 'label': '256.18790.16.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057445
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dm1.b1', '8.dn1.a1'], 'contains': ['32.bd1.a1', '32.bf1.a1', '32.bg1.b1', '32.bm1.b1', '32.bn1.b1', '32.bx1.d1', '32.cc1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2636, -1, 762, -1, 2642, -1, 761, -1], 'generators': [37, 34, 8], 'label': '256.18790.16.cz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057446
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dm1.a1', '8.dn1.b1'], 'contains': ['32.bd1.b1', '32.bf1.a1', '32.bg1.a1', '32.bm1.c1', '32.bn1.c1', '32.bx1.a1', '32.cc1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2636, -1, 685, -1, 2642, -1, 683, -1], 'generators': [53, 34, 8], 'label': '256.18790.16.cz1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cz1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057447
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.dm1.b1', '8.dn1.b1'], 'contains': ['32.bd1.b1', '32.bf1.a1', '32.bg1.b1', '32.bm1.d1', '32.bn1.d1', '32.bx1.c1', '32.cc1.c1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2636, -1, 560, -1, 2642, -1, 559, -1], 'generators': [101, 34, 8], 'label': '256.18790.16.cz1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.cz1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057448
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.dk1.a1', '8.dk1.b1', '8.dm1.a1', '8.dm1.b1', '8.dp1.a1', '8.dp1.b1'], 'contains': ['32.f1.a1', '32.bd1.a1', '32.bd1.b1', '32.bo1.a1', '32.bo1.b1', '32.br1.a1', '32.cq1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6661, -1, 3400, -1, 6676, -1, 3396, -1], 'generators': [37, 200, 64], 'label': '256.18790.16.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.da1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.da1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057449
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.db1', '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': ['8.b1.a1', '8.dk1.a1', '8.dk1.b1', '8.dr1.a1', '8.dr1.b1', '8.ds1.a1', '8.ds1.b1'], 'contains': ['32.f1.a1', '32.be1.a1', '32.bs1.a1', '32.bv1.a1', '32.cm1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8085, -1, 4291, -1, 8104, -1, 4285, -1], 'generators': [2, 200, 64], 'label': '256.18790.16.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.db1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.db1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057450
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dc1', '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': ['8.b1.a1', '8.dl1.a1', '8.dl1.b1', '8.dt1.a1', '8.dt1.b1', '8.du1.a1', '8.du1.b1'], 'contains': ['32.g1.a1', '32.be1.a1', '32.bt1.a1', '32.bw1.a1', '32.cv1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6404, -1, 7200, -1, 6418, -1, 7191, -1], 'generators': [2, 216, 80], 'label': '256.18790.16.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057451
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dd1', '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': ['8.c1.a1', '8.dm1.a1', '8.dm1.b1', '8.dr1.a1', '8.dr1.b1', '8.dw1.a1', '8.dw1.b1'], 'contains': ['32.f1.a1', '32.bf1.a1', '32.by1.a1', '32.ca1.a1', '32.cl1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5495, -1, 1532, -1, 5508, -1, 1531, -1], 'generators': [34, 200, 64], 'label': '256.18790.16.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057452
    {'ambient': '256.18790', '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': ['128.g1.a1', '128.i1.a1', '128.h1.a1', '128.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '4.k1.a1', '4.l1.a1', '4.bb1.a1', '4.bf1.a1', '4.by1.a1', '4.by1.b1', '4.by1.c1', '4.by1.d1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4424, 5337, 8185, 3346, 4434, 5352, 8175, 3367], 'generators': [33, 2, 4, 64], 'label': '256.18790.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.f1.a1', '4.k1.a1', '4.l1.a1', '4.bb1.a1', '4.bf1.a1'], '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: 26057453
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['64.bd1.b1', '64.bd1.d1', '64.bd1.c1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.k1.a1', '8.ck1.a1', '8.ck1.b1', '8.dh1.a1', '8.ec1.a1', '8.ec1.b1'], 'core': '4.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2668, 8568, 6972, 6023, 2675, 8593, 6963, 6059], 'generators': [3, 36, 16, 64], 'label': '256.18790.4.x1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.x1.a1', 'normal_contained_in': ['2.b1.a1', '2.n1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.k1.a1'], 'normalizer': '1.a1.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: 26057454
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.de1', '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': ['8.c1.a1', '8.dn1.a1', '8.dn1.b1', '8.dv1.a1', '8.dv1.b1', '8.dx1.a1', '8.dx1.b1'], 'contains': ['32.g1.a1', '32.bf1.a1', '32.bz1.a1', '32.cb1.a1', '32.cu1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3614, -1, 4181, -1, 3621, -1, 4176, -1], 'generators': [34, 216, 80], 'label': '256.18790.16.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.de1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.de1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057455
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.df1', '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.bc1.a1', '8.dy1.a1', '8.dz1.a1'], 'contains': ['32.bg1.a1', '32.bh1.a1', '32.bi1.a1', '32.dj1.a1', '32.dj1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [905, -1, 9268, -1, 906, -1, 9256, -1], 'generators': [3, 4, 128], 'label': '256.18790.16.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '16.df1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057456
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.df1', '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.bc1.a1', '8.dy1.a1', '8.dz1.b1'], 'contains': ['32.bg1.a1', '32.bh1.a1', '32.bi1.b1', '32.dj1.c1', '32.dj1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [905, -1, 9361, -1, 906, -1, 9349, -1], 'generators': [3, 68, 128], 'label': '256.18790.16.df1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '16.df1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057457
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.df1', '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.bc1.a1', '8.dy1.b1', '8.dz1.a1'], 'contains': ['32.bg1.b1', '32.bh1.a1', '32.bi1.a1', '32.dj1.e1', '32.dj1.f1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [905, -1, 9222, -1, 906, -1, 9209, -1], 'generators': [83, 4, 128], 'label': '256.18790.16.df1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '16.df1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057458
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.df1', '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.bc1.a1', '8.dy1.b1', '8.dz1.b1'], 'contains': ['32.bg1.b1', '32.bh1.a1', '32.bi1.b1', '32.dj1.g1', '32.dj1.h1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [905, -1, 9314, -1, 906, -1, 9302, -1], 'generators': [83, 68, 128], 'label': '256.18790.16.df1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '16.df1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057459
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dg1', '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.d1.a1', '8.dn1.a1', '8.dn1.b1', '8.dz1.a1', '8.dz1.b1', '8.eb1.a1', '8.eb1.b1'], 'contains': ['32.g1.a1', '32.bg1.a1', '32.bg1.b1', '32.cf1.a1', '32.cg1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2994, -1, 6947, -1, 3001, -1, 6938, -1], 'generators': [7, 216, 80], 'label': '256.18790.16.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.dg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057460
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dh1', '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.e1.a1', '8.dy1.a1', '8.dy1.b1', '8.ec1.a1', '8.ec1.b1', '8.ed1.a1', '8.ed1.b1'], 'contains': ['32.f1.a1', '32.bh1.a1', '32.ch1.a1', '32.ci1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2354, -1, 7470, -1, 2359, -1, 7460, -1], 'generators': [3, 200, 64], 'label': '256.18790.16.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.dh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057461
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.di1', '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.e1.a1', '8.do1.a1', '8.do1.b1', '8.dv1.a1', '8.dv1.b1', '8.dz1.a1', '8.dz1.b1'], 'contains': ['32.g1.a1', '32.bh1.a1', '32.cj1.a1', '32.ck1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3071, -1, 8335, -1, 3078, -1, 8325, -1], 'generators': [3, 216, 80], 'label': '256.18790.16.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.di1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.di1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057462
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.dy1.a1', '8.dy1.b1', '8.ee1.a1', '8.ee1.b1', '8.ef1.a1', '8.ef1.b1'], 'contains': ['32.f1.a1', '32.bi1.a1', '32.bi1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1679, -1, 9032, -1, 1682, -1, 9020, -1], 'generators': [4, 64], 'label': '256.18790.16.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.dj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057463
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dk1', '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.i1.a1', '8.ea1.a1', '8.ea1.b1', '8.ed1.a1', '8.ed1.b1', '8.ee1.a1', '8.ee1.b1'], 'contains': ['32.f1.a1', '32.bk1.a1', '32.co1.a1', '32.cs1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3678, -1, 7423, -1, 3686, -1, 7414, -1], 'generators': [35, 200, 64], 'label': '256.18790.16.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.dk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057464
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['64.bd1.c1', '64.bd1.d1', '64.bd1.b1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.i1.a1', '8.j1.a1', '8.ch1.a1', '8.ci1.a1', '8.df1.a1', '8.df1.b1', '8.ed1.a1', '8.ed1.b1'], 'core': '4.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4884, 743, 6890, 7116, 4895, 745, 6881, 7160], 'generators': [3, 32, 216, 16], 'label': '256.18790.4.y1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.y1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'normal_contains': ['8.e1.a1', '8.i1.a1', '8.j1.a1'], 'normalizer': '1.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: 26057465
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.ea1.a1', '8.ea1.b1', '8.ec1.a1', '8.ec1.b1', '8.ef1.a1', '8.ef1.b1'], 'contains': ['32.f1.a1', '32.ct1.a1', '32.ct1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1618, -1, 6834, -1, 1621, -1, 6825, -1], 'generators': [36, 64], 'label': '256.18790.16.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.dl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057466
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.dp1.a1', '8.dp1.b1', '8.ds1.a1', '8.ds1.b1', '8.dw1.a1', '8.dw1.b1'], 'contains': ['32.f1.a1', '32.cp1.a1', '32.cp1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8348, -1, 2643, -1, 8367, -1, 2640, -1], 'generators': [5, 200], 'label': '256.18790.16.dm1.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.dm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057467
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dn1', '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.h1.a1', '8.dl1.a1', '8.dl1.b1', '8.eg1.a1', '8.eg1.b1', '8.eh1.a1', '8.eh1.b1'], 'contains': ['32.g1.a1', '32.bj1.a1', '32.bj1.b1', '32.cw1.a1', '32.cz1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5048, -1, 7028, -1, 5059, -1, 7019, -1], 'generators': [39, 216, 80], 'label': '256.18790.16.dn1.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.dn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057468
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.do1', '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.i1.a1', '8.dq1.a1', '8.dq1.b1', '8.du1.a1', '8.du1.b1', '8.eg1.a1', '8.eg1.b1'], 'contains': ['32.g1.a1', '32.bk1.a1', '32.cx1.a1', '32.da1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4511, -1, 8196, -1, 4522, -1, 8185, -1], 'generators': [35, 216, 80], 'label': '256.18790.16.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.do1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.do1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057469
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dp1', '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': ['8.n1.a1', '8.dq1.a1', '8.dq1.b1', '8.dt1.a1', '8.dt1.b1', '8.eh1.a1', '8.eh1.b1'], 'contains': ['32.g1.a1', '32.db1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4633, -1, 7168, -1, 4643, -1, 7159, -1], 'generators': [6, 80], 'label': '256.18790.16.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057470
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dq1', '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': ['8.o1.a1', '8.do1.a1', '8.do1.b1', '8.dx1.a1', '8.dx1.b1', '8.eb1.a1', '8.eb1.b1'], 'contains': ['32.g1.a1', '32.dc1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3514, -1, 6987, -1, 3522, -1, 6979, -1], 'generators': [38, 80], 'label': '256.18790.16.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.dq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057471
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dr1', '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.bd1.a1', '8.ee1.a1', '8.eg1.a1'], 'contains': ['32.bi1.a1', '32.bj1.a1', '32.bk1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2049, -1, 9092, -1, 2053, -1, 9080, -1], 'generators': [35, 4], 'label': '256.18790.16.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.dr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057472
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dr1', '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.bd1.a1', '8.ee1.b1', '8.eg1.a1'], 'contains': ['32.bi1.a1', '32.bj1.b1', '32.bk1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2049, -1, 9061, -1, 2053, -1, 9049, -1], 'generators': [115, 4], 'label': '256.18790.16.dr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.dr1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057473
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dr1', '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.bd1.a1', '8.ee1.a1', '8.eg1.b1'], 'contains': ['32.bi1.b1', '32.bj1.a1', '32.bk1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2049, -1, 9155, -1, 2053, -1, 9143, -1], 'generators': [35, 68], 'label': '256.18790.16.dr1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.dr1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057474
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dr1', '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.bd1.a1', '8.ee1.b1', '8.eg1.b1'], 'contains': ['32.bi1.b1', '32.bj1.b1', '32.bk1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2049, -1, 9123, -1, 2053, -1, 9112, -1], 'generators': [115, 68], 'label': '256.18790.16.dr1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.dr1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057475
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': ['64.bd1.c1', '64.bd1.b1', '64.bd1.d1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'contains': ['8.e1.a1', '8.m1.a1', '8.n1.a1', '8.dg1.a1', '8.dg1.b1'], 'core': '4.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5145, 6071, 5511, 1309, 5157, 6088, 5504, 1317], 'generators': [5, 6, 16], 'label': '256.18790.4.z1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.z1.a1', 'normal_contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.m1.a1', '8.n1.a1'], 'normalizer': '1.a1.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: 26057476
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cs1.a1', '8.dk1.a1', '8.ei1.a1', '8.ei1.c1', '8.ej1.a1', '8.ej1.c1'], 'contains': ['32.bl1.a1', '32.bo1.a1', '32.bu1.a1', '32.bv1.a1', '32.cn1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8530, -1, 3369, -1, 8550, -1, 3365, -1], 'generators': [253, 2, 64], 'label': '256.18790.16.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ds1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057477
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cs1.a1', '8.dk1.b1', '8.ei1.b1', '8.ei1.d1', '8.ej1.b1', '8.ej1.d1'], 'contains': ['32.bl1.b1', '32.bo1.a1', '32.bu1.b1', '32.bv1.a1', '32.cn1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8530, -1, 3260, -1, 8550, -1, 3256, -1], 'generators': [37, 2, 64], 'label': '256.18790.16.ds1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ds1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057478
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cs1.b1', '8.dk1.a1', '8.ei1.e1', '8.ei1.g1', '8.ej1.e1', '8.ej1.g1'], 'contains': ['32.bl1.c1', '32.bo1.b1', '32.bu1.c1', '32.bv1.a1', '32.cn1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8530, -1, 3431, -1, 8550, -1, 3427, -1], 'generators': [53, 2, 64], 'label': '256.18790.16.ds1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ds1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057479
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.cs1.b1', '8.dk1.b1', '8.ei1.f1', '8.ei1.h1', '8.ej1.f1', '8.ej1.h1'], 'contains': ['32.bl1.d1', '32.bo1.b1', '32.bu1.d1', '32.bv1.a1', '32.cn1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8530, -1, 3338, -1, 8550, -1, 3334, -1], 'generators': [237, 2, 64], 'label': '256.18790.16.ds1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ds1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057480
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.ct1.a1', '8.dl1.a1'], 'contains': ['32.bl1.a1', '32.bl1.b1', '32.bp1.a1', '32.bu1.c1', '32.bu1.d1', '32.bw1.a1', '32.cw1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7021, -1, 5015, -1, 7037, -1, 5008, -1], 'generators': [37, 2, 80], 'label': '256.18790.16.dt1.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.dt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057481
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.ct1.a1', '8.dl1.b1'], 'contains': ['32.bl1.c1', '32.bl1.d1', '32.bp1.b1', '32.bu1.a1', '32.bu1.b1', '32.bw1.a1', '32.cw1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7021, -1, 4921, -1, 7037, -1, 4914, -1], 'generators': [101, 2, 80], 'label': '256.18790.16.dt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.dt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057482
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cu1.a1', '8.dm1.a1', '8.ei1.a1', '8.ei1.b1', '8.ek1.a1', '8.ek1.b1'], 'contains': ['32.bm1.a1', '32.bo1.a1', '32.bx1.a1', '32.ca1.a1', '32.cd1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7664, -1, 1081, -1, 7682, -1, 1079, -1], 'generators': [37, 250, 64], 'label': '256.18790.16.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.du1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057483
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cu1.a1', '8.dm1.b1', '8.ei1.c1', '8.ei1.d1', '8.ek1.c1', '8.ek1.d1'], 'contains': ['32.bm1.b1', '32.bo1.a1', '32.bx1.c1', '32.ca1.a1', '32.cd1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7664, -1, 1033, -1, 7682, -1, 1033, -1], 'generators': [253, 250, 64], 'label': '256.18790.16.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.du1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057484
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cu1.b1', '8.dm1.a1', '8.ei1.e1', '8.ei1.f1', '8.ek1.e1', '8.ek1.f1'], 'contains': ['32.bm1.c1', '32.bo1.b1', '32.bx1.b1', '32.ca1.a1', '32.cd1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7664, -1, 1205, -1, 7682, -1, 1203, -1], 'generators': [237, 250, 64], 'label': '256.18790.16.du1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.du1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057485
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cu1.b1', '8.dm1.b1', '8.ei1.g1', '8.ei1.h1', '8.ek1.g1', '8.ek1.h1'], 'contains': ['32.bm1.d1', '32.bo1.b1', '32.bx1.d1', '32.ca1.a1', '32.cd1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7664, -1, 1127, -1, 7682, -1, 1125, -1], 'generators': [53, 250, 64], 'label': '256.18790.16.du1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.du1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057486
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['64.bd1.c1', '64.bd1.d1', '64.bd1.b1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'contains': ['8.f1.a1', '8.g1.a1', '8.m1.a1'], 'core': '4.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2322, 6605, 8703, 2064, 2328, 6624, 8692, 2076], 'generators': [1, 4], 'label': '256.18790.4.ba1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ba1.a1', 'normal_contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'normal_contains': ['8.f1.a1', '8.g1.a1', '8.m1.a1'], 'normalizer': '1.a1.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: 26057487
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cv1.a1', '8.dn1.a1'], 'contains': ['32.bm1.a1', '32.bm1.b1', '32.bp1.a1', '32.bx1.b1', '32.bx1.d1', '32.cb1.a1', '32.cf1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3300, -1, 513, -1, 3308, -1, 513, -1], 'generators': [37, 250, 80], 'label': '256.18790.16.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.dv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057488
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.cv1.a1', '8.dn1.b1'], 'contains': ['32.bm1.c1', '32.bm1.d1', '32.bp1.b1', '32.bx1.a1', '32.bx1.c1', '32.cb1.a1', '32.cf1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3300, -1, 374, -1, 3308, -1, 373, -1], 'generators': [101, 250, 80], 'label': '256.18790.16.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.dv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057489
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cu1.a1', '8.dm1.a1', '8.ej1.a1', '8.ej1.b1', '8.el1.a1', '8.el1.b1'], 'contains': ['32.bn1.a1', '32.bo1.a1', '32.cc1.a1', '32.cd1.a1', '32.cl1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 1275, -1, 7976, -1, 1274, -1], 'generators': [253, 34, 64], 'label': '256.18790.16.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057490
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cu1.a1', '8.dm1.b1', '8.ej1.c1', '8.ej1.d1', '8.el1.c1', '8.el1.d1'], 'contains': ['32.bn1.b1', '32.bo1.a1', '32.cc1.c1', '32.cd1.b1', '32.cl1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 1166, -1, 7976, -1, 1164, -1], 'generators': [37, 34, 64], 'label': '256.18790.16.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057491
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cu1.b1', '8.dm1.a1', '8.ej1.e1', '8.ej1.f1', '8.el1.e1', '8.el1.f1'], 'contains': ['32.bn1.c1', '32.bo1.b1', '32.cc1.b1', '32.cd1.a1', '32.cl1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 1307, -1, 7976, -1, 1305, -1], 'generators': [53, 34, 64], 'label': '256.18790.16.dw1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dw1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057492
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cu1.b1', '8.dm1.b1', '8.ej1.g1', '8.ej1.h1', '8.el1.g1', '8.el1.h1'], 'contains': ['32.bn1.d1', '32.bo1.b1', '32.cc1.d1', '32.cd1.b1', '32.cl1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7957, -1, 1244, -1, 7976, -1, 1242, -1], 'generators': [237, 34, 64], 'label': '256.18790.16.dw1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dw1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057493
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cv1.a1', '8.dn1.a1'], 'contains': ['32.bn1.a1', '32.bn1.b1', '32.bp1.a1', '32.cc1.b1', '32.cc1.d1', '32.cf1.a1', '32.cu1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3364, -1, 895, -1, 3372, -1, 894, -1], 'generators': [37, 34, 80], 'label': '256.18790.16.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.dx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057494
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.cv1.a1', '8.dn1.b1'], 'contains': ['32.bn1.c1', '32.bn1.d1', '32.bp1.b1', '32.cc1.a1', '32.cc1.c1', '32.cf1.a1', '32.cu1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3364, -1, 645, -1, 3372, -1, 644, -1], 'generators': [101, 34, 80], 'label': '256.18790.16.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.dx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057495
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.cs1.a1', '8.dk1.a1', '8.ek1.a1', '8.ek1.c1', '8.el1.a1', '8.el1.c1'], 'contains': ['32.bo1.a1', '32.bq1.a1', '32.cm1.a1', '32.cn1.a1', '32.dd1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8414, -1, 3221, -1, 8434, -1, 3217, -1], 'generators': [37, 218, 64], 'label': '256.18790.16.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dy1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057496
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.cs1.a1', '8.dk1.b1', '8.ek1.b1', '8.ek1.d1', '8.el1.b1', '8.el1.d1'], 'contains': ['32.bo1.a1', '32.bq1.b1', '32.cm1.a1', '32.cn1.b1', '32.dd1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8414, -1, 3028, -1, 8434, -1, 3024, -1], 'generators': [253, 218, 64], 'label': '256.18790.16.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dy1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057497
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': ['64.bd1.b1', '64.bd1.c1', '64.bd1.d1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.m1.a1', '2.n1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1', '8.bd1.a1', '8.ee1.a1', '8.ee1.b1', '8.eg1.a1', '8.eg1.b1'], 'core': '4.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3490, 2347, 9488, 6555, 3499, 2353, 9476, 6595], 'generators': [35, 4, 16, 64], 'label': '256.18790.4.bb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bb1.a1', 'normal_contained_in': ['2.c1.a1', '2.n1.a1', '2.m1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1'], 'normalizer': '1.a1.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: 26057498
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.cs1.b1', '8.dk1.a1', '8.ek1.e1', '8.ek1.g1', '8.el1.e1', '8.el1.g1'], 'contains': ['32.bo1.b1', '32.bq1.c1', '32.cm1.a1', '32.cn1.a1', '32.dd1.c1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8414, -1, 3298, -1, 8434, -1, 3295, -1], 'generators': [237, 218, 64], 'label': '256.18790.16.dy1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dy1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057538
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.en1', '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.bt1.a1', '8.da1.a1', '8.du1.b1'], 'contains': ['32.bw1.a1', '32.cx1.a1', '32.cy1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5598, -1, 8516, -1, 5611, -1, 8505, -1], 'generators': [97, 2], 'label': '256.18790.16.en1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.en1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057499
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.cs1.b1', '8.dk1.b1', '8.ek1.f1', '8.ek1.h1', '8.el1.f1', '8.el1.h1'], 'contains': ['32.bo1.b1', '32.bq1.d1', '32.cm1.a1', '32.cn1.b1', '32.dd1.d1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8414, -1, 3174, -1, 8434, -1, 3170, -1], 'generators': [53, 218, 64], 'label': '256.18790.16.dy1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dy1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057500
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.bi1.a1', '8.dp1.a1', '8.ej1.a1', '8.ej1.d1', '8.ek1.a1', '8.ek1.d1'], 'contains': ['32.i1.a1', '32.bo1.a1', '32.cp1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8939, -1, 2037, -1, 8960, -1, 2035, -1], 'generators': [5, 32], 'label': '256.18790.16.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057501
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '8.bi1.a1', '8.dp1.b1', '8.ej1.b1', '8.ej1.c1', '8.ek1.b1', '8.ek1.c1'], 'contains': ['32.i1.b1', '32.bo1.a1', '32.cp1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8939, -1, 1992, -1, 8960, -1, 1989, -1], 'generators': [21, 48], 'label': '256.18790.16.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057502
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.c1', '8.bi1.a1', '8.dp1.a1', '8.ej1.e1', '8.ej1.h1', '8.ek1.e1', '8.ek1.h1'], 'contains': ['32.i1.a1', '32.bo1.b1', '32.cp1.b1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8939, -1, 1571, -1, 8960, -1, 1569, -1], 'generators': [21, 32], 'label': '256.18790.16.dz1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dz1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057503
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.d1', '8.bi1.a1', '8.dp1.b1', '8.ej1.f1', '8.ej1.g1', '8.ek1.f1', '8.ek1.g1'], 'contains': ['32.i1.b1', '32.bo1.b1', '32.cp1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8939, -1, 2817, -1, 8960, -1, 2813, -1], 'generators': [5, 48], 'label': '256.18790.16.dz1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.dz1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057504
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.b1', '8.bj1.a1', '8.dp1.a1', '8.ei1.a1', '8.ei1.d1', '8.el1.a1', '8.el1.d1'], 'contains': ['32.j1.a1', '32.bo1.a1', '32.cp1.b1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 1691, -1, 9227, -1, 1689, -1], 'generators': [21, 232], 'label': '256.18790.16.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ea1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057505
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.bj1.a1', '8.dp1.b1', '8.ei1.b1', '8.ei1.c1', '8.el1.b1', '8.el1.c1'], 'contains': ['32.j1.b1', '32.bo1.a1', '32.cp1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 2677, -1, 9227, -1, 2674, -1], 'generators': [5, 248], 'label': '256.18790.16.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ea1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057506
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.d1', '8.bj1.a1', '8.dp1.a1', '8.ei1.e1', '8.ei1.h1', '8.el1.e1', '8.el1.h1'], 'contains': ['32.j1.a1', '32.bo1.b1', '32.cp1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 2275, -1, 9227, -1, 2272, -1], 'generators': [5, 232], 'label': '256.18790.16.ea1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ea1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057507
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.c1', '8.bj1.a1', '8.dp1.b1', '8.ei1.f1', '8.ei1.g1', '8.el1.f1', '8.el1.g1'], 'contains': ['32.j1.b1', '32.bo1.b1', '32.cp1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9206, -1, 1951, -1, 9227, -1, 1949, -1], 'generators': [21, 248], 'label': '256.18790.16.ea1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ea1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057508
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': ['64.bd1.b1', '64.bd1.c1', '64.bd1.d1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'contains': ['8.f1.a1', '8.j1.a1', '8.k1.a1', '8.ef1.a1', '8.ef1.b1'], 'core': '4.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3279, 9345, 7049, 3457, 3287, 9373, 7040, 3478], 'generators': [4, 32, 16], 'label': '256.18790.4.bc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bc1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'normal_contains': ['8.f1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.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: 26057509
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.ct1.a1', '8.dl1.a1'], 'contains': ['32.bp1.a1', '32.bq1.a1', '32.bq1.b1', '32.cv1.a1', '32.cw1.a1', '32.dd1.c1', '32.dd1.d1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6468, -1, 4616, -1, 6483, -1, 4611, -1], 'generators': [37, 218, 80], 'label': '256.18790.16.eb1.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.eb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057510
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.ct1.a1', '8.dl1.b1'], 'contains': ['32.bp1.b1', '32.bq1.c1', '32.bq1.d1', '32.cv1.a1', '32.cw1.a1', '32.dd1.a1', '32.dd1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6468, -1, 4570, -1, 6483, -1, 4564, -1], 'generators': [101, 218, 80], 'label': '256.18790.16.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.eb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057511
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.ct1.a1', '8.dk1.a1'], 'contains': ['32.bl1.a1', '32.bl1.c1', '32.bq1.a1', '32.bq1.c1', '32.br1.a1', '32.bs1.a1', '32.cr1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6224, -1, 4531, -1, 6238, -1, 4525, -1], 'generators': [53, 2, 200], 'label': '256.18790.16.ec1.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.ec1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ec1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057512
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.ct1.a1', '8.dk1.b1'], 'contains': ['32.bl1.b1', '32.bl1.d1', '32.bq1.b1', '32.bq1.d1', '32.br1.a1', '32.bs1.a1', '32.cr1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6224, -1, 4500, -1, 6238, -1, 4494, -1], 'generators': [37, 2, 200], 'label': '256.18790.16.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ec1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ec1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057513
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.cs1.a1', '8.dl1.a1'], 'contains': ['32.h1.a1', '32.bl1.a1', '32.bl1.b1', '32.bq1.a1', '32.bq1.b1', '32.bt1.a1', '32.cz1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6789, -1, 4733, -1, 6805, -1, 4727, -1], 'generators': [37, 2, 216], 'label': '256.18790.16.ed1.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.ed1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ed1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057514
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.cs1.b1', '8.dl1.b1'], 'contains': ['32.h1.b1', '32.bl1.c1', '32.bl1.d1', '32.bq1.c1', '32.bq1.d1', '32.bt1.a1', '32.cz1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6789, -1, 4469, -1, 6805, -1, 4463, -1], 'generators': [53, 2, 216], 'label': '256.18790.16.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ed1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ed1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057515
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.cv1.a1', '8.dm1.a1'], 'contains': ['32.bm1.a1', '32.bm1.c1', '32.bn1.a1', '32.bn1.c1', '32.br1.a1', '32.by1.a1', '32.ce1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2430, -1, 188, -1, 2436, -1, 187, -1], 'generators': [53, 34, 200], 'label': '256.18790.16.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ee1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057516
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.cv1.a1', '8.dm1.b1'], 'contains': ['32.bm1.b1', '32.bm1.d1', '32.bn1.b1', '32.bn1.d1', '32.br1.a1', '32.by1.a1', '32.ce1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2430, -1, 48, -1, 2436, -1, 48, -1], 'generators': [37, 34, 200], 'label': '256.18790.16.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ee1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057517
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.cu1.a1', '8.dn1.a1'], 'contains': ['32.h1.a1', '32.bm1.a1', '32.bm1.b1', '32.bn1.a1', '32.bn1.b1', '32.bz1.a1', '32.cg1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2865, -1, 141, -1, 2872, -1, 141, -1], 'generators': [37, 34, 216], 'label': '256.18790.16.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ef1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ef1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057518
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.cu1.b1', '8.dn1.b1'], 'contains': ['32.h1.b1', '32.bm1.c1', '32.bm1.d1', '32.bn1.c1', '32.bn1.d1', '32.bz1.a1', '32.cg1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2865, -1, 95, -1, 2872, -1, 95, -1], 'generators': [53, 34, 216], 'label': '256.18790.16.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ef1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ef1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057519
    {'ambient': '256.18790', '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': ['64.bd1.a1', '64.bd1.c1', '64.bd1.d1', '64.bd1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.m1.a1', '2.o1.a1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.o1.a1', '8.cr1.a1', '8.cr1.b1'], 'core': '4.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2223, 4936, 6532, 6315, 2228, 4951, 6524, 6353], 'generators': [1, 38, 64], 'label': '256.18790.4.bd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bd1.a1', 'normal_contained_in': ['2.b1.a1', '2.o1.a1', '2.m1.a1'], 'normal_contains': ['8.g1.a1', '8.h1.a1', '8.o1.a1'], 'normalizer': '1.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: 26057520
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eg1', '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.bm1.a1', '8.cw1.a1', '8.do1.a1'], 'contains': ['32.h1.a1', '32.ck1.a1', '32.dc1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3411, -1, 6129, -1, 3418, -1, 6122, -1], 'generators': [37, 38], 'label': '256.18790.16.eg1.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.eg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057521
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eg1', '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.bm1.a1', '8.cw1.b1', '8.do1.b1'], 'contains': ['32.h1.b1', '32.ck1.a1', '32.dc1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3411, -1, 6105, -1, 3418, -1, 6097, -1], 'generators': [53, 38], 'label': '256.18790.16.eg1.b1', '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.eg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057522
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eh1', '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.bn1.a1', '8.cx1.a1', '8.dq1.a1'], 'contains': ['32.h1.a1', '32.da1.a1', '32.db1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4578, -1, 5776, -1, 4588, -1, 5769, -1], 'generators': [37, 6], 'label': '256.18790.16.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.eh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057523
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eh1', '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.bn1.a1', '8.cx1.b1', '8.dq1.b1'], 'contains': ['32.h1.b1', '32.da1.a1', '32.db1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4578, -1, 5742, -1, 4588, -1, 5736, -1], 'generators': [53, 6], 'label': '256.18790.16.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.eh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057524
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bp1.a1', '8.ct1.a1', '8.dk1.a1'], 'contains': ['32.bs1.a1', '32.bu1.a1', '32.bu1.c1', '32.cq1.a1', '32.cr1.a1', '32.dd1.a1', '32.dd1.c1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6288, -1, 5256, -1, 6302, -1, 5249, -1], 'generators': [117, 2, 200], 'label': '256.18790.16.ei1.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.ei1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ei1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057525
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bp1.a1', '8.ct1.a1', '8.dk1.b1'], 'contains': ['32.bs1.a1', '32.bu1.b1', '32.bu1.d1', '32.cq1.a1', '32.cr1.b1', '32.dd1.b1', '32.dd1.d1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6288, -1, 5162, -1, 6302, -1, 5156, -1], 'generators': [101, 2, 200], 'label': '256.18790.16.ei1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ei1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ei1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057526
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bp1.a1', '8.cs1.a1', '8.dl1.b1'], 'contains': ['32.k1.a1', '32.bt1.a1', '32.bu1.a1', '32.bu1.b1', '32.cz1.a1', '32.dd1.a1', '32.dd1.b1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6905, -1, 5209, -1, 6921, -1, 5202, -1], 'generators': [101, 2, 216], 'label': '256.18790.16.ej1.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.ej1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ej1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057527
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bp1.a1', '8.cs1.b1', '8.dl1.a1'], 'contains': ['32.k1.b1', '32.bt1.a1', '32.bu1.c1', '32.bu1.d1', '32.cz1.a1', '32.dd1.c1', '32.dd1.d1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6905, -1, 5355, -1, 6921, -1, 5349, -1], 'generators': [117, 2, 216], 'label': '256.18790.16.ej1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ej1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ej1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057528
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ek1', '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': ['8.q1.a1', '8.cy1.b1', '8.dr1.a1', '8.ei1.a1', '8.ei1.d1', '8.ei1.e1', '8.ei1.h1'], 'contains': ['32.j1.a1', '32.bv1.a1', '32.ca1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9157, -1, 2139, -1, 9179, -1, 2136, -1], 'generators': [2, 232], 'label': '256.18790.16.ek1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ek1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ek1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057529
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ek1', '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': ['8.q1.a1', '8.cy1.a1', '8.dr1.b1', '8.ei1.b1', '8.ei1.c1', '8.ei1.f1', '8.ei1.g1'], 'contains': ['32.j1.b1', '32.bv1.a1', '32.ca1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9157, -1, 2551, -1, 9179, -1, 2547, -1], 'generators': [2, 248], 'label': '256.18790.16.ek1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ek1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ek1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057530
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['64.bd1.a1', '64.bd1.b1', '64.bd1.d1', '64.bd1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'contains': ['8.g1.a1', '8.j1.a1', '8.l1.a1', '8.cm1.a1', '8.cn1.a1'], 'core': '4.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4760, 4164, 8571, 4017, 4772, 4176, 8560, 4041], 'generators': [1, 32, 216], 'label': '256.18790.4.be1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.be1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'normal_contains': ['8.g1.a1', '8.j1.a1', '8.l1.a1'], 'normalizer': '1.a1.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: 26057531
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.cz1.a1', '8.ds1.a1', '8.ei1.b1', '8.ei1.e1', '8.ej1.a1', '8.ej1.f1'], 'contains': ['32.bv1.a1', '32.cd1.a1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9437, -1, 2371, -1, 9459, -1, 2368, -1], 'generators': [221, 2], 'label': '256.18790.16.el1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.el1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057532
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.cz1.b1', '8.ds1.a1', '8.ei1.a1', '8.ei1.f1', '8.ej1.b1', '8.ej1.e1'], 'contains': ['32.bv1.a1', '32.cd1.a1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9437, -1, 1637, -1, 9459, -1, 1635, -1], 'generators': [21, 2], 'label': '256.18790.16.el1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.el1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057533
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.cz1.a1', '8.ds1.b1', '8.ei1.c1', '8.ei1.h1', '8.ej1.d1', '8.ej1.g1'], 'contains': ['32.bv1.a1', '32.cd1.b1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9437, -1, 2396, -1, 9459, -1, 2392, -1], 'generators': [5, 2], 'label': '256.18790.16.el1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.el1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057534
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.cz1.b1', '8.ds1.b1', '8.ei1.d1', '8.ei1.g1', '8.ej1.c1', '8.ej1.h1'], 'contains': ['32.bv1.a1', '32.cd1.b1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9437, -1, 1662, -1, 9459, -1, 1659, -1], 'generators': [205, 2], 'label': '256.18790.16.el1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.el1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057535
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.cy1.a1', '8.dr1.a1', '8.ej1.a1', '8.ej1.d1', '8.ej1.e1', '8.ej1.h1'], 'contains': ['32.i1.a1', '32.bv1.a1', '32.cl1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9110, -1, 1884, -1, 9131, -1, 1882, -1], 'generators': [2, 32], 'label': '256.18790.16.em1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.em1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.em1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057536
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.cy1.b1', '8.dr1.b1', '8.ej1.b1', '8.ej1.c1', '8.ej1.f1', '8.ej1.g1'], 'contains': ['32.i1.b1', '32.bv1.a1', '32.cl1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9110, -1, 2856, -1, 9131, -1, 2853, -1], 'generators': [2, 48], 'label': '256.18790.16.em1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.em1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.em1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057539
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1', '8.cv1.a1', '8.dm1.a1'], 'contains': ['32.bx1.a1', '32.bx1.b1', '32.by1.a1', '32.cc1.a1', '32.cc1.b1', '32.ce1.a1', '32.cq1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2495, -1, 832, -1, 2500, -1, 832, -1], 'generators': [117, 34, 200], 'label': '256.18790.16.eo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.eo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057540
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1', '8.cv1.a1', '8.dm1.b1'], 'contains': ['32.bx1.c1', '32.bx1.d1', '32.by1.a1', '32.cc1.c1', '32.cc1.d1', '32.ce1.b1', '32.cq1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2495, -1, 801, -1, 2500, -1, 800, -1], 'generators': [101, 34, 200], 'label': '256.18790.16.eo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.eo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057541
    {'ambient': '256.18790', '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': ['64.bd1.b1', '64.bd1.a1', '64.bd1.d1', '64.bd1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.l1.a1', '2.o1.a1'], 'contains': ['8.h1.a1', '8.l1.a1', '8.n1.a1', '8.eh1.a1', '8.eh1.b1'], 'core': '4.bf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4392, 5762, 7270, 2364, 4402, 5779, 7260, 2378], 'generators': [33, 6, 64], 'label': '256.18790.4.bf1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bf1.a1', 'normal_contained_in': ['2.c1.a1', '2.o1.a1', '2.l1.a1'], 'normal_contains': ['8.h1.a1', '8.l1.a1', '8.n1.a1'], 'normalizer': '1.a1.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: 26057542
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1', '8.cu1.a1', '8.dn1.b1'], 'contains': ['32.k1.a1', '32.bx1.a1', '32.bx1.c1', '32.bz1.a1', '32.cc1.a1', '32.cc1.c1', '32.cg1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2930, -1, 723, -1, 2936, -1, 722, -1], 'generators': [101, 34, 216], 'label': '256.18790.16.ep1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ep1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ep1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057543
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1', '8.cu1.b1', '8.dn1.a1'], 'contains': ['32.k1.b1', '32.bx1.b1', '32.bx1.d1', '32.bz1.a1', '32.cc1.b1', '32.cc1.d1', '32.cg1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2930, -1, 864, -1, 2936, -1, 863, -1], 'generators': [117, 34, 216], 'label': '256.18790.16.ep1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.ep1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ep1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057544
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eq1', '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.bx1.a1', '8.db1.a1', '8.dv1.a1'], 'contains': ['32.cb1.a1', '32.cj1.a1', '32.cy1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3993, -1, 8036, -1, 4002, -1, 8025, -1], 'generators': [33, 250], 'label': '256.18790.16.eq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.eq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057545
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eq1', '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.bx1.a1', '8.db1.a1', '8.dv1.b1'], 'contains': ['32.cb1.a1', '32.cj1.a1', '32.cy1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3993, -1, 8060, -1, 4002, -1, 8049, -1], 'generators': [97, 250], 'label': '256.18790.16.eq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.eq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057546
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.cy1.a1', '8.dr1.a1', '8.ek1.a1', '8.ek1.d1', '8.ek1.e1', '8.ek1.h1'], 'contains': ['32.i1.a1', '32.ca1.a1', '32.cm1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8769, -1, 1818, -1, 8789, -1, 1815, -1], 'generators': [218, 32], 'label': '256.18790.16.er1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.er1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.er1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057547
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.cy1.b1', '8.dr1.b1', '8.ek1.b1', '8.ek1.c1', '8.ek1.f1', '8.ek1.g1'], 'contains': ['32.i1.b1', '32.ca1.a1', '32.cm1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8769, -1, 2710, -1, 8789, -1, 2707, -1], 'generators': [218, 48], 'label': '256.18790.16.er1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.er1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.er1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057548
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bz1.a1', '8.dc1.a1', '8.dw1.a1', '8.ei1.c1', '8.ei1.e1', '8.ek1.a1', '8.ek1.g1'], 'contains': ['32.ca1.a1', '32.cn1.a1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8714, -1, 2110, -1, 8734, -1, 2108, -1], 'generators': [5, 250], 'label': '256.18790.16.es1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.es1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.es1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057549
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bz1.a1', '8.dc1.b1', '8.dw1.a1', '8.ei1.a1', '8.ei1.g1', '8.ek1.c1', '8.ek1.e1'], 'contains': ['32.ca1.a1', '32.cn1.a1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8714, -1, 1372, -1, 8734, -1, 1370, -1], 'generators': [205, 250], 'label': '256.18790.16.es1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.es1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.es1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057550
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bz1.a1', '8.dc1.a1', '8.dw1.b1', '8.ei1.b1', '8.ei1.h1', '8.ek1.d1', '8.ek1.f1'], 'contains': ['32.ca1.a1', '32.cn1.b1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8714, -1, 2077, -1, 8734, -1, 2074, -1], 'generators': [221, 250], 'label': '256.18790.16.es1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.es1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.es1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057551
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bz1.a1', '8.dc1.b1', '8.dw1.b1', '8.ei1.d1', '8.ei1.f1', '8.ek1.b1', '8.ek1.h1'], 'contains': ['32.ca1.a1', '32.cn1.b1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8714, -1, 1339, -1, 8734, -1, 1337, -1], 'generators': [21, 250], 'label': '256.18790.16.es1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.es1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.es1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057552
    {'ambient': '256.18790', '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': ['64.bd1.a1', '64.bd1.d1', '64.bd1.b1', '64.bd1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'contains': ['8.i1.a1', '8.m1.a1', '8.o1.a1', '8.di1.a1', '8.di1.b1'], 'core': '4.bg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5362, 1426, 5586, 4331, 5375, 1430, 5579, 4357], 'generators': [5, 38, 16], 'label': '256.18790.4.bg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bg1.a1', 'normal_contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'normal_contains': ['8.i1.a1', '8.m1.a1', '8.o1.a1'], 'normalizer': '1.a1.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: 26057553
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.cz1.a1', '8.ds1.a1', '8.ek1.a1', '8.ek1.f1', '8.el1.b1', '8.el1.e1'], 'contains': ['32.cd1.a1', '32.cm1.a1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9005, -1, 2309, -1, 9026, -1, 2306, -1], 'generators': [5, 218], 'label': '256.18790.16.et1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057554
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.cz1.b1', '8.ds1.a1', '8.ek1.b1', '8.ek1.e1', '8.el1.a1', '8.el1.f1'], 'contains': ['32.cd1.a1', '32.cm1.a1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9005, -1, 1467, -1, 9026, -1, 1465, -1], 'generators': [205, 218], 'label': '256.18790.16.et1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057555
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.cz1.a1', '8.ds1.b1', '8.ek1.d1', '8.ek1.g1', '8.el1.c1', '8.el1.h1'], 'contains': ['32.cd1.b1', '32.cm1.a1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9005, -1, 2342, -1, 9026, -1, 2339, -1], 'generators': [221, 218], 'label': '256.18790.16.et1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057556
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.cz1.b1', '8.ds1.b1', '8.ek1.c1', '8.ek1.h1', '8.el1.d1', '8.el1.g1'], 'contains': ['32.cd1.b1', '32.cm1.a1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9005, -1, 1500, -1, 9026, -1, 1498, -1], 'generators': [21, 218], 'label': '256.18790.16.et1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057557
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.cb1.a1', '8.dd1.a1', '8.ej1.a1', '8.ej1.e1', '8.ek1.a1', '8.ek1.e1'], 'contains': ['32.i1.a1', '32.cd1.a1', '32.cn1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8583, -1, 1917, -1, 8603, -1, 1915, -1], 'generators': [7, 32], 'label': '256.18790.16.eu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.eu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057558
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.b1', '8.cb1.a1', '8.dd1.b1', '8.ej1.b1', '8.ej1.f1', '8.ek1.b1', '8.ek1.f1'], 'contains': ['32.i1.b1', '32.cd1.a1', '32.cn1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8583, -1, 2744, -1, 8603, -1, 2740, -1], 'generators': [7, 48], 'label': '256.18790.16.eu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.eu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057559
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.c1', '8.cb1.a1', '8.dd1.b1', '8.ej1.c1', '8.ej1.g1', '8.ek1.c1', '8.ek1.g1'], 'contains': ['32.i1.b1', '32.cd1.b1', '32.cn1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8583, -1, 2777, -1, 8603, -1, 2774, -1], 'generators': [223, 48], 'label': '256.18790.16.eu1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.eu1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057560
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.d1', '8.cb1.a1', '8.dd1.a1', '8.ej1.d1', '8.ej1.h1', '8.ek1.d1', '8.ek1.h1'], 'contains': ['32.i1.a1', '32.cd1.b1', '32.cn1.b1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8583, -1, 1851, -1, 8603, -1, 1849, -1], 'generators': [223, 32], 'label': '256.18790.16.eu1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.eu1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057561
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ev1', '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.x1.a1', '8.cc1.a1', '8.dd1.b1', '8.ei1.a1', '8.ei1.e1', '8.el1.a1', '8.el1.e1'], 'contains': ['32.j1.a1', '32.cd1.a1', '32.cn1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8824, -1, 2488, -1, 8844, -1, 2485, -1], 'generators': [7, 232], 'label': '256.18790.16.ev1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ev1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057562
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ev1', '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.x1.b1', '8.cc1.a1', '8.dd1.a1', '8.ei1.b1', '8.ei1.f1', '8.el1.b1', '8.el1.f1'], 'contains': ['32.j1.b1', '32.cd1.a1', '32.cn1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8824, -1, 2521, -1, 8844, -1, 2518, -1], 'generators': [7, 248], 'label': '256.18790.16.ev1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ev1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057563
    {'ambient': '256.18790', '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.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.n1.a1', '4.o1.a1', '4.s1.a1', '4.w1.a1', '4.bz1.a1', '4.bz1.b1', '4.bz1.c1', '4.bz1.d1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3685, 7058, 7945, 4308, 3694, 7004, 7935, 4334], 'generators': [33, 34, 4, 64], 'label': '256.18790.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.s1.a1', '4.w1.a1', '4.n1.a1', '4.o1.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: 26057564
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.c1.a1', 'complements': ['64.bd1.c1', '64.bd1.d1', '64.bd1.b1', '64.bd1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'contains': ['8.j1.a1', '8.n1.a1', '8.o1.a1', '8.dj1.a1', '8.dj1.b1'], 'core': '4.bh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5245, 4695, 5384, 3194, 5257, 4709, 5376, 3213], 'generators': [6, 32, 16], 'label': '256.18790.4.bh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bh1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'normal_contains': ['8.j1.a1', '8.o1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057565
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ev1', '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.x1.c1', '8.cc1.a1', '8.dd1.a1', '8.ei1.c1', '8.ei1.g1', '8.el1.c1', '8.el1.g1'], 'contains': ['32.j1.b1', '32.cd1.b1', '32.cn1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8824, -1, 2610, -1, 8844, -1, 2606, -1], 'generators': [223, 248], 'label': '256.18790.16.ev1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ev1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057566
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ev1', '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.x1.d1', '8.cc1.a1', '8.dd1.b1', '8.ei1.d1', '8.ei1.h1', '8.el1.d1', '8.el1.h1'], 'contains': ['32.j1.a1', '32.cd1.b1', '32.cn1.b1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8824, -1, 2424, -1, 8844, -1, 2421, -1], 'generators': [223, 232], 'label': '256.18790.16.ev1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.ev1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057567
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ew1', '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.ce1.a1', '8.de1.a1', '8.ea1.a1'], 'contains': ['32.ce1.a1', '32.cs1.a1', '32.ct1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1346, -1, 6681, -1, 1348, -1, 6673, -1], 'generators': [35, 36], 'label': '256.18790.16.ew1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '16.ew1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057568
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ew1', '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.ce1.b1', '8.de1.a1', '8.ea1.a1'], 'contains': ['32.ce1.a1', '32.cs1.a1', '32.ct1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1346, -1, 6568, -1, 1348, -1, 6560, -1], 'generators': [35, 100], 'label': '256.18790.16.ew1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '16.ew1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057569
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ew1', '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.ce1.a1', '8.de1.a1', '8.ea1.b1'], 'contains': ['32.ce1.b1', '32.cs1.a1', '32.ct1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1346, -1, 6648, -1, 1348, -1, 6640, -1], 'generators': [51, 36], 'label': '256.18790.16.ew1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '16.ew1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057570
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ew1', '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.ce1.b1', '8.de1.a1', '8.ea1.b1'], 'contains': ['32.ce1.b1', '32.cs1.a1', '32.ct1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1346, -1, 6535, -1, 1348, -1, 6527, -1], 'generators': [51, 100], 'label': '256.18790.16.ew1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '16.ew1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057571
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ex1', '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.ch1.a1', '8.df1.a1', '8.ed1.a1'], 'contains': ['32.i1.a1', '32.ch1.a1', '32.co1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5653, -1, 6010, -1, 5666, -1, 6002, -1], 'generators': [3, 32], 'label': '256.18790.16.ex1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '16.ex1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ex1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057572
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ex1', '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.ch1.a1', '8.df1.b1', '8.ed1.b1'], 'contains': ['32.i1.b1', '32.ch1.a1', '32.co1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5653, -1, 6417, -1, 5666, -1, 6409, -1], 'generators': [3, 48], 'label': '256.18790.16.ex1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '16.ex1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ex1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057573
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ey1', '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.ci1.a1', '8.df1.b1', '8.ed1.a1'], 'contains': ['32.j1.a1', '32.ch1.a1', '32.co1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5709, -1, 6043, -1, 5721, -1, 6035, -1], 'generators': [3, 232], 'label': '256.18790.16.ey1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '16.ey1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ey1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057574
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ey1', '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.ci1.a1', '8.df1.a1', '8.ed1.b1'], 'contains': ['32.j1.b1', '32.ch1.a1', '32.co1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5709, -1, 6076, -1, 5721, -1, 6068, -1], 'generators': [3, 248], 'label': '256.18790.16.ey1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '16.ey1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ey1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057575
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.g1.a1', 'complements': ['64.bd1.b1', '64.bd1.a1', '64.bd1.c1', '64.bd1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'contains': ['8.k1.a1', '8.l1.a1', '8.m1.a1'], 'core': '4.bi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4144, 8829, 6710, 1849, 4154, 8855, 6703, 1859], 'generators': [33, 36], 'label': '256.18790.4.bi1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bi1.a1', 'normal_contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'normal_contains': ['8.k1.a1', '8.l1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057576
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ez1', '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.ck1.a1', '8.dh1.a1', '8.ec1.a1'], 'contains': ['32.ci1.a1', '32.cr1.a1', '32.ct1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1476, -1, 6907, -1, 1479, -1, 6898, -1], 'generators': [3, 36], 'label': '256.18790.16.ez1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '16.ez1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057577
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ez1', '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.ck1.b1', '8.dh1.a1', '8.ec1.a1'], 'contains': ['32.ci1.a1', '32.cr1.a1', '32.ct1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1476, -1, 6873, -1, 1479, -1, 6865, -1], 'generators': [3, 100], 'label': '256.18790.16.ez1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '16.ez1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057578
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ez1', '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.ck1.a1', '8.dh1.a1', '8.ec1.b1'], 'contains': ['32.ci1.a1', '32.cr1.b1', '32.ct1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1476, -1, 6794, -1, 1479, -1, 6786, -1], 'generators': [19, 36], 'label': '256.18790.16.ez1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '16.ez1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057579
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ez1', '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.ck1.b1', '8.dh1.a1', '8.ec1.b1'], 'contains': ['32.ci1.a1', '32.cr1.b1', '32.ct1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1476, -1, 6761, -1, 1479, -1, 6752, -1], 'generators': [19, 100], 'label': '256.18790.16.ez1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '16.ez1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057580
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fa1', '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.cg1.a1', '8.db1.a1', '8.dv1.a1'], 'contains': ['32.cj1.a1', '32.cu1.a1', '32.cy1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4040, -1, 8089, -1, 4049, -1, 8078, -1], 'generators': [33, 34], 'label': '256.18790.16.fa1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.fa1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fa1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057581
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fa1', '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.cg1.a1', '8.db1.a1', '8.dv1.b1'], 'contains': ['32.cj1.a1', '32.cu1.a1', '32.cy1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4040, -1, 8122, -1, 4049, -1, 8111, -1], 'generators': [97, 34], 'label': '256.18790.16.fa1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.fa1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fa1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057582
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fb1', '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.cj1.a1', '8.cw1.a1', '8.do1.b1'], 'contains': ['32.k1.a1', '32.ck1.a1', '32.dc1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3458, -1, 6159, -1, 3466, -1, 6150, -1], 'generators': [101, 38], 'label': '256.18790.16.fb1.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.fb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057583
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fb1', '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.cj1.a1', '8.cw1.b1', '8.do1.a1'], 'contains': ['32.k1.b1', '32.ck1.a1', '32.dc1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3458, -1, 6192, -1, 3466, -1, 6184, -1], 'generators': [117, 38], 'label': '256.18790.16.fb1.b1', '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.fb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057584
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fc1', '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': ['8.t1.a1', '8.cy1.b1', '8.dr1.a1', '8.el1.a1', '8.el1.d1', '8.el1.e1', '8.el1.h1'], 'contains': ['32.j1.a1', '32.cl1.a1', '32.cm1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9057, -1, 2456, -1, 9078, -1, 2453, -1], 'generators': [218, 232], 'label': '256.18790.16.fc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057585
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fc1', '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': ['8.t1.a1', '8.cy1.a1', '8.dr1.b1', '8.el1.b1', '8.el1.c1', '8.el1.f1', '8.el1.g1'], 'contains': ['32.j1.b1', '32.cl1.a1', '32.cm1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9057, -1, 2578, -1, 9078, -1, 2574, -1], 'generators': [218, 248], 'label': '256.18790.16.fc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057586
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bj1', '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.q1.a1', '8.be1.a1', '8.bf1.a1', '8.bj1.a1', '8.br1.a1', '8.bz1.a1', '8.cc1.a1', '8.ei1.a1', '8.ei1.b1', '8.ei1.c1', '8.ei1.d1', '8.ei1.e1', '8.ei1.f1', '8.ei1.g1', '8.ei1.h1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8677, -1, 2062, -1, 8698, -1, 2081, -1], 'generators': [5, 2, 248, 16], 'label': '256.18790.4.bj1.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.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057587
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.co1.a1', '8.dc1.a1', '8.dw1.a1', '8.ej1.a1', '8.ej1.g1', '8.el1.c1', '8.el1.e1'], 'contains': ['32.cl1.a1', '32.cn1.a1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8876, -1, 2243, -1, 8897, -1, 2240, -1], 'generators': [221, 34], 'label': '256.18790.16.fd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057588
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.co1.a1', '8.dc1.b1', '8.dw1.a1', '8.ej1.c1', '8.ej1.e1', '8.el1.a1', '8.el1.g1'], 'contains': ['32.cl1.a1', '32.cn1.a1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8876, -1, 1610, -1, 8897, -1, 1608, -1], 'generators': [21, 34], 'label': '256.18790.16.fd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057589
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.co1.a1', '8.dc1.a1', '8.dw1.b1', '8.ej1.d1', '8.ej1.f1', '8.el1.b1', '8.el1.h1'], 'contains': ['32.cl1.a1', '32.cn1.b1', '32.cp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8876, -1, 2213, -1, 8897, -1, 2210, -1], 'generators': [5, 34], 'label': '256.18790.16.fd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fd1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fd1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057590
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.co1.a1', '8.dc1.b1', '8.dw1.b1', '8.ej1.b1', '8.ej1.h1', '8.el1.d1', '8.el1.f1'], 'contains': ['32.cl1.a1', '32.cn1.b1', '32.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8876, -1, 1435, -1, 8897, -1, 1433, -1], 'generators': [205, 34], 'label': '256.18790.16.fd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fd1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fd1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057591
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fe1', '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.cp1.a1', '8.da1.a1', '8.du1.a1'], 'contains': ['32.cv1.a1', '32.cx1.a1', '32.cy1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5546, -1, 8421, -1, 5558, -1, 8409, -1], 'generators': [33, 218], 'label': '256.18790.16.fe1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.fe1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fe1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057592
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fe1', '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.cp1.a1', '8.da1.a1', '8.du1.b1'], 'contains': ['32.cv1.a1', '32.cx1.a1', '32.cy1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5546, -1, 8451, -1, 5558, -1, 8440, -1], 'generators': [97, 218], 'label': '256.18790.16.fe1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.fe1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fe1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057593
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ff1', '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.cq1.a1', '8.cx1.a1', '8.dq1.b1'], 'contains': ['32.k1.a1', '32.da1.a1', '32.db1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4686, -1, 5808, -1, 4697, -1, 5800, -1], 'generators': [101, 6], 'label': '256.18790.16.ff1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.ff1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ff1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057594
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.ff1', '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.cq1.a1', '8.cx1.b1', '8.dq1.a1'], 'contains': ['32.k1.b1', '32.da1.a1', '32.db1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4686, -1, 5884, -1, 4697, -1, 5877, -1], 'generators': [117, 6], 'label': '256.18790.16.ff1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.ff1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ff1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057595
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fg1', '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.bc1.a1'], 'contains': ['32.de1.a1', '32.df1.a1', '32.dg1.a1', '32.dj1.a1', '32.dj1.c1', '32.dj1.e1', '32.dj1.g1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [601, -1, 9408, -1, 601, -1, 9395, -1], 'generators': [3, 4, 16], 'label': '256.18790.16.fg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '16.fg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057596
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fg1', '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.bc1.a1'], 'contains': ['32.de1.a1', '32.df1.a1', '32.dg1.b1', '32.dj1.b1', '32.dj1.d1', '32.dj1.f1', '32.dj1.h1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [601, -1, 9600, -1, 601, -1, 9588, -1], 'generators': [3, 132, 16], 'label': '256.18790.16.fg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '16.fg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057597
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.r1.a1', '8.be1.a1', '8.bg1.a1', '8.bi1.a1', '8.br1.a1', '8.cb1.a1', '8.co1.a1', '8.ej1.a1', '8.ej1.b1', '8.ej1.c1', '8.ej1.d1', '8.ej1.e1', '8.ej1.f1', '8.ej1.g1', '8.ej1.h1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8522, -1, 1979, -1, 8543, -1, 1999, -1], 'generators': [5, 2, 32, 16], 'label': '256.18790.4.bk1.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.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057630
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.b1.a1'], 'contains': ['8.p1.a1', '8.bk1.a1', '8.bm1.a1', '8.bo1.a1', '8.bq1.a1', '8.ck1.a1', '8.cr1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1018, -1, 6388, -1, 1021, -1, 6380, -1], 'generators': [1, 2, 36], 'label': '256.18790.4.bn1.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.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057598
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fg1', '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.bc1.a1'], 'contains': ['32.de1.b1', '32.df1.b1', '32.dg1.c1', '32.dj1.a1', '32.dj1.d1', '32.dj1.e1', '32.dj1.h1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [601, -1, 9507, -1, 601, -1, 9495, -1], 'generators': [3, 4, 144], 'label': '256.18790.16.fg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '16.fg1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fg1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057599
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '16.fg1', '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.bc1.a1'], 'contains': ['32.de1.b1', '32.df1.b1', '32.dg1.d1', '32.dj1.b1', '32.dj1.c1', '32.dj1.f1', '32.dj1.g1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [601, -1, 9554, -1, 601, -1, 9541, -1], 'generators': [3, 132, 144], 'label': '256.18790.16.fg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '16.fg1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fg1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057600
    {'ambient': '256.18790', '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': '2.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.r1.a1', '64.r1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2083, 4363, 7239, 4513, 2087, 4350, 7230, 4541], 'generators': [24, 16, 128], 'label': '256.18790.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': 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: 26057601
    {'ambient': '256.18790', '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.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.bg1.a1', '16.bp1.a1', '16.bs1.a1', '16.bu1.a1', '16.bv1.a1', '16.bw1.a1', '16.bx1.a1', '16.by1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.f1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7284, 2493, 5086, 6849, 7301, 2500, 5079, 6911], 'generators': [16, 64], 'label': '256.18790.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.f1.a1', '16.e1.a1', '16.g1.a1', '16.h1.a1'], 'normal_contains': ['64.a1.a1', '64.f1.a1', '64.d1.a1'], '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: 26057602
    {'ambient': '256.18790', '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.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.j1.a1', '16.j1.b1', '16.k1.a1', '16.k1.b1', '16.bj1.a1', '16.bm1.a1', '16.bq1.a1', '16.bt1.a1', '16.bz1.a1', '16.ca1.a1', '16.cb1.a1', '16.cc1.a1'], 'contains': ['64.a1.a1', '64.e1.a1', '64.g1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2266, 5155, 6141, 3678, 2271, 5138, 6132, 3700], 'generators': [216, 16], 'label': '256.18790.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.j1.a1', '16.j1.b1', '16.k1.b1', '16.k1.a1'], 'normal_contains': ['64.a1.a1', '64.e1.a1', '64.g1.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: 26057603
    {'ambient': '256.18790', '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.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.l1.a1', '16.l1.b1', '16.m1.a1', '16.m1.b1', '16.n1.a1', '16.n1.b1', '16.ci1.a1', '16.ck1.a1', '16.cm1.a1', '16.co1.a1', '16.cq1.a1', '16.cr1.a1', '16.cs1.a1', '16.ct1.a1'], 'contains': ['64.b1.a1', '64.d1.a1', '64.g1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6840, 3999, 4052, 2549, 6856, 3997, 4047, 2564], 'generators': [216, 64], 'label': '256.18790.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.a1.a1', '16.l1.b1', '16.l1.a1', '16.m1.b1', '16.m1.a1', '16.n1.b1', '16.n1.a1'], 'normal_contains': ['64.b1.a1', '64.g1.a1', '64.d1.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: 26057604
    {'ambient': '256.18790', '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.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.ch1.a1', '16.cj1.a1', '16.cl1.a1', '16.cn1.a1', '16.cp1.a1', '16.cu1.a1', '16.cv1.a1', '16.cw1.a1', '16.cx1.a1'], 'contains': ['64.b1.a1', '64.e1.a1', '64.f1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4119, 4536, 6187, 4334, 4128, 4517, 6179, 4360], 'generators': [24, 80], 'label': '256.18790.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.b1.a1', '64.e1.a1', '64.f1.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: 26057605
    {'ambient': '256.18790', '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.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.p1.a1', '16.p1.b1', '16.q1.a1', '16.q1.b1', '16.r1.a1', '16.r1.b1', '16.da1.a1', '16.db1.a1', '16.dd1.a1', '16.dh1.a1', '16.dj1.a1', '16.dk1.a1', '16.dl1.a1', '16.dm1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.e1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4270, 4189, 5249, 5830, 4280, 4187, 5242, 5887], 'generators': [200, 64], 'label': '256.18790.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.a1.a1', '16.p1.b1', '16.p1.a1', '16.q1.a1', '16.q1.b1', '16.r1.b1', '16.r1.a1'], 'normal_contains': ['64.c1.a1', '64.e1.a1', '64.d1.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: 26057606
    {'ambient': '256.18790', '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.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.o1.a1', '16.o1.b1', '16.s1.a1', '16.s1.b1', '16.t1.a1', '16.t1.b1', '16.dc1.a1', '16.de1.a1', '16.dg1.a1', '16.di1.a1', '16.dn1.a1', '16.do1.a1', '16.dp1.a1', '16.dq1.a1'], 'contains': ['64.c1.a1', '64.f1.a1', '64.g1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3725, 4960, 6917, 3108, 3733, 4943, 6908, 3127], 'generators': [216, 80], 'label': '256.18790.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.a1.a1', '16.o1.b1', '16.o1.a1', '16.s1.b1', '16.s1.a1', '16.t1.a1', '16.t1.b1'], 'normal_contains': ['64.c1.a1', '64.f1.a1', '64.g1.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: 26057607
    {'ambient': '256.18790', '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': '8.s1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.l1.a1', '16.o1.a1', '16.ed1.a1', '16.ef1.a1', '16.eg1.a1', '16.eh1.a1'], 'contains': ['64.g1.a1', '64.h1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3864, 4815, 4741, 2209, 3872, 4797, 4735, 2223], 'generators': [37, 216], 'label': '256.18790.32.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': ['16.b1.a1', '16.l1.a1', '16.o1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.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: 26057608
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.s1.a1', '8.bf1.a1', '8.bh1.a1', '8.bi1.a1', '8.bz1.a1', '8.ca1.a1', '8.cb1.a1', '8.ek1.a1', '8.ek1.b1', '8.ek1.c1', '8.ek1.d1', '8.ek1.e1', '8.ek1.f1', '8.ek1.g1', '8.ek1.h1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8212, -1, 1889, -1, 8232, -1, 1886, -1], 'generators': [5, 218, 32, 16], 'label': '256.18790.4.bl1.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.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057609
    {'ambient': '256.18790', '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': '8.s1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.l1.b1', '16.o1.b1', '16.ed1.b1', '16.ef1.b1', '16.eg1.b1', '16.eh1.b1'], 'contains': ['64.g1.a1', '64.h1.b1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3864, 4815, 4433, 2009, 3872, 4797, 4428, 2022], 'generators': [53, 216], 'label': '256.18790.32.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': ['16.b1.a1', '16.l1.b1', '16.o1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057610
    {'ambient': '256.18790', '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': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.m1.a1', '16.r1.a1', '16.dz1.a1', '16.dz1.c1', '16.em1.a1', '16.er1.a1', '16.eu1.a1', '16.eu1.d1', '16.ex1.a1'], 'contains': ['64.d1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8331, 2945, 2628, 5685, 8350, 2931, 2625, 5742], 'generators': [32], 'label': '256.18790.32.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': ['16.g1.a1', '16.m1.a1', '16.r1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.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: 26057611
    {'ambient': '256.18790', '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': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.m1.b1', '16.r1.b1', '16.dz1.b1', '16.dz1.d1', '16.em1.b1', '16.er1.b1', '16.eu1.b1', '16.eu1.c1', '16.ex1.b1'], 'contains': ['64.d1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8331, 2945, 2833, 6077, 8350, 2931, 2829, 6177], 'generators': [48], 'label': '256.18790.32.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': ['16.g1.a1', '16.m1.b1', '16.r1.b1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.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: 26057612
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.m1.b1', '16.r1.a1', '16.ea1.a1', '16.ea1.c1', '16.ek1.a1', '16.ev1.a1', '16.ev1.d1', '16.ey1.a1', '16.fc1.a1'], 'contains': ['64.d1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8420, 2800, 2784, 5585, 8449, 2808, 2781, 5641], 'generators': [232], 'label': '256.18790.32.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1.a1', 'normal_contained_in': ['16.h1.a1', '16.m1.b1', '16.r1.a1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.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: 26057613
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.m1.a1', '16.r1.b1', '16.ea1.b1', '16.ea1.d1', '16.ek1.b1', '16.ev1.b1', '16.ev1.c1', '16.ey1.b1', '16.fc1.b1'], 'contains': ['64.d1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8420, 2800, 2809, 6307, 8449, 2808, 2805, 6394], 'generators': [248], 'label': '256.18790.32.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1.b1', 'normal_contained_in': ['16.h1.a1', '16.m1.a1', '16.r1.b1'], 'normal_contains': ['64.d1.a1'], 'normalizer': '1.a1.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: 26057614
    {'ambient': '256.18790', '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': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.l1.a1', '16.o1.b1', '16.ej1.a1', '16.ep1.a1', '16.fb1.a1', '16.ff1.a1'], 'contains': ['64.g1.a1', '64.m1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3904, 4714, 5002, 2346, 3913, 4696, 4995, 2360], 'generators': [101, 216], 'label': '256.18790.32.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': ['16.i1.a1', '16.l1.a1', '16.o1.b1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.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: 26057615
    {'ambient': '256.18790', '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': '8.r1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.l1.b1', '16.o1.a1', '16.ej1.b1', '16.ep1.b1', '16.fb1.b1', '16.ff1.b1'], 'contains': ['64.g1.a1', '64.m1.b1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3904, 4714, 5050, 2109, 3913, 4696, 5044, 2122], 'generators': [117, 216], 'label': '256.18790.32.k1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.k1.b1', 'normal_contained_in': ['16.i1.a1', '16.l1.b1', '16.o1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057616
    {'ambient': '256.18790', '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': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.u1.a1', '16.bd1.a1', '16.be1.a1', '16.bf1.a1', '16.bg1.a1', '16.bh1.a1'], 'contains': ['64.a1.a1', '64.h1.a1', '64.h1.b1', '64.s1.a1', '64.s1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3505, -1, 3587, -1, 3513, -1, 3582, -1], 'generators': [37, 16, 128], 'label': '256.18790.32.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.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: 26057617
    {'ambient': '256.18790', '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': '8.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.v1.a1', '16.bd1.a1', '16.bi1.a1', '16.bi1.b1', '16.bj1.a1', '16.bk1.a1'], 'contains': ['64.a1.a1', '64.i1.a1', '64.t1.a1', '64.t1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5835, -1, 6954, -1, 5848, -1, 6945, -1], 'generators': [2, 16, 128], 'label': '256.18790.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.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: 26057618
    {'ambient': '256.18790', '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.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.w1.a1', '16.be1.a1', '16.bl1.a1', '16.bm1.a1', '16.bn1.a1', '16.bn1.b1'], 'contains': ['64.a1.a1', '64.j1.a1', '64.u1.a1', '64.u1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2129, -1, 2509, -1, 2133, -1, 2506, -1], 'generators': [250, 16, 128], 'label': '256.18790.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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: 26057619
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bm1', '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.t1.a1', '8.bg1.a1', '8.bh1.a1', '8.bj1.a1', '8.ca1.a1', '8.cc1.a1', '8.co1.a1', '8.el1.a1', '8.el1.b1', '8.el1.c1', '8.el1.d1', '8.el1.e1', '8.el1.f1', '8.el1.g1', '8.el1.h1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8405, -1, 2321, -1, 8426, -1, 2319, -1], 'generators': [5, 218, 248, 16], 'label': '256.18790.4.bm1.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.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057620
    {'ambient': '256.18790', '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': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.be1.a1', '16.bf1.a1', '16.bl1.a1', '16.bo1.a1', '16.bp1.a1', '16.bq1.a1'], 'contains': ['64.a1.a1', '64.k1.a1', '64.k1.b1', '64.v1.a1', '64.v1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2327, -1, 1238, -1, 2332, -1, 1236, -1], 'generators': [7, 16, 128], 'label': '256.18790.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057621
    {'ambient': '256.18790', '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': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.bi1.a1', '16.bi1.b1', '16.br1.a1', '16.br1.b1', '16.bs1.a1', '16.bt1.a1'], 'contains': ['64.a1.a1', '64.l1.a1', '64.w1.a1', '64.w1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1754, -1, 8745, -1, 1757, -1, 8734, -1], 'generators': [3, 16, 128], 'label': '256.18790.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.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: 26057622
    {'ambient': '256.18790', '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': '4.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.u1.a1', '16.bg1.a1', '16.bk1.a1', '16.bl1.a1', '16.bo1.a1', '16.cd1.a1'], 'contains': ['64.a1.a1', '64.m1.a1', '64.m1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3609, -1, 3888, -1, 3617, -1, 3882, -1], 'generators': [101, 16], 'label': '256.18790.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 26057623
    {'ambient': '256.18790', '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': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.ba1.a1', '16.bi1.a1', '16.bn1.a1', '16.br1.a1', '16.bu1.a1', '16.ce1.a1'], 'contains': ['64.a1.a1', '64.x1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [524, -1, 8593, -1, 525, -1, 8581, -1], 'generators': [1, 128], 'label': '256.18790.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.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: 26057624
    {'ambient': '256.18790', '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': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '16.ba1.a1', '16.bi1.b1', '16.bn1.b1', '16.br1.b1', '16.bu1.a1', '16.ce1.b1'], 'contains': ['64.a1.a1', '64.x1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [524, -1, 8677, -1, 525, -1, 8671, -1], 'generators': [65, 128], 'label': '256.18790.32.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057625
    {'ambient': '256.18790', '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': '8.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.w1.a1', '16.bf1.a1', '16.bm1.a1', '16.bo1.a1', '16.ce1.a1', '16.ce1.b1'], 'contains': ['64.a1.a1', '64.n1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2189, -1, 4006, -1, 2195, -1, 4001, -1], 'generators': [34, 16], 'label': '256.18790.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.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: 26057626
    {'ambient': '256.18790', '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': '8.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.v1.a1', '16.bh1.a1', '16.bj1.a1', '16.br1.a1', '16.br1.b1', '16.cd1.a1'], 'contains': ['64.a1.a1', '64.o1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5774, -1, 6257, -1, 5787, -1, 6249, -1], 'generators': [218, 16], 'label': '256.18790.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.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: 26057627
    {'ambient': '256.18790', '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': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.bd1.a1', '16.bh1.a1', '16.bk1.a1', '16.bv1.a1', '16.bz1.a1', '16.cd1.a1'], 'contains': ['64.a1.a1', '64.p1.a1', '64.p1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5995, -1, 5295, -1, 6009, -1, 5288, -1], 'generators': [39, 16], 'label': '256.18790.32.u1.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.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: 26057628
    {'ambient': '256.18790', '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': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.bn1.a1', '16.bn1.b1', '16.bw1.a1', '16.ca1.a1', '16.ce1.a1', '16.ce1.b1'], 'contains': ['64.a1.a1', '64.q1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1814, -1, 8546, -1, 1818, -1, 8535, -1], 'generators': [35, 16], 'label': '256.18790.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.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: 26057629
    {'ambient': '256.18790', '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.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.u1.a1', '16.cf1.a1', '16.cf1.a2', '16.cg1.a1', '16.cg1.a2', '16.ch1.a1'], 'contains': ['64.b1.a1', '64.h1.a1', '64.m1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4329, -1, 3637, -1, 4339, -1, 3633, -1], 'generators': [37, 24], 'label': '256.18790.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', '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: 26057631
    {'ambient': '256.18790', '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.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.u1.a1', '16.cf1.b1', '16.cf1.b2', '16.cg1.b1', '16.cg1.b2', '16.ch1.a1'], 'contains': ['64.b1.a1', '64.h1.b1', '64.m1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4329, -1, 3732, -1, 4339, -1, 3728, -1], 'generators': [53, 24], 'label': '256.18790.32.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 26057632
    {'ambient': '256.18790', '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': '16.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.cf1.a1', '16.cf1.a2', '16.cf1.b1', '16.cf1.b2', '16.ci1.a1', '16.cj1.a1'], 'contains': ['64.b1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6624, -1, 5376, -1, 6640, -1, 5369, -1], 'generators': [2, 24], 'label': '256.18790.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.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: 26057633
    {'ambient': '256.18790', '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': '16.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.cg1.a1', '16.cg1.a2', '16.cg1.b1', '16.cg1.b2', '16.ck1.a1', '16.cl1.a1'], 'contains': ['64.b1.a1', '64.j1.a1', '64.n1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3323, -1, 1067, -1, 3330, -1, 1065, -1], 'generators': [34, 24], 'label': '256.18790.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057634
    {'ambient': '256.18790', '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': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.cg1.a1', '16.cg1.a2', '16.cg1.b1', '16.cg1.b2', '16.cm1.a1', '16.cn1.a1'], 'contains': ['64.b1.a1', '64.k1.a1', '64.k1.b1', '64.y1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2728, -1, 1117, -1, 2734, -1, 1116, -1], 'generators': [7, 24, 128], 'label': '256.18790.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057635
    {'ambient': '256.18790', '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': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.co1.a1', '16.cp1.a1'], 'contains': ['64.b1.a1', '64.l1.a1', '64.z1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2682, -1, 7674, -1, 2688, -1, 7664, -1], 'generators': [3, 24, 128], 'label': '256.18790.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.z1.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: 26057636
    {'ambient': '256.18790', '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.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.cf1.a1', '16.cf1.a2', '16.cf1.b1', '16.cf1.b2', '16.cq1.a1', '16.cu1.a1'], 'contains': ['64.b1.a1', '64.p1.a1', '64.p1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6137, -1, 5156, -1, 6152, -1, 5150, -1], 'generators': [39, 24], 'label': '256.18790.32.bb1.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.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: 26057637
    {'ambient': '256.18790', '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': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.cr1.a1', '16.cv1.a1'], 'contains': ['64.b1.a1', '64.q1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4042, -1, 7015, -1, 4052, -1, 7007, -1], 'generators': [35, 24], 'label': '256.18790.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bg1.a1', '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: 26057638
    {'ambient': '256.18790', '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': '8.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.u1.a1', '16.cy1.a1', '16.cy1.b1', '16.cz1.a1', '16.cz1.b1', '16.da1.a1'], 'contains': ['64.c1.a1', '64.h1.a1', '64.m1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3823, -1, 3827, -1, 3832, -1, 3822, -1], 'generators': [37, 8], 'label': '256.18790.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.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: 26057639
    {'ambient': '256.18790', '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': '8.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.u1.a1', '16.cy1.c1', '16.cy1.d1', '16.cz1.c1', '16.cz1.d1', '16.da1.a1'], 'contains': ['64.c1.a1', '64.h1.b1', '64.m1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3823, -1, 3757, -1, 3832, -1, 3752, -1], 'generators': [101, 8], 'label': '256.18790.32.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.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: 26057640
    {'ambient': '256.18790', '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': '16.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.cy1.a1', '16.cy1.b1', '16.cy1.c1', '16.cy1.d1', '16.db1.a1', '16.dc1.a1'], 'contains': ['64.c1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6392, -1, 5447, -1, 6407, -1, 5440, -1], 'generators': [2, 8], 'label': '256.18790.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.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: 26057641
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.b1.a1'], 'contains': ['8.p1.b1', '8.bk1.a1', '8.bm1.a1', '8.bo1.b1', '8.bq1.b1', '8.ck1.b1', '8.cr1.b1'], 'core': '8.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1018, -1, 6208, -1, 1021, -1, 6200, -1], 'generators': [65, 2, 100], 'label': '256.18790.4.bn1.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.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057642
    {'ambient': '256.18790', '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': '16.bq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.cz1.a1', '16.cz1.b1', '16.cz1.c1', '16.cz1.d1', '16.dd1.a1', '16.de1.a1'], 'contains': ['64.c1.a1', '64.j1.a1', '64.n1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3009, -1, 1288, -1, 3015, -1, 1286, -1], 'generators': [34, 8], 'label': '256.18790.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057643
    {'ambient': '256.18790', '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.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.x1.a1', '16.cz1.a1', '16.cz1.c1', '16.df1.a1', '16.df1.b1', '16.dg1.a1'], 'contains': ['64.c1.a1', '64.k1.a1', '64.ba1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2636, -1, 6715, -1, 2642, -1, 6706, -1], 'generators': [7, 8, 128], 'label': '256.18790.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.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: 26057644
    {'ambient': '256.18790', '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.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.x1.a1', '16.cz1.b1', '16.cz1.d1', '16.df1.c1', '16.df1.d1', '16.dg1.a1'], 'contains': ['64.c1.a1', '64.k1.b1', '64.ba1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2636, -1, 6686, -1, 2642, -1, 6678, -1], 'generators': [87, 8, 128], 'label': '256.18790.32.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.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: 26057645
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.df1.a1', '16.df1.b1', '16.df1.c1', '16.df1.d1', '16.dh1.a1', '16.di1.a1'], 'contains': ['64.c1.a1', '64.l1.a1', '64.bb1.a1', '64.bb1.a2'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2037, -1, 9092, -1, 2042, -1, 9080, -1], 'generators': [3, 8, 128], 'label': '256.18790.32.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '32.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057646
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.z1.a1', '16.df1.a1', '16.df1.c1', '16.dj1.a1', '16.dr1.a1', '16.dr1.b1'], 'contains': ['64.c1.a1', '64.bc1.a1', '64.bc1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1930, -1, 9055, -1, 1934, -1, 9043, -1], 'generators': [4, 128], 'label': '256.18790.32.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057647
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.b1', '16.z1.a1', '16.df1.b1', '16.df1.d1', '16.dj1.a1', '16.dr1.c1', '16.dr1.d1'], 'contains': ['64.c1.a1', '64.bc1.c1', '64.bc1.d1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1930, -1, 9157, -1, 1934, -1, 9144, -1], 'generators': [68, 128], 'label': '256.18790.32.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057648
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bb1.a1', '16.cy1.a1', '16.cy1.c1', '16.dn1.a1', '16.dr1.a1', '16.dr1.c1'], 'contains': ['64.c1.a1', '64.p1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4195, -1, 6822, -1, 4204, -1, 6813, -1], 'generators': [39, 8], 'label': '256.18790.32.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057649
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.bb1.a1', '16.cy1.b1', '16.cy1.d1', '16.dn1.a1', '16.dr1.b1', '16.dr1.d1'], 'contains': ['64.c1.a1', '64.p1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4195, -1, 6776, -1, 4204, -1, 6767, -1], 'generators': [119, 8], 'label': '256.18790.32.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057650
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.dk1.a1', '16.do1.a1', '16.dr1.a1', '16.dr1.b1', '16.dr1.c1', '16.dr1.d1'], 'contains': ['64.c1.a1', '64.q1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2834, -1, 8783, -1, 2841, -1, 8771, -1], 'generators': [35, 8], 'label': '256.18790.32.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '32.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057651
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.cf1.a2', '16.cy1.a1', '16.ds1.a1', '16.dt1.a1', '16.ec1.a1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.i1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6665, -1, 4716, -1, 6681, -1, 4710, -1], 'generators': [253, 2], 'label': '256.18790.32.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057652
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.e1.a1'], 'contains': ['8.p1.a1', '8.bl1.a1', '8.bn1.a1', '8.bv1.a1', '8.bw1.a1', '8.cd1.a1', '8.ce1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [506, -1, 5885, -1, 508, -1, 5878, -1], 'generators': [1, 34, 36], 'label': '256.18790.4.bo1.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.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057653
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.cf1.a1', '16.cy1.b1', '16.ds1.b1', '16.dt1.a1', '16.ec1.b1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.i1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6665, -1, 4692, -1, 6681, -1, 4686, -1], 'generators': [37, 2], 'label': '256.18790.32.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057654
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.cf1.b1', '16.cy1.c1', '16.ds1.c1', '16.dt1.b1', '16.ec1.a1', '16.ed1.b1'], 'contains': ['64.h1.b1', '64.i1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6665, -1, 4668, -1, 6681, -1, 4662, -1], 'generators': [53, 2], 'label': '256.18790.32.bl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bl1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057655
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.cf1.b2', '16.cy1.d1', '16.ds1.d1', '16.dt1.b1', '16.ec1.b1', '16.ed1.b1'], 'contains': ['64.h1.b1', '64.i1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6665, -1, 4643, -1, 6681, -1, 4637, -1], 'generators': [237, 2], 'label': '256.18790.32.bl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bl1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057656
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cg1.a2', '16.cz1.a1', '16.du1.a1', '16.dv1.a1', '16.ee1.a1', '16.ef1.a1'], 'contains': ['64.h1.a1', '64.j1.a1', '64.k1.a1', '64.bd1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2774, -1, 661, -1, 2780, -1, 660, -1], 'generators': [37, 250, 128], 'label': '256.18790.32.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057657
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cg1.a1', '16.cz1.b1', '16.du1.b1', '16.dv1.a1', '16.ee1.b1', '16.ef1.a1'], 'contains': ['64.h1.a1', '64.j1.a1', '64.k1.b1', '64.bd1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2774, -1, 605, -1, 2780, -1, 604, -1], 'generators': [253, 250, 128], 'label': '256.18790.32.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057658
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cg1.b1', '16.cz1.c1', '16.du1.c1', '16.dv1.b1', '16.ee1.a1', '16.ef1.b1'], 'contains': ['64.h1.b1', '64.j1.a1', '64.k1.a1', '64.bd1.c1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2774, -1, 632, -1, 2780, -1, 632, -1], 'generators': [237, 250, 128], 'label': '256.18790.32.bm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bm1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057659
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.cg1.b2', '16.cz1.d1', '16.du1.d1', '16.dv1.b1', '16.ee1.b1', '16.ef1.b1'], 'contains': ['64.h1.b1', '64.j1.a1', '64.k1.b1', '64.bd1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2774, -1, 577, -1, 2780, -1, 576, -1], 'generators': [53, 250, 128], 'label': '256.18790.32.bm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bm1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057660
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.cg1.a1', '16.cz1.a1', '16.dw1.a1', '16.dx1.a1', '16.ee1.a1', '16.ef1.a1'], 'contains': ['64.h1.a1', '64.k1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3049, -1, 760, -1, 3056, -1, 759, -1], 'generators': [253, 34], 'label': '256.18790.32.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057661
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.cg1.a2', '16.cz1.b1', '16.dw1.b1', '16.dx1.a1', '16.ee1.b1', '16.ef1.a1'], 'contains': ['64.h1.a1', '64.k1.b1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3049, -1, 711, -1, 3056, -1, 710, -1], 'generators': [37, 34], 'label': '256.18790.32.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057662
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.cg1.b2', '16.cz1.c1', '16.dw1.c1', '16.dx1.b1', '16.ee1.a1', '16.ef1.b1'], 'contains': ['64.h1.b1', '64.k1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3049, -1, 736, -1, 3056, -1, 735, -1], 'generators': [53, 34], 'label': '256.18790.32.bn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bn1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057663
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.e1.a1'], 'contains': ['8.p1.b1', '8.bl1.a1', '8.bn1.a1', '8.bv1.b1', '8.bw1.b1', '8.cd1.b1', '8.ce1.b1'], 'core': '8.p1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [506, -1, 5747, -1, 508, -1, 5740, -1], 'generators': [65, 34, 100], 'label': '256.18790.4.bo1.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.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057664
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.cg1.b1', '16.cz1.d1', '16.dw1.d1', '16.dx1.b1', '16.ee1.b1', '16.ef1.b1'], 'contains': ['64.h1.b1', '64.k1.b1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3049, -1, 687, -1, 3056, -1, 686, -1], 'generators': [237, 34], 'label': '256.18790.32.bn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bn1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057665
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.bg1.a1', '16.da1.a1', '16.ds1.a1', '16.ds1.b1', '16.du1.a1', '16.du1.b1', '16.dw1.a1', '16.dw1.b1', '16.dy1.a1', '16.dy1.b1', '16.dz1.a1', '16.dz1.b1', '16.ea1.a1', '16.ea1.b1'], 'contains': ['64.d1.a1', '64.h1.a1', '64.m1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7880, -1, 2546, -1, 7898, -1, 2543, -1], 'generators': [37, 64], 'label': '256.18790.32.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057666
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '16.bg1.a1', '16.da1.a1', '16.ds1.c1', '16.ds1.d1', '16.du1.c1', '16.du1.d1', '16.dw1.c1', '16.dw1.d1', '16.dy1.c1', '16.dy1.d1', '16.dz1.c1', '16.dz1.d1', '16.ea1.c1', '16.ea1.d1'], 'contains': ['64.d1.a1', '64.h1.b1', '64.m1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7880, -1, 2593, -1, 7898, -1, 2589, -1], 'generators': [53, 64], 'label': '256.18790.32.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057667
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.bg1.a1', '16.ch1.a1', '16.dt1.a1', '16.dv1.a1', '16.dx1.a1', '16.eb1.a1'], 'contains': ['64.f1.a1', '64.h1.a1', '64.m1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4387, -1, 3792, -1, 4397, -1, 3787, -1], 'generators': [37, 80], 'label': '256.18790.32.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057668
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '16.bg1.a1', '16.ch1.a1', '16.dt1.b1', '16.dv1.b1', '16.dx1.b1', '16.eb1.b1'], 'contains': ['64.f1.a1', '64.h1.b1', '64.m1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4387, -1, 3697, -1, 4397, -1, 3692, -1], 'generators': [101, 80], 'label': '256.18790.32.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057669
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.cf1.a1', '16.cy1.a1', '16.dy1.a1', '16.eb1.a1', '16.ec1.a1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.o1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6451, -1, 4607, -1, 6465, -1, 4602, -1], 'generators': [37, 218], 'label': '256.18790.32.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057670
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.cf1.a2', '16.cy1.b1', '16.dy1.b1', '16.eb1.a1', '16.ec1.b1', '16.ed1.a1'], 'contains': ['64.h1.a1', '64.o1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6451, -1, 4561, -1, 6465, -1, 4556, -1], 'generators': [253, 218], 'label': '256.18790.32.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057671
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.cf1.b2', '16.cy1.c1', '16.dy1.c1', '16.eb1.b1', '16.ec1.a1', '16.ed1.b1'], 'contains': ['64.h1.b1', '64.o1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6451, -1, 4515, -1, 6465, -1, 4510, -1], 'generators': [237, 218], 'label': '256.18790.32.bq1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bq1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057672
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bh1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.cf1.b1', '16.cy1.d1', '16.dy1.d1', '16.eb1.b1', '16.ec1.b1', '16.ed1.b1'], 'contains': ['64.h1.b1', '64.o1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6451, -1, 4470, -1, 6465, -1, 4464, -1], 'generators': [53, 218], 'label': '256.18790.32.bq1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bq1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057673
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.ch1.a1', '16.da1.a1', '16.ec1.a1', '16.ec1.b1', '16.ee1.a1', '16.ee1.b1'], 'contains': ['64.e1.a1', '64.h1.a1', '64.h1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3667, -1, 3613, -1, 3675, -1, 3608, -1], 'generators': [37, 200], 'label': '256.18790.32.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057674
    {'ambient': '256.18790', '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': '64.a1.a1', 'complements': ['128.f1.a1', '128.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '4.p1.a1', '4.r1.a1', '4.t1.a1', '4.v1.a1', '4.bo1.a1', '4.bo1.b1', '4.bs1.a1', '4.bs1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2325, 4653, 5919, 4583, 2331, 4667, 5912, 4610], 'generators': [1, 34, 36, 64], 'label': '256.18790.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '4.t1.a1', '4.v1.a1', '4.p1.a1', '4.r1.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: 26057675
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bp1', '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.u1.a1', '8.bo1.a1', '8.bp1.a1', '8.bq1.b1', '8.cj1.a1', '8.ck1.b1', '8.cr1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1132, -1, 6312, -1, 1135, -1, 6304, -1], 'generators': [1, 2, 100], 'label': '256.18790.4.bp1.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.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057676
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cj1.a1', '16.db1.a1', '16.ec1.a1', '16.ec1.b1', '16.ei1.a1', '16.ei1.b1'], 'contains': ['64.e1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6214, -1, 5412, -1, 6228, -1, 5405, -1], 'generators': [2, 200], 'label': '256.18790.32.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057677
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.ci1.a1', '16.dc1.a1', '16.ed1.a1', '16.ed1.b1', '16.ej1.a1', '16.ej1.b1'], 'contains': ['64.g1.a1', '64.i1.a1', '64.o1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6566, -1, 5340, -1, 6582, -1, 5334, -1], 'generators': [2, 216], 'label': '256.18790.32.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057678
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.cf1.a1', '16.cy1.c1', '16.ds1.a1', '16.dt1.b1', '16.ei1.a1', '16.ej1.a1'], 'contains': ['64.i1.a1', '64.m1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6723, -1, 4920, -1, 6739, -1, 4914, -1], 'generators': [61, 2], 'label': '256.18790.32.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057679
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.cf1.a2', '16.cy1.d1', '16.ds1.b1', '16.dt1.b1', '16.ei1.b1', '16.ej1.a1'], 'contains': ['64.i1.a1', '64.m1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6723, -1, 4850, -1, 6739, -1, 4843, -1], 'generators': [101, 2], 'label': '256.18790.32.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057680
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.cf1.b2', '16.cy1.a1', '16.ds1.c1', '16.dt1.a1', '16.ei1.a1', '16.ej1.b1'], 'contains': ['64.i1.a1', '64.m1.b1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6723, -1, 5203, -1, 6739, -1, 5196, -1], 'generators': [117, 2], 'label': '256.18790.32.bu1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bu1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057681
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.cf1.b1', '16.cy1.b1', '16.ds1.d1', '16.dt1.a1', '16.ei1.b1', '16.ej1.b1'], 'contains': ['64.i1.a1', '64.m1.b1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6723, -1, 4966, -1, 6739, -1, 4960, -1], 'generators': [45, 2], 'label': '256.18790.32.bu1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.bu1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057682
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.ci1.a1', '16.db1.a1', '16.ds1.a1', '16.ds1.b1', '16.ds1.c1', '16.ds1.d1', '16.ek1.a1', '16.ek1.b1', '16.el1.a1', '16.el1.b1', '16.el1.c1', '16.el1.d1', '16.em1.a1', '16.em1.b1'], 'contains': ['64.d1.a1', '64.i1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8478, -1, 2760, -1, 8498, -1, 2756, -1], 'generators': [2, 64], 'label': '256.18790.32.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057683
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.cj1.a1', '16.dc1.a1', '16.dt1.a1', '16.dt1.b1', '16.en1.a1', '16.en1.b1'], 'contains': ['64.f1.a1', '64.i1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6352, -1, 6741, -1, 6367, -1, 6732, -1], 'generators': [2, 80], 'label': '256.18790.32.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057684
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.cg1.a1', '16.cz1.c1', '16.du1.a1', '16.dv1.b1', '16.eo1.a1', '16.ep1.a1'], 'contains': ['64.j1.a1', '64.k1.a1', '64.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2969, -1, 809, -1, 2975, -1, 808, -1], 'generators': [101, 250], 'label': '256.18790.32.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057685
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.cg1.b2', '16.cz1.a1', '16.du1.c1', '16.dv1.a1', '16.eo1.a1', '16.ep1.b1'], 'contains': ['64.j1.a1', '64.k1.a1', '64.m1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2969, -1, 904, -1, 2975, -1, 903, -1], 'generators': [45, 250], 'label': '256.18790.32.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057686
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bp1', '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.u1.b1', '8.bo1.b1', '8.bp1.a1', '8.bq1.a1', '8.cj1.a1', '8.ck1.a1', '8.cr1.b1'], 'core': '8.u1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1132, -1, 6457, -1, 1135, -1, 6449, -1], 'generators': [65, 2, 36], 'label': '256.18790.4.bp1.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.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057687
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.cg1.a2', '16.cz1.d1', '16.du1.b1', '16.dv1.b1', '16.eo1.b1', '16.ep1.a1'], 'contains': ['64.j1.a1', '64.k1.b1', '64.m1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2969, -1, 784, -1, 2975, -1, 783, -1], 'generators': [61, 250], 'label': '256.18790.32.bx1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bx1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057688
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bf1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.cg1.b1', '16.cz1.b1', '16.du1.d1', '16.dv1.a1', '16.eo1.b1', '16.ep1.b1'], 'contains': ['64.j1.a1', '64.k1.b1', '64.m1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2969, -1, 833, -1, 2975, -1, 832, -1], 'generators': [117, 250], 'label': '256.18790.32.bx1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bx1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057689
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.cl1.a1', '16.dd1.a1', '16.ee1.a1', '16.ee1.b1', '16.eo1.a1', '16.eo1.b1'], 'contains': ['64.e1.a1', '64.j1.a1', '64.n1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2911, -1, 1031, -1, 2917, -1, 1030, -1], 'generators': [34, 200], 'label': '256.18790.32.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057690
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.ck1.a1', '16.de1.a1', '16.ef1.a1', '16.ef1.b1', '16.ep1.a1', '16.ep1.b1'], 'contains': ['64.g1.a1', '64.j1.a1', '64.n1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3224, -1, 985, -1, 3231, -1, 984, -1], 'generators': [34, 216], 'label': '256.18790.32.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057691
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.ck1.a1', '16.dd1.a1', '16.du1.a1', '16.du1.b1', '16.du1.c1', '16.du1.d1', '16.ek1.a1', '16.ek1.b1', '16.er1.a1', '16.er1.b1', '16.es1.a1', '16.es1.b1', '16.es1.c1', '16.es1.d1'], 'contains': ['64.d1.a1', '64.j1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7664, -1, 1532, -1, 7682, -1, 1531, -1], 'generators': [250, 64], 'label': '256.18790.32.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057692
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.cl1.a1', '16.de1.a1', '16.dv1.a1', '16.dv1.b1', '16.eq1.a1', '16.eq1.b1'], 'contains': ['64.f1.a1', '64.j1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3944, -1, 3661, -1, 3953, -1, 3657, -1], 'generators': [250, 80], 'label': '256.18790.32.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057693
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cg1.a2', '16.cz1.c1', '16.dw1.a1', '16.dx1.b1', '16.eo1.a1', '16.ep1.a1'], 'contains': ['64.k1.a1', '64.m1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3107, -1, 939, -1, 3114, -1, 938, -1], 'generators': [61, 34], 'label': '256.18790.32.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057694
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cg1.b1', '16.cz1.a1', '16.dw1.c1', '16.dx1.a1', '16.eo1.a1', '16.ep1.b1'], 'contains': ['64.k1.a1', '64.m1.b1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3107, -1, 1200, -1, 3114, -1, 1199, -1], 'generators': [117, 34], 'label': '256.18790.32.cc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057695
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cg1.a1', '16.cz1.d1', '16.dw1.b1', '16.dx1.b1', '16.eo1.b1', '16.ep1.a1'], 'contains': ['64.k1.b1', '64.m1.a1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3107, -1, 869, -1, 3114, -1, 867, -1], 'generators': [101, 34], 'label': '256.18790.32.cc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cc1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057696
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.bo1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cg1.b2', '16.cz1.b1', '16.dw1.d1', '16.dx1.a1', '16.eo1.b1', '16.ep1.b1'], 'contains': ['64.k1.b1', '64.m1.b1', '64.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3107, -1, 1154, -1, 3114, -1, 1153, -1], 'generators': [45, 34], 'label': '256.18790.32.cc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cc1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057697
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bq1', '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.h1.a1'], 'contains': ['8.q1.a1', '8.bs1.a1', '8.bt1.a1', '8.bx1.a1', '8.by1.a1', '8.ci1.a1', '8.cn1.a1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5510, -1, 8904, -1, 5523, -1, 8893, -1], 'generators': [1, 2, 248], 'label': '256.18790.4.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057698
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bp1.a1', '16.cm1.a1', '16.du1.a1', '16.du1.c1', '16.dw1.a1', '16.dw1.c1', '16.el1.a1', '16.el1.b1', '16.et1.a1', '16.et1.b1', '16.eu1.a1', '16.eu1.b1', '16.ev1.a1', '16.ev1.b1'], 'contains': ['64.d1.a1', '64.k1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7781, -1, 1789, -1, 7800, -1, 1788, -1], 'generators': [7, 64], 'label': '256.18790.32.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057699
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.bp1.a1', '16.cm1.a1', '16.du1.b1', '16.du1.d1', '16.dw1.b1', '16.dw1.d1', '16.el1.c1', '16.el1.d1', '16.et1.c1', '16.et1.d1', '16.eu1.c1', '16.eu1.d1', '16.ev1.c1', '16.ev1.d1'], 'contains': ['64.d1.a1', '64.k1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7781, -1, 1765, -1, 7800, -1, 1763, -1], 'generators': [223, 64], 'label': '256.18790.32.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057700
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.bq1.a1', '16.cn1.a1', '16.ee1.a1', '16.eo1.a1', '16.ew1.a1', '16.ew1.b1'], 'contains': ['64.e1.a1', '64.k1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2528, -1, 3947, -1, 2532, -1, 3942, -1], 'generators': [7, 200], 'label': '256.18790.32.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057701
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.b1', '16.bq1.a1', '16.cn1.a1', '16.ee1.b1', '16.eo1.b1', '16.ew1.c1', '16.ew1.d1'], 'contains': ['64.e1.a1', '64.k1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2528, -1, 3923, -1, 2532, -1, 3917, -1], 'generators': [23, 200], 'label': '256.18790.32.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.ce1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057702
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bp1.a1', '16.cn1.a1', '16.dg1.a1', '16.dv1.a1', '16.dv1.b1', '16.dx1.a1', '16.dx1.b1'], 'contains': ['64.f1.a1', '64.k1.a1', '64.k1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3363, -1, 1264, -1, 3371, -1, 1262, -1], 'generators': [7, 80], 'label': '256.18790.32.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057703
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.cm1.a1', '16.dg1.a1', '16.ef1.a1', '16.ef1.b1', '16.ep1.a1', '16.ep1.b1'], 'contains': ['64.g1.a1', '64.k1.a1', '64.k1.b1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3166, -1, 1091, -1, 3172, -1, 1090, -1], 'generators': [7, 216], 'label': '256.18790.32.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057704
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ch1', '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.bs1.a1', '16.co1.a1', '16.dh1.a1', '16.ex1.a1', '16.ex1.b1', '16.ey1.a1', '16.ey1.b1'], 'contains': ['64.d1.a1', '64.l1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5201, -1, 6857, -1, 5213, -1, 6849, -1], 'generators': [3, 64], 'label': '256.18790.32.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '32.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057705
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ci1', '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.bt1.a1', '16.cp1.a1', '16.dh1.a1', '16.ez1.a1', '16.ez1.b1', '16.ez1.c1', '16.ez1.d1'], 'contains': ['64.e1.a1', '64.l1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2370, -1, 6980, -1, 2375, -1, 6971, -1], 'generators': [3, 200], 'label': '256.18790.32.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '32.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057706
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cj1', '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.bs1.a1', '16.cp1.a1', '16.di1.a1', '16.eq1.a1', '16.eq1.b1', '16.fa1.a1', '16.fa1.b1'], 'contains': ['64.f1.a1', '64.l1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3550, -1, 8060, -1, 3559, -1, 8049, -1], 'generators': [3, 80], 'label': '256.18790.32.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '32.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057707
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ck1', '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.bt1.a1', '16.co1.a1', '16.di1.a1', '16.eg1.a1', '16.eg1.b1', '16.fb1.a1', '16.fb1.b1'], 'contains': ['64.g1.a1', '64.l1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3411, -1, 6881, -1, 3418, -1, 6873, -1], 'generators': [3, 216], 'label': '256.18790.32.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057708
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.h1.a1'], 'contains': ['8.r1.a1', '8.bs1.a1', '8.bt1.a1', '8.cg1.a1', '8.ch1.a1', '8.cl1.a1', '8.cm1.a1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5709, -1, 9092, -1, 5722, -1, 9081, -1], 'generators': [1, 2, 32], 'label': '256.18790.4.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057709
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.ck1.a1', '16.dd1.a1', '16.dw1.a1', '16.dw1.b1', '16.dw1.c1', '16.dw1.d1', '16.em1.a1', '16.em1.b1', '16.fc1.a1', '16.fc1.b1', '16.fd1.a1', '16.fd1.b1', '16.fd1.c1', '16.fd1.d1'], 'contains': ['64.d1.a1', '64.n1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7822, -1, 1610, -1, 7840, -1, 1608, -1], 'generators': [34, 64], 'label': '256.18790.32.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057710
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.ci1.a1', '16.db1.a1', '16.dy1.a1', '16.dy1.b1', '16.dy1.c1', '16.dy1.d1', '16.er1.a1', '16.er1.b1', '16.et1.a1', '16.et1.b1', '16.et1.c1', '16.et1.d1', '16.fc1.a1', '16.fc1.b1'], 'contains': ['64.d1.a1', '64.o1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8380, -1, 2710, -1, 8408, -1, 2707, -1], 'generators': [218, 64], 'label': '256.18790.32.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057711
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bv1.a1', '16.cq1.a1', '16.ds1.a1', '16.ds1.c1', '16.dy1.a1', '16.dy1.c1', '16.es1.a1', '16.es1.b1', '16.eu1.a1', '16.eu1.c1', '16.ev1.a1', '16.ev1.c1', '16.fd1.a1', '16.fd1.b1'], 'contains': ['64.d1.a1', '64.p1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8291, -1, 2735, -1, 8309, -1, 2732, -1], 'generators': [39, 64], 'label': '256.18790.32.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057712
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.bv1.a1', '16.cq1.a1', '16.ds1.b1', '16.ds1.d1', '16.dy1.b1', '16.dy1.d1', '16.es1.c1', '16.es1.d1', '16.eu1.b1', '16.eu1.d1', '16.ev1.b1', '16.ev1.d1', '16.fd1.c1', '16.fd1.d1'], 'contains': ['64.d1.a1', '64.p1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8291, -1, 2686, -1, 8309, -1, 2683, -1], 'generators': [255, 64], 'label': '256.18790.32.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057713
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.co1', '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.bw1.a1', '16.cr1.a1', '16.dk1.a1', '16.ex1.a1', '16.ex1.b1', '16.ey1.a1', '16.ey1.b1'], 'contains': ['64.d1.a1', '64.q1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5653, -1, 6076, -1, 5666, -1, 6068, -1], 'generators': [35, 64], 'label': '256.18790.32.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '32.co1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057714
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.by1.a1', '16.dm1.a1', '16.dz1.a1', '16.dz1.d1', '16.ea1.b1', '16.ea1.c1', '16.el1.a1', '16.el1.c1', '16.es1.a1', '16.es1.c1', '16.et1.a1', '16.et1.c1', '16.fd1.a1', '16.fd1.c1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8795, -1, 2652, -1, 8816, -1, 2649, -1], 'generators': [5], 'label': '256.18790.32.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057715
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '16.by1.a1', '16.dm1.a1', '16.dz1.b1', '16.dz1.c1', '16.ea1.a1', '16.ea1.d1', '16.el1.b1', '16.el1.d1', '16.es1.b1', '16.es1.d1', '16.et1.b1', '16.et1.d1', '16.fd1.b1', '16.fd1.d1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8795, -1, 1650, -1, 8816, -1, 1647, -1], 'generators': [21], 'label': '256.18790.32.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057716
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.ch1.a1', '16.da1.a1', '16.ei1.a1', '16.ei1.b1', '16.eo1.a1', '16.eo1.b1'], 'contains': ['64.e1.a1', '64.m1.a1', '64.m1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3783, -1, 3851, -1, 3792, -1, 3847, -1], 'generators': [101, 200], 'label': '256.18790.32.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057717
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bz1.a1', '16.cu1.a1', '16.ec1.a1', '16.ei1.a1', '16.ez1.a1', '16.ez1.b1'], 'contains': ['64.e1.a1', '64.p1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5354, -1, 5541, -1, 5366, -1, 5534, -1], 'generators': [39, 200], 'label': '256.18790.32.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.cr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057718
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.b1', '16.bz1.a1', '16.cu1.a1', '16.ec1.b1', '16.ei1.b1', '16.ez1.c1', '16.ez1.d1'], 'contains': ['64.e1.a1', '64.p1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5354, -1, 5495, -1, 5366, -1, 5488, -1], 'generators': [55, 200], 'label': '256.18790.32.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.cr1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057719
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.e1.a1'], 'contains': ['8.u1.a1', '8.bu1.a1', '8.bv1.a1', '8.bw1.b1', '8.cd1.a1', '8.ce1.b1', '8.cq1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [620, -1, 5817, -1, 621, -1, 5809, -1], 'generators': [1, 34, 100], 'label': '256.18790.4.bs1.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.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057720
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cs1', '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.ca1.a1', '16.cv1.a1', '16.dk1.a1', '16.ew1.a1', '16.ew1.b1', '16.ew1.c1', '16.ew1.d1'], 'contains': ['64.e1.a1', '64.q1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3283, -1, 6636, -1, 3290, -1, 6628, -1], 'generators': [35, 200], 'label': '256.18790.32.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.v1.a1', 'old_label': '32.cs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057721
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.cw1.a1', '16.dl1.a1', '16.ew1.a1', '16.ew1.c1', '16.ez1.a1', '16.ez1.c1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1872, -1, 6660, -1, 1876, -1, 6652, -1], 'generators': [36], 'label': '256.18790.32.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.ct1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ct1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057722
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '16.cw1.a1', '16.dl1.a1', '16.ew1.b1', '16.ew1.d1', '16.ez1.b1', '16.ez1.d1'], 'contains': ['64.e1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1872, -1, 6590, -1, 1876, -1, 6581, -1], 'generators': [100], 'label': '256.18790.32.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.ct1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ct1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057723
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.cl1.a1', '16.de1.a1', '16.dx1.a1', '16.dx1.b1', '16.fa1.a1', '16.fa1.b1'], 'contains': ['64.f1.a1', '64.n1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3984, -1, 3971, -1, 3993, -1, 3966, -1], 'generators': [34, 80], 'label': '256.18790.32.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.cu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057724
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.cj1.a1', '16.dc1.a1', '16.eb1.a1', '16.eb1.b1', '16.fe1.a1', '16.fe1.b1'], 'contains': ['64.f1.a1', '64.o1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6312, -1, 6222, -1, 6326, -1, 6214, -1], 'generators': [218, 80], 'label': '256.18790.32.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057725
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bv1.a1', '16.cu1.a1', '16.dn1.a1', '16.dt1.a1', '16.dt1.b1', '16.eb1.a1', '16.eb1.b1'], 'contains': ['64.f1.a1', '64.p1.a1', '64.p1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6272, -1, 5026, -1, 6286, -1, 5019, -1], 'generators': [39, 80], 'label': '256.18790.32.cw1.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.cw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057726
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cx1', '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.bw1.a1', '16.cv1.a1', '16.do1.a1', '16.en1.a1', '16.en1.b1', '16.fe1.a1', '16.fe1.b1'], 'contains': ['64.f1.a1', '64.q1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4618, -1, 8289, -1, 4628, -1, 8278, -1], 'generators': [35, 80], 'label': '256.18790.32.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '32.cx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057727
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.bx1.a1', '16.cx1.a1', '16.en1.a1', '16.eq1.a1', '16.fa1.a1', '16.fe1.a1'], 'contains': ['64.f1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4445, -1, 8101, -1, 4455, -1, 8091, -1], 'generators': [33], 'label': '256.18790.32.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.cy1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cy1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057728
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.b1', '16.bx1.a1', '16.cx1.a1', '16.en1.b1', '16.eq1.b1', '16.fa1.b1', '16.fe1.b1'], 'contains': ['64.f1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4445, -1, 8139, -1, 4455, -1, 8128, -1], 'generators': [97], 'label': '256.18790.32.cy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.cy1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cy1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057729
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bz1.a1', '16.cq1.a1', '16.dn1.a1', '16.ed1.a1', '16.ed1.b1', '16.ej1.a1', '16.ej1.b1'], 'contains': ['64.g1.a1', '64.p1.a1', '64.p1.b1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6079, -1, 5121, -1, 6093, -1, 5114, -1], 'generators': [39, 216], 'label': '256.18790.32.cz1.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.cz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057730
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.e1.a1'], 'contains': ['8.u1.b1', '8.bu1.a1', '8.bv1.b1', '8.bw1.a1', '8.cd1.b1', '8.ce1.a1', '8.cq1.a1'], 'core': '8.u1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [620, -1, 5954, -1, 621, -1, 5946, -1], 'generators': [65, 34, 36], 'label': '256.18790.4.bs1.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.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057731
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.da1', '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.ca1.a1', '16.cr1.a1', '16.do1.a1', '16.eh1.a1', '16.eh1.b1', '16.ff1.a1', '16.ff1.b1'], 'contains': ['64.g1.a1', '64.q1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4511, -1, 5846, -1, 4522, -1, 5839, -1], 'generators': [35, 216], 'label': '256.18790.32.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '32.da1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.da1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057732
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cb1.a1', '16.cs1.a1', '16.dp1.a1', '16.eh1.a1', '16.eh1.b1', '16.ff1.a1', '16.ff1.b1'], 'contains': ['64.g1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4578, -1, 5792, -1, 4588, -1, 5785, -1], 'generators': [6], 'label': '256.18790.32.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '32.db1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.db1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057733
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.cc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cc1.a1', '16.ct1.a1', '16.dq1.a1', '16.eg1.a1', '16.eg1.b1', '16.fb1.a1', '16.fb1.b1'], 'contains': ['64.g1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3460, -1, 6105, -1, 3468, -1, 6097, -1], 'generators': [38], 'label': '256.18790.32.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.dc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057734
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dd1', '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.cd1.a1', '16.cf1.a2', '16.cy1.c1', '16.dy1.a1', '16.eb1.b1', '16.ei1.a1', '16.ej1.a1'], 'contains': ['64.m1.a1', '64.o1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6508, -1, 4789, -1, 6524, -1, 4784, -1], 'generators': [101, 218], 'label': '256.18790.32.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.dd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057735
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dd1', '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.cd1.a1', '16.cf1.a1', '16.cy1.d1', '16.dy1.b1', '16.eb1.b1', '16.ei1.b1', '16.ej1.a1'], 'contains': ['64.m1.a1', '64.o1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6508, -1, 4765, -1, 6524, -1, 4759, -1], 'generators': [61, 218], 'label': '256.18790.32.dd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.dd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057736
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dd1', '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.cd1.a1', '16.cf1.b1', '16.cy1.a1', '16.dy1.c1', '16.eb1.a1', '16.ei1.a1', '16.ej1.b1'], 'contains': ['64.m1.b1', '64.o1.a1', '64.p1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6508, -1, 4885, -1, 6524, -1, 4879, -1], 'generators': [45, 218], 'label': '256.18790.32.dd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.dd1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dd1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057737
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dd1', '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.cd1.a1', '16.cf1.b2', '16.cy1.b1', '16.dy1.d1', '16.eb1.a1', '16.ei1.b1', '16.ej1.b1'], 'contains': ['64.m1.b1', '64.o1.a1', '64.p1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6508, -1, 4815, -1, 6524, -1, 4808, -1], 'generators': [117, 218], 'label': '256.18790.32.dd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.dd1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dd1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057738
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.fg1.a1', '16.fg1.b1'], 'contains': ['64.r1.a1', '64.v1.a1', '64.y1.a1', '64.ba1.a1', '64.ba1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1707, -1, 9018, -1, 1711, -1, 9006, -1], 'generators': [7, 24, 16], 'label': '256.18790.32.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.de1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.de1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057739
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.fg1.c1', '16.fg1.d1'], 'contains': ['64.r1.b1', '64.v1.b1', '64.y1.a1', '64.ba1.a1', '64.ba1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1707, -1, 9119, -1, 1711, -1, 9107, -1], 'generators': [7, 152, 144], 'label': '256.18790.32.de1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.de1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.de1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057740
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.fg1.a1', '16.fg1.b1'], 'contains': ['64.r1.a1', '64.w1.a1', '64.z1.a1', '64.bb1.a1', '64.bb1.a2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1661, -1, 9194, -1, 1665, -1, 9181, -1], 'generators': [3, 24, 16], 'label': '256.18790.32.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.df1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.df1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057741
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.h1.a1'], 'contains': ['8.s1.a1', '8.bx1.a1', '8.by1.a1', '8.cf1.a1', '8.ch1.a1', '8.cm1.a1', '8.cp1.a1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5458, -1, 8873, -1, 5472, -1, 8862, -1], 'generators': [1, 218, 32], 'label': '256.18790.4.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057742
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.fg1.c1', '16.fg1.d1'], 'contains': ['64.r1.b1', '64.w1.b1', '64.z1.a1', '64.bb1.a1', '64.bb1.a2'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1661, -1, 9341, -1, 1665, -1, 9328, -1], 'generators': [3, 24, 144], 'label': '256.18790.32.df1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.df1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.df1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057743
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.fg1.a1'], 'contains': ['64.r1.a1', '64.bc1.a1', '64.bc1.c1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1561, -1, 9304, -1, 1564, -1, 9291, -1], 'generators': [4, 16], 'label': '256.18790.32.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057744
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.fg1.b1'], 'contains': ['64.r1.a1', '64.bc1.b1', '64.bc1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1561, -1, 9593, -1, 1564, -1, 9580, -1], 'generators': [132, 16], 'label': '256.18790.32.dg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057745
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.fg1.c1'], 'contains': ['64.r1.b1', '64.bc1.a1', '64.bc1.d1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1561, -1, 9403, -1, 1564, -1, 9390, -1], 'generators': [4, 144], 'label': '256.18790.32.dg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dg1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dg1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057746
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.fg1.d1'], 'contains': ['64.r1.b1', '64.bc1.b1', '64.bc1.c1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1561, -1, 9547, -1, 1564, -1, 9534, -1], 'generators': [132, 144], 'label': '256.18790.32.dg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dg1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dg1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057747
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1'], 'contains': ['64.s1.a1', '64.u1.a1', '64.v1.a1', '64.bd1.a1', '64.bd1.b1', '64.bd1.c1', '64.bd1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1992, -1, 522, -1, 1996, -1, 521, -1], 'generators': [37, 250, 16], 'label': '256.18790.32.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '32.dh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057748
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1'], 'contains': ['64.s1.b1', '64.u1.b1', '64.v1.b1', '64.bd1.a1', '64.bd1.b1', '64.bd1.c1', '64.bd1.d1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1992, -1, 549, -1, 1996, -1, 548, -1], 'generators': [37, 250, 144], 'label': '256.18790.32.dh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '32.dh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057749
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.di1', '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': ['16.bi1.a1'], 'contains': ['64.t1.a1', '64.w1.a1', '64.x1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1502, -1, 8818, -1, 1505, -1, 8806, -1], 'generators': [1, 2], 'label': '256.18790.32.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.bi1.a1', 'old_label': '32.di1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.di1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057750
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.di1', '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': ['16.bi1.b1'], 'contains': ['64.t1.b1', '64.w1.b1', '64.x1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [1502, -1, 8842, -1, 1505, -1, 8831, -1], 'generators': [65, 2], 'label': '256.18790.32.di1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.bi1.b1', 'old_label': '32.di1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.di1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057751
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.a1', '16.fg1.a1', '16.fg1.c1'], 'contains': ['64.ba1.a1', '64.bb1.a1', '64.bc1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9244, -1, 1622, -1, 9232, -1], 'generators': [3, 4], 'label': '256.18790.32.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057752
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.h1.a1'], 'contains': ['8.t1.a1', '8.cf1.a1', '8.cg1.a1', '8.ci1.a1', '8.cl1.a1', '8.cn1.a1', '8.cp1.a1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5597, -1, 8957, -1, 5611, -1, 8946, -1], 'generators': [1, 218, 248], 'label': '256.18790.4.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '4.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057753
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.a1', '16.fg1.b1', '16.fg1.d1'], 'contains': ['64.ba1.a1', '64.bb1.a1', '64.bc1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9511, -1, 1622, -1, 9498, -1], 'generators': [3, 132], 'label': '256.18790.32.dj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057754
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.b1', '16.fg1.a1', '16.fg1.d1'], 'contains': ['64.ba1.a1', '64.bb1.a2', '64.bc1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9367, -1, 1622, -1, 9354, -1], 'generators': [3, 68], 'label': '256.18790.32.dj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057755
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.b1', '16.fg1.b1', '16.fg1.c1'], 'contains': ['64.ba1.a1', '64.bb1.a2', '64.bc1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9486, -1, 1622, -1, 9474, -1], 'generators': [3, 196], 'label': '256.18790.32.dj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057756
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.c1', '16.fg1.a1', '16.fg1.c1'], 'contains': ['64.ba1.b1', '64.bb1.a2', '64.bc1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9220, -1, 1622, -1, 9207, -1], 'generators': [83, 4], 'label': '256.18790.32.dj1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057757
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.c1', '16.fg1.b1', '16.fg1.d1'], 'contains': ['64.ba1.b1', '64.bb1.a2', '64.bc1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9462, -1, 1622, -1, 9449, -1], 'generators': [83, 132], 'label': '256.18790.32.dj1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057758
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.d1', '16.fg1.a1', '16.fg1.d1'], 'contains': ['64.ba1.b1', '64.bb1.a1', '64.bc1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9268, -1, 1622, -1, 9256, -1], 'generators': [83, 68], 'label': '256.18790.32.dj1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057759
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '32.dj1', '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.df1.d1', '16.fg1.b1', '16.fg1.c1'], 'contains': ['64.ba1.b1', '64.bb1.a1', '64.bc1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T5615', 'count': 8, 'diagramx': [1618, -1, 9438, -1, 1622, -1, 9425, -1], 'generators': [83, 196], 'label': '256.18790.32.dj1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '32.dj1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057760
    {'ambient': '256.18790', '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.l1.a1', '32.m1.a1', '32.n1.a1', '32.o1.a1', '32.p1.a1', '32.q1.a1', '32.r1.a1', '32.r1.b1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.v1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.b1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2415, 4200, 5823, 4627, 2421, 4180, 5984, 4655], 'generators': [16, 128], 'label': '256.18790.64.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'], 'normal_contains': ['128.a1.a1', '128.b1.a1', '128.b1.b1'], '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: 26057761
    {'ambient': '256.18790', '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.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '32.w1.a1', '32.w1.b1', '32.x1.a1', '32.y1.a1', '32.z1.a1', '32.ba1.a1', '32.bb1.a1', '32.bc1.a1'], 'contains': ['128.a1.a1', '128.c1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3774, 4315, 5116, 4199, 3783, 4295, 5128, 4224], 'generators': [24, 128], 'label': '256.18790.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.e1.a1', '32.d1.a1'], 'normal_contains': ['128.a1.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: 26057762
    {'ambient': '256.18790', '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.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '32.bd1.a1', '32.bd1.b1', '32.be1.a1', '32.bf1.a1', '32.bg1.a1', '32.bg1.b1', '32.bh1.a1', '32.bi1.a1', '32.bi1.b1', '32.bj1.a1', '32.bj1.b1', '32.bk1.a1'], 'contains': ['128.a1.a1', '128.d1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3009, 4428, 6776, 4513, 3015, 4410, 6767, 4541], 'generators': [8, 128], 'label': '256.18790.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': 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: 26057763
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.v1.a1', '8.cs1.a1', '8.cu1.a1', '8.cy1.a1', '8.cz1.a1', '8.dc1.a1', '8.dd1.a1', '8.ei1.b1', '8.ei1.c1', '8.ej1.a1', '8.ej1.d1', '8.ek1.a1', '8.ek1.d1', '8.el1.b1', '8.el1.c1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9400, -1, 2464, -1, 9490, -1, 2461, -1], 'generators': [5, 2, 32, 216], 'label': '256.18790.4.bv1.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.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057764
    {'ambient': '256.18790', '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': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '32.i1.a1', '32.i1.b1', '32.j1.a1', '32.j1.b1', '32.bo1.a1', '32.bo1.b1', '32.bv1.a1', '32.ca1.a1', '32.cd1.a1', '32.cd1.b1', '32.ch1.a1', '32.cl1.a1', '32.cm1.a1', '32.cn1.a1', '32.cn1.b1', '32.co1.a1', '32.cp1.a1', '32.cp1.b1'], 'contains': ['128.a1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7802, 3472, 2723, 5757, 7820, 3491, 2719, 5815], 'generators': [64], 'label': '256.18790.64.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1.a1', 'normal_contained_in': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '32.i1.b1', '32.i1.a1', '32.j1.b1', '32.j1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.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: 26057765
    {'ambient': '256.18790', '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': '2.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.e1.a1', '32.f1.a1', '32.br1.a1', '32.bs1.a1', '32.by1.a1', '32.ce1.a1', '32.ce1.b1', '32.ci1.a1', '32.cq1.a1', '32.cr1.a1', '32.cr1.b1', '32.cs1.a1', '32.ct1.a1', '32.ct1.b1'], 'contains': ['128.a1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3667, 4636, 5454, 4306, 3675, 4618, 5447, 4332], 'generators': [200], 'label': '256.18790.64.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.e1.a1', 'normal_contained_in': ['32.c1.a1', '32.e1.a1', '32.f1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.e1.a1', 'projective_image': 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: 26057766
    {'ambient': '256.18790', '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': '2.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '32.bp1.a1', '32.bp1.b1', '32.bw1.a1', '32.cb1.a1', '32.cf1.a1', '32.cj1.a1', '32.cu1.a1', '32.cv1.a1', '32.cw1.a1', '32.cx1.a1', '32.cy1.a1', '32.cy1.b1'], 'contains': ['128.a1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4252, 4536, 5637, 4406, 4262, 4517, 5619, 4433], 'generators': [80], 'label': '256.18790.64.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.f1.a1', 'normal_contained_in': ['32.b1.a1', '32.e1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.f1.a1', 'projective_image': 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: 26057767
    {'ambient': '256.18790', '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': '2.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '32.h1.a1', '32.h1.b1', '32.k1.a1', '32.k1.b1', '32.bt1.a1', '32.bz1.a1', '32.cg1.a1', '32.ck1.a1', '32.cz1.a1', '32.da1.a1', '32.db1.a1', '32.dc1.a1'], 'contains': ['128.a1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3817, 4749, 5070, 2465, 3826, 4730, 5079, 2469], 'generators': [216], 'label': '256.18790.64.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.g1.a1', 'normal_contained_in': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '32.h1.b1', '32.h1.a1', '32.k1.a1', '32.k1.b1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.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: 26057768
    {'ambient': '256.18790', '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': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.l1.a1', '32.w1.a1', '32.bd1.a1', '32.bl1.a1', '32.bl1.b1', '32.bm1.a1', '32.bm1.b1', '32.bn1.a1', '32.bn1.b1', '32.bo1.a1', '32.bp1.a1', '32.bq1.a1', '32.bq1.b1', '32.br1.a1'], 'contains': ['128.a1.a1', '128.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3861, -1, 3683, -1, 3870, -1, 3678, -1], 'generators': [37, 128], 'label': '256.18790.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 26057769
    {'ambient': '256.18790', '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': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.l1.a1', '32.w1.b1', '32.bd1.b1', '32.bl1.c1', '32.bl1.d1', '32.bm1.c1', '32.bm1.d1', '32.bn1.c1', '32.bn1.d1', '32.bo1.b1', '32.bp1.b1', '32.bq1.c1', '32.bq1.d1', '32.br1.a1'], 'contains': ['128.a1.a1', '128.e1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3861, -1, 3655, -1, 3870, -1, 3650, -1], 'generators': [53, 128], 'label': '256.18790.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', '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: 26057770
    {'ambient': '256.18790', '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': '8.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.x1.a1', '32.be1.a1', '32.bl1.a1', '32.bl1.b1', '32.bl1.c1', '32.bl1.d1', '32.bs1.a1', '32.bt1.a1', '32.bu1.a1', '32.bu1.b1', '32.bu1.c1', '32.bu1.d1', '32.bv1.a1', '32.bw1.a1'], 'contains': ['128.a1.a1', '128.f1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6436, -1, 5144, -1, 6450, -1, 5155, -1], 'generators': [2, 128], 'label': '256.18790.64.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.i1.a1', 'projective_image': 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: 26057771
    {'ambient': '256.18790', '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': '8.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.n1.a1', '32.y1.a1', '32.bf1.a1', '32.bm1.a1', '32.bm1.b1', '32.bm1.c1', '32.bm1.d1', '32.bx1.a1', '32.bx1.b1', '32.bx1.c1', '32.bx1.d1', '32.by1.a1', '32.bz1.a1', '32.ca1.a1', '32.cb1.a1'], 'contains': ['128.a1.a1', '128.g1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3055, -1, 985, -1, 3061, -1, 984, -1], 'generators': [250, 128], 'label': '256.18790.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057772
    {'ambient': '256.18790', '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': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.z1.a1', '32.bg1.a1', '32.bm1.a1', '32.bm1.c1', '32.bn1.a1', '32.bn1.c1', '32.bx1.a1', '32.bx1.b1', '32.cc1.a1', '32.cc1.b1', '32.cd1.a1', '32.ce1.a1', '32.cf1.a1', '32.cg1.a1'], 'contains': ['128.a1.a1', '128.h1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2963, -1, 1118, -1, 2970, -1, 1117, -1], 'generators': [7, 128], 'label': '256.18790.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.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: 26057773
    {'ambient': '256.18790', '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': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.z1.a1', '32.bg1.b1', '32.bm1.b1', '32.bm1.d1', '32.bn1.b1', '32.bn1.d1', '32.bx1.c1', '32.bx1.d1', '32.cc1.c1', '32.cc1.d1', '32.cd1.b1', '32.ce1.b1', '32.cf1.a1', '32.cg1.a1'], 'contains': ['128.a1.a1', '128.h1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2963, -1, 1090, -1, 2970, -1, 1089, -1], 'generators': [223, 128], 'label': '256.18790.64.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '64.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057774
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.v1.b1', '8.cs1.a1', '8.cu1.a1', '8.cy1.b1', '8.cz1.b1', '8.dc1.b1', '8.dd1.b1', '8.ei1.a1', '8.ei1.d1', '8.ej1.b1', '8.ej1.c1', '8.ek1.b1', '8.ek1.c1', '8.el1.a1', '8.el1.d1'], 'core': '8.v1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9400, -1, 1321, -1, 9490, -1, 1319, -1], 'generators': [21, 2, 48, 216], 'label': '256.18790.4.bv1.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.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057775
    {'ambient': '256.18790', '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.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.ba1.a1', '32.bh1.a1', '32.ch1.a1', '32.ci1.a1', '32.cj1.a1', '32.ck1.a1'], 'contains': ['128.a1.a1', '128.i1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2370, -1, 6953, -1, 2375, -1, 6944, -1], 'generators': [3, 128], 'label': '256.18790.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.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: 26057776
    {'ambient': '256.18790', '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': '4.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.q1.a1', '32.w1.a1', '32.bd1.b1', '32.bo1.a1', '32.bp1.b1', '32.bu1.a1', '32.bu1.b1', '32.bx1.a1', '32.bx1.c1', '32.cc1.a1', '32.cc1.c1', '32.cq1.a1', '32.dd1.a1', '32.dd1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3904, -1, 3786, -1, 3913, -1, 3781, -1], 'generators': [101], 'label': '256.18790.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.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: 26057777
    {'ambient': '256.18790', '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': '4.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.b1', '32.q1.a1', '32.w1.b1', '32.bd1.a1', '32.bo1.b1', '32.bp1.a1', '32.bu1.c1', '32.bu1.d1', '32.bx1.b1', '32.bx1.d1', '32.cc1.b1', '32.cc1.d1', '32.cq1.a1', '32.dd1.c1', '32.dd1.d1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3904, -1, 3839, -1, 3913, -1, 3835, -1], 'generators': [117], 'label': '256.18790.64.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057778
    {'ambient': '256.18790', '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': '8.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.y1.a1', '32.bf1.a1', '32.bn1.a1', '32.bn1.b1', '32.bn1.c1', '32.bn1.d1', '32.by1.a1', '32.bz1.a1', '32.cc1.a1', '32.cc1.b1', '32.cc1.c1', '32.cc1.d1', '32.cl1.a1', '32.cu1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3166, -1, 1144, -1, 3172, -1, 1143, -1], 'generators': [34], 'label': '256.18790.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.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: 26057779
    {'ambient': '256.18790', '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': '8.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.t1.a1', '32.x1.a1', '32.be1.a1', '32.bq1.a1', '32.bq1.b1', '32.bq1.c1', '32.bq1.d1', '32.bs1.a1', '32.bt1.a1', '32.cm1.a1', '32.cv1.a1', '32.dd1.a1', '32.dd1.b1', '32.dd1.c1', '32.dd1.d1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6392, -1, 4879, -1, 6407, -1, 4876, -1], 'generators': [218], 'label': '256.18790.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.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: 26057780
    {'ambient': '256.18790', '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': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.a1', '32.bb1.a1', '32.bj1.a1', '32.bl1.a1', '32.bl1.c1', '32.bq1.a1', '32.bq1.c1', '32.bu1.a1', '32.bu1.c1', '32.cn1.a1', '32.cr1.a1', '32.cw1.a1', '32.cz1.a1', '32.dd1.a1', '32.dd1.c1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6205, -1, 4912, -1, 6219, -1, 4906, -1], 'generators': [39], 'label': '256.18790.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.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: 26057781
    {'ambient': '256.18790', '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': '8.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.a1', '32.bb1.a1', '32.bj1.b1', '32.bl1.b1', '32.bl1.d1', '32.bq1.b1', '32.bq1.d1', '32.bu1.b1', '32.bu1.d1', '32.cn1.b1', '32.cr1.b1', '32.cw1.a1', '32.cz1.a1', '32.dd1.b1', '32.dd1.d1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6205, -1, 4852, -1, 6219, -1, 4849, -1], 'generators': [255], 'label': '256.18790.64.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057782
    {'ambient': '256.18790', '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': '16.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.v1.a1', '32.bc1.a1', '32.bk1.a1', '32.co1.a1', '32.cs1.a1', '32.cx1.a1', '32.da1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3732, -1, 6864, -1, 3740, -1, 6842, -1], 'generators': [35], 'label': '256.18790.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.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: 26057783
    {'ambient': '256.18790', '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': '2.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.de1.a1', '32.df1.a1', '32.dg1.a1', '32.dg1.b1'], 'contains': ['128.b1.a1', '128.c1.a1', '128.d1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1827, -1, 9133, -1, 1830, -1, 9121, -1], 'generators': [24, 16], 'label': '256.18790.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.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: 26057784
    {'ambient': '256.18790', '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': '2.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.de1.b1', '32.df1.b1', '32.dg1.c1', '32.dg1.d1'], 'contains': ['128.b1.b1', '128.c1.a1', '128.d1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1827, -1, 9241, -1, 1830, -1, 9228, -1], 'generators': [24, 144], 'label': '256.18790.64.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '64.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057785
    {'ambient': '256.18790', '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.f1.a1', '128.h1.a1', '128.h1.b1', '128.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '4.y1.a1', '4.z1.a1', '4.bg1.a1', '4.bh1.a1', '4.bw1.a1', '4.bw1.b1', '4.bw1.c1', '4.bw1.d1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5145, 3395, 5447, 2786, 5157, 3405, 5440, 2802], 'generators': [5, 6, 32, 16], 'label': '256.18790.2.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.y1.a1', '4.z1.a1', '4.bg1.a1', '4.bh1.a1'], '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: 26057786
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.v1.c1', '8.cs1.b1', '8.cu1.b1', '8.cy1.a1', '8.cz1.b1', '8.dc1.b1', '8.dd1.a1', '8.ei1.f1', '8.ei1.g1', '8.ej1.e1', '8.ej1.h1', '8.ek1.e1', '8.ek1.h1', '8.el1.f1', '8.el1.g1'], 'core': '8.v1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9400, -1, 1178, -1, 9490, -1, 1176, -1], 'generators': [21, 2, 32, 216], 'label': '256.18790.4.bv1.c1', '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.bv1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bv1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057787
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.dh1.a1'], 'contains': ['128.b1.a1', '128.e1.a1', '128.e1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2129, -1, 902, -1, 2133, -1, 901, -1], 'generators': [37, 16], 'label': '256.18790.64.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bl1.a1', 'old_label': '64.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057788
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.dh1.b1'], 'contains': ['128.b1.b1', '128.e1.a1', '128.e1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2129, -1, 957, -1, 2133, -1, 956, -1], 'generators': [37, 144], 'label': '256.18790.64.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bl1.a1', 'old_label': '64.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057789
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.di1.a1'], 'contains': ['128.b1.a1', '128.f1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2174, -1, 6981, -1, 2179, -1, 6972, -1], 'generators': [2, 16], 'label': '256.18790.64.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bp1.a1', 'old_label': '64.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057790
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.m1.a1', '32.di1.b1'], 'contains': ['128.b1.b1', '128.f1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2174, -1, 7033, -1, 2179, -1, 7024, -1], 'generators': [2, 144], 'label': '256.18790.64.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bp1.b1', 'old_label': '64.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057791
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.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': ['32.n1.a1', '32.dh1.a1'], 'contains': ['128.b1.a1', '128.g1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2083, -1, 781, -1, 2087, -1, 826, -1], 'generators': [250, 16], 'label': '256.18790.64.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bo1.b1', 'old_label': '64.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057792
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.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': ['32.n1.a1', '32.dh1.b1'], 'contains': ['128.b1.b1', '128.g1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2083, -1, 930, -1, 2087, -1, 929, -1], 'generators': [250, 144], 'label': '256.18790.64.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bo1.a1', 'old_label': '64.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057793
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.de1.a1', '32.dh1.a1'], 'contains': ['128.b1.a1', '128.h1.a1', '128.h1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1992, -1, 1950, -1, 1996, -1, 1936, -1], 'generators': [7, 16], 'label': '256.18790.64.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1.a1', 'old_label': '64.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057794
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.de1.b1', '32.dh1.b1'], 'contains': ['128.b1.b1', '128.h1.a1', '128.h1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1992, -1, 1978, -1, 1996, -1, 1964, -1], 'generators': [7, 144], 'label': '256.18790.64.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1.a1', 'old_label': '64.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057795
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.df1.a1', '32.di1.a1'], 'contains': ['128.b1.a1', '128.i1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1767, -1, 8815, -1, 1770, -1, 8803, -1], 'generators': [3, 16], 'label': '256.18790.64.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '64.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057796
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.df1.b1', '32.di1.b1'], 'contains': ['128.b1.b1', '128.i1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1767, -1, 8842, -1, 1770, -1, 8831, -1], 'generators': [3, 144], 'label': '256.18790.64.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ba1.a1', 'old_label': '64.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057797
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.v1.d1', '8.cs1.b1', '8.cu1.b1', '8.cy1.b1', '8.cz1.a1', '8.dc1.a1', '8.dd1.b1', '8.ei1.e1', '8.ei1.h1', '8.ej1.f1', '8.ej1.g1', '8.ek1.f1', '8.ek1.g1', '8.el1.e1', '8.el1.h1'], 'core': '8.v1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9400, -1, 2806, -1, 9490, -1, 2803, -1], 'generators': [5, 2, 48, 216], 'label': '256.18790.4.bv1.d1', '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.bv1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bv1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057798
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.a1', '32.di1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1502, -1, 7007, -1, 1505, -1, 6998, -1], 'generators': [1], 'label': '256.18790.64.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.br1.a1', 'old_label': '64.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057799
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.cm1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.b1', '32.di1.b1'], 'contains': ['128.b1.b1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1502, -1, 8677, -1, 1505, -1, 8671, -1], 'generators': [65], 'label': '256.18790.64.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.br1.a1', 'old_label': '64.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057800
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.z1.a1', '32.de1.a1', '32.de1.b1'], 'contains': ['128.c1.a1', '128.h1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2037, -1, 8755, -1, 2042, -1, 8723, -1], 'generators': [7, 24], 'label': '256.18790.64.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.x1.a1', 'old_label': '64.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057801
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ba1.a1', '32.df1.a1', '32.df1.b1'], 'contains': ['128.c1.a1', '128.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1945, -1, 9161, -1, 1950, -1, 9148, -1], 'generators': [3, 24], 'label': '256.18790.64.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.y1.a1', 'old_label': '64.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057802
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bg1.a1', '32.de1.a1', '32.de1.b1', '32.dj1.a1', '32.dj1.b1', '32.dj1.c1', '32.dj1.d1'], 'contains': ['128.d1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1872, -1, 9189, -1, 1876, -1, 9176, -1], 'generators': [7, 8], 'label': '256.18790.64.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '64.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057803
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bg1.b1', '32.de1.a1', '32.de1.b1', '32.dj1.e1', '32.dj1.f1', '32.dj1.g1', '32.dj1.h1'], 'contains': ['128.d1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1872, -1, 9105, -1, 1876, -1, 9093, -1], 'generators': [87, 8], 'label': '256.18790.64.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '64.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057804
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bh1.a1', '32.df1.a1', '32.df1.b1', '32.dj1.a1', '32.dj1.b1', '32.dj1.g1', '32.dj1.h1'], 'contains': ['128.d1.a1', '128.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1720, -1, 9268, -1, 1724, -1, 9256, -1], 'generators': [3, 8], 'label': '256.18790.64.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '64.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057805
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bh1.a1', '32.df1.a1', '32.df1.b1', '32.dj1.c1', '32.dj1.d1', '32.dj1.e1', '32.dj1.f1'], 'contains': ['128.d1.a1', '128.i1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1720, -1, 9296, -1, 1724, -1, 9284, -1], 'generators': [3, 136], 'label': '256.18790.64.bb1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bc1.a1', 'old_label': '64.bb1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057806
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bi1.a1', '32.dg1.a1', '32.dg1.c1', '32.dj1.a1', '32.dj1.e1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1641, -1, 9215, -1, 1658, -1, 9202, -1], 'generators': [4], 'label': '256.18790.64.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '64.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057807
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bi1.a1', '32.dg1.b1', '32.dg1.d1', '32.dj1.b1', '32.dj1.f1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1641, -1, 9486, -1, 1658, -1, 9458, -1], 'generators': [132], 'label': '256.18790.64.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '64.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057808
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.f1.a1'], 'contains': ['8.v1.a1', '8.cw1.a1', '8.cx1.a1', '8.df1.a1', '8.dg1.a1', '8.di1.a1', '8.dj1.a1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6840, -1, 5180, -1, 6857, -1, 5177, -1], 'generators': [5, 6, 32], 'label': '256.18790.4.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057809
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bi1.b1', '32.dg1.a1', '32.dg1.d1', '32.dj1.c1', '32.dj1.g1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1641, -1, 9322, -1, 1658, -1, 9310, -1], 'generators': [68], 'label': '256.18790.64.bc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '64.bc1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057810
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bi1.b1', '32.dg1.b1', '32.dg1.c1', '32.dj1.d1', '32.dj1.h1'], 'contains': ['128.d1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1641, -1, 9420, -1, 1658, -1, 9416, -1], 'generators': [196], 'label': '256.18790.64.bc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '64.bc1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057811
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bm1.a1', '32.dh1.a1', '32.dh1.b1'], 'contains': ['128.e1.a1', '128.g1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2221, -1, 691, -1, 2225, -1, 706, -1], 'generators': [37, 250], 'label': '256.18790.64.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057812
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bm1.b1', '32.dh1.a1', '32.dh1.b1'], 'contains': ['128.e1.a1', '128.g1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2221, -1, 605, -1, 2225, -1, 604, -1], 'generators': [253, 250], 'label': '256.18790.64.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057813
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bm1.c1', '32.dh1.a1', '32.dh1.b1'], 'contains': ['128.e1.b1', '128.g1.a1', '128.h1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2221, -1, 632, -1, 2225, -1, 655, -1], 'generators': [237, 250], 'label': '256.18790.64.bd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.bd1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057814
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bm1.d1', '32.dh1.a1', '32.dh1.b1'], 'contains': ['128.e1.b1', '128.g1.a1', '128.h1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2221, -1, 577, -1, 2225, -1, 576, -1], 'generators': [53, 250], 'label': '256.18790.64.bd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.be1.a1', 'old_label': '64.bd1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057834
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.x1.d1', '8.dk1.b1', '8.dm1.b1', '8.dp1.a1', '8.dr1.a1', '8.ds1.b1', '8.dw1.b1', '8.ei1.d1', '8.ei1.h1', '8.ej1.d1', '8.ej1.h1', '8.ek1.d1', '8.ek1.h1', '8.el1.d1', '8.el1.h1'], 'core': '8.x1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9270, -1, 1718, -1, 9292, -1, 1716, -1], 'generators': [5, 2, 32, 200], 'label': '256.18790.4.bx1.d1', '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.bx1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bx1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057815
    {'ambient': '256.18790', '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.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.h1.a1', '64.h1.b1', '64.i1.a1', '64.j1.a1', '64.k1.a1', '64.k1.b1', '64.l1.a1', '64.m1.a1', '64.m1.b1', '64.n1.a1', '64.o1.a1', '64.p1.a1', '64.p1.b1', '64.q1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3753, 4371, 4894, 4417, 3761, 4352, 4899, 4444], 'generators': [128], 'label': '256.18790.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1', '64.d1.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: 26057816
    {'ambient': '256.18790', '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.r1.a1', '64.s1.a1', '64.t1.a1', '64.u1.a1', '64.v1.a1', '64.w1.a1', '64.x1.a1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1995, 4264, 5798, 4627, 1998, 4245, 5960, 4655], 'generators': [16], 'label': '256.18790.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': 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: 26057817
    {'ambient': '256.18790', '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.r1.b1', '64.s1.b1', '64.t1.b1', '64.u1.b1', '64.v1.b1', '64.w1.b1', '64.x1.b1'], 'contains': ['256.a1.a1'], 'core': '128.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1995, 4264, 5847, 4527, 1998, 4245, 6009, 4555], 'generators': [144], 'label': '256.18790.128.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.b1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057818
    {'ambient': '256.18790', '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': '2.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.r1.a1', '64.r1.b1', '64.y1.a1', '64.z1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2035, -1, 8797, -1, 2039, -1, 8765, -1], 'generators': [24], 'label': '256.18790.128.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.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: 26057819
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.f1.a1'], 'contains': ['8.v1.b1', '8.cw1.a1', '8.cx1.a1', '8.df1.b1', '8.dg1.b1', '8.di1.b1', '8.dj1.b1'], 'core': '8.v1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6840, -1, 5124, -1, 6857, -1, 5121, -1], 'generators': [21, 6, 48], 'label': '256.18790.4.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057820
    {'ambient': '256.18790', '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': '2.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.r1.a1', '64.r1.b1', '64.ba1.a1', '64.ba1.b1', '64.bb1.a1', '64.bb1.a2', '64.bc1.a1', '64.bc1.b1', '64.bc1.c1', '64.bc1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1849, -1, 9228, -1, 1853, -1, 9215, -1], 'generators': [8], 'label': '256.18790.128.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.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: 26057821
    {'ambient': '256.18790', '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': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.s1.a1', '64.s1.b1', '64.bd1.a1', '64.bd1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2155, -1, 950, -1, 2160, -1, 949, -1], 'generators': [37], 'label': '256.18790.128.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bl1.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: 26057822
    {'ambient': '256.18790', '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': '4.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.s1.a1', '64.s1.b1', '64.bd1.c1', '64.bd1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2155, -1, 910, -1, 2160, -1, 908, -1], 'generators': [53], 'label': '256.18790.128.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bl1.a1', 'old_label': '128.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057823
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '128.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.bp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.t1.a1', '64.t1.b1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2195, -1, 5823, -1, 2200, -1, 5984, -1], 'generators': [2], 'label': '256.18790.128.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bp1.a1', 'old_label': '128.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057824
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '128.g1', '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': ['64.j1.a1', '64.u1.a1', '64.u1.b1', '64.bd1.a1', '64.bd1.b1', '64.bd1.c1', '64.bd1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2115, -1, 721, -1, 2119, -1, 766, -1], 'generators': [250], 'label': '256.18790.128.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bl1.a1', 'old_label': '128.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057825
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1.a1', '64.v1.a1', '64.v1.b1', '64.y1.a1', '64.ba1.a1', '64.bd1.a1', '64.bd1.c1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2075, -1, 1976, -1, 2079, -1, 1963, -1], 'generators': [7], 'label': '256.18790.128.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1.a1', 'old_label': '128.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057826
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.k1.b1', '64.v1.a1', '64.v1.b1', '64.y1.a1', '64.ba1.b1', '64.bd1.b1', '64.bd1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2075, -1, 1951, -1, 2079, -1, 1937, -1], 'generators': [223], 'label': '256.18790.128.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.z1.a1', 'old_label': '128.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057827
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.l1.a1', '64.w1.a1', '64.w1.b1', '64.z1.a1', '64.bb1.a1', '64.bb1.a2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1945, -1, 8842, -1, 1950, -1, 8831, -1], 'generators': [3], 'label': '256.18790.128.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.y1.a1', 'old_label': '128.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057828
    {'ambient': '256.18790', '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.b1.b1', '128.c1.a1', '128.d1.a1', '128.e1.a1', '128.e1.b1', '128.f1.a1', '128.g1.a1', '128.h1.a1', '128.h1.b1', '128.i1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2075, 4319, 5213, 4527, 2079, 4295, 5168, 4555], 'generators': [], 'label': '256.18790.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1', '128.b1.a1', '128.b1.b1'], '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: 26057829
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.f1.a1'], 'contains': ['8.v1.c1', '8.cw1.b1', '8.cx1.b1', '8.df1.a1', '8.dg1.b1', '8.di1.b1', '8.dj1.a1'], 'core': '8.v1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6840, -1, 5069, -1, 6857, -1, 5063, -1], 'generators': [21, 6, 32], 'label': '256.18790.4.bw1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.bw1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bw1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057830
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.f1.a1'], 'contains': ['8.v1.d1', '8.cw1.b1', '8.cx1.b1', '8.df1.b1', '8.dg1.a1', '8.di1.a1', '8.dj1.b1'], 'core': '8.v1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [6840, -1, 5239, -1, 6857, -1, 5232, -1], 'generators': [5, 6, 48], 'label': '256.18790.4.bw1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '4.bw1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bw1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057831
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.x1.a1', '8.dk1.a1', '8.dm1.a1', '8.dp1.a1', '8.dr1.a1', '8.ds1.a1', '8.dw1.a1', '8.ei1.a1', '8.ei1.e1', '8.ej1.a1', '8.ej1.e1', '8.ek1.a1', '8.ek1.e1', '8.el1.a1', '8.el1.e1'], 'core': '8.x1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9270, -1, 1828, -1, 9292, -1, 1826, -1], 'generators': [21, 2, 32, 200], 'label': '256.18790.4.bx1.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.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057832
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.x1.b1', '8.dk1.b1', '8.dm1.a1', '8.dp1.b1', '8.dr1.b1', '8.ds1.a1', '8.dw1.b1', '8.ei1.b1', '8.ei1.f1', '8.ej1.b1', '8.ej1.f1', '8.ek1.b1', '8.ek1.f1', '8.el1.b1', '8.el1.f1'], 'core': '8.x1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9270, -1, 2502, -1, 9292, -1, 2499, -1], 'generators': [21, 2, 48, 200], 'label': '256.18790.4.bx1.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.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057833
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.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': ['2.a1.a1'], 'contains': ['8.x1.c1', '8.dk1.a1', '8.dm1.b1', '8.dp1.b1', '8.dr1.b1', '8.ds1.b1', '8.dw1.a1', '8.ei1.c1', '8.ei1.g1', '8.ej1.c1', '8.ej1.g1', '8.ek1.c1', '8.ek1.g1', '8.el1.c1', '8.el1.g1'], 'core': '8.x1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9270, -1, 2541, -1, 9292, -1, 2539, -1], 'generators': [5, 2, 48, 200], 'label': '256.18790.4.bx1.c1', '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.bx1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bx1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057835
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': ['128.f1.a1', '128.i1.a1', '128.h1.a1', '128.h1.b1', '128.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.g1.a1', '4.ba1.a1', '4.bc1.a1', '4.be1.a1', '4.bi1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3810, 8608, 6967, 1957, 3820, 8721, 6957, 1969], 'generators': [1, 4, 32], 'label': '256.18790.2.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.ba1.a1', '4.bc1.a1', '4.be1.a1', '4.bi1.a1'], '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: 26057836
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.by1', '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.c1.a1'], 'contains': ['8.w1.a1', '8.dl1.a1', '8.dq1.a1', '8.dt1.a1', '8.du1.a1', '8.eg1.a1', '8.eh1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4648, -1, 8075, -1, 4659, -1, 8064, -1], 'generators': [33, 2, 4], 'label': '256.18790.4.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057837
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.by1', '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.c1.a1'], 'contains': ['8.w1.b1', '8.dl1.a1', '8.dq1.a1', '8.dt1.b1', '8.du1.b1', '8.eg1.b1', '8.eh1.b1'], 'core': '8.w1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4648, -1, 8439, -1, 4659, -1, 8428, -1], 'generators': [97, 2, 68], 'label': '256.18790.4.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057838
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.by1', '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.c1.a1'], 'contains': ['8.w1.c1', '8.dl1.b1', '8.dq1.b1', '8.dt1.a1', '8.du1.b1', '8.eg1.a1', '8.eh1.b1'], 'core': '8.w1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4648, -1, 8292, -1, 4659, -1, 8281, -1], 'generators': [97, 2, 4], 'label': '256.18790.4.by1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.by1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.by1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057839
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.by1', '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.c1.a1'], 'contains': ['8.w1.d1', '8.dl1.b1', '8.dq1.b1', '8.dt1.b1', '8.du1.a1', '8.eg1.b1', '8.eh1.a1'], 'core': '8.w1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4648, -1, 8222, -1, 4659, -1, 8211, -1], 'generators': [33, 2, 68], 'label': '256.18790.4.by1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.by1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.by1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057840
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bz1', '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.w1.a1', '8.dn1.a1', '8.do1.a1', '8.dv1.a1', '8.dx1.a1', '8.dz1.a1', '8.eb1.a1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2972, -1, 7929, -1, 2979, -1, 7919, -1], 'generators': [33, 34, 4], 'label': '256.18790.4.bz1.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.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057841
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bz1', '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.w1.b1', '8.dn1.a1', '8.do1.a1', '8.dv1.b1', '8.dx1.b1', '8.dz1.b1', '8.eb1.b1'], 'core': '8.w1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2972, -1, 8024, -1, 2979, -1, 8014, -1], 'generators': [97, 34, 68], 'label': '256.18790.4.bz1.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.bz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057842
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bz1', '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.w1.c1', '8.dn1.b1', '8.do1.b1', '8.dv1.b1', '8.dx1.a1', '8.dz1.a1', '8.eb1.b1'], 'core': '8.w1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2972, -1, 7992, -1, 2979, -1, 7982, -1], 'generators': [97, 34, 4], 'label': '256.18790.4.bz1.c1', '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.bz1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bz1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057843
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.bz1', '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.w1.d1', '8.dn1.b1', '8.do1.b1', '8.dv1.a1', '8.dx1.b1', '8.dz1.b1', '8.eb1.a1'], 'core': '8.w1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [2972, -1, 7961, -1, 2979, -1, 7951, -1], 'generators': [33, 34, 68], 'label': '256.18790.4.bz1.d1', '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.bz1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bz1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057844
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.ca1', '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': ['2.n1.a1'], 'contains': ['8.x1.a1', '8.dy1.a1', '8.ea1.a1', '8.ec1.a1', '8.ed1.a1', '8.ee1.a1', '8.ef1.a1'], 'core': '8.x1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 7402, -1, 2904, -1, 7393, -1], 'generators': [3, 4, 32], 'label': '256.18790.4.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '4.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057845
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.ca1', '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': ['2.n1.a1'], 'contains': ['8.x1.b1', '8.dy1.a1', '8.ea1.a1', '8.ec1.b1', '8.ed1.b1', '8.ee1.b1', '8.ef1.b1'], 'core': '8.x1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 7462, -1, 2904, -1, 7452, -1], 'generators': [3, 4, 48], 'label': '256.18790.4.ca1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '4.ca1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ca1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057846
    {'ambient': '256.18790', '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.h1.a1', '128.h1.b1', '128.e1.a1', '128.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.l1.a1', '4.n1.a1', '4.p1.a1', '4.y1.a1', '4.be1.a1', '4.bq1.a1', '4.br1.a1', '4.bt1.a1', '4.bu1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4947, 3061, 8707, 6993, 4960, 3070, 8696, 7036], 'generators': [1, 2, 32, 216], 'label': '256.18790.2.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.j1.a1', '4.l1.a1', '4.n1.a1', '4.p1.a1', '4.y1.a1', '4.be1.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: 26057847
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.ca1', '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': ['2.n1.a1'], 'contains': ['8.x1.c1', '8.dy1.b1', '8.ea1.b1', '8.ec1.a1', '8.ed1.b1', '8.ee1.a1', '8.ef1.b1'], 'core': '8.x1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 7599, -1, 2904, -1, 7595, -1], 'generators': [19, 4, 48], 'label': '256.18790.4.ca1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '4.ca1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ca1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057848
    {'ambient': '256.18790', 'aut_centralizer_order': None, 'aut_label': '4.ca1', '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': ['2.n1.a1'], 'contains': ['8.x1.d1', '8.dy1.b1', '8.ea1.b1', '8.ec1.b1', '8.ed1.a1', '8.ee1.b1', '8.ef1.a1'], 'core': '8.x1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 7342, -1, 2904, -1, 7333, -1], 'generators': [19, 4, 32], 'label': '256.18790.4.ca1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '4.ca1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.ca1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 26057849
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.i1.a1', '16.l1.a1', '16.l1.b1', '16.o1.a1', '16.o1.b1', '16.u1.a1', '16.bg1.a1', '16.ch1.a1', '16.da1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 5492, 4527, 1546, 4045, 5508, 4522, 1556], 'generators': [37, 216, 16, 64], 'label': '256.18790.8.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.a1.a1', '16.b1.a1', '16.i1.a1', '16.l1.b1', '16.l1.a1', '16.o1.b1', '16.o1.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: 26057850
    {'ambient': '256.18790', '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': '32.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.f1.a1', '16.v1.a1', '16.bj1.a1', '16.ci1.a1', '16.cj1.a1', '16.db1.a1', '16.dc1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6855, 4394, 6540, 6205, 6872, 4407, 6531, 6264], 'generators': [2, 216, 16, 64], 'label': '256.18790.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.i1.a1', '4.h1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.f1.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: 26057851
    {'ambient': '256.18790', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.w1.a1', '16.bm1.a1', '16.ck1.a1', '16.cl1.a1', '16.dd1.a1', '16.de1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3818, 3719, 3579, 6437, 3828, 3730, 3574, 6497], 'generators': [34, 216, 16, 64], 'label': '256.18790.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.e1.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: 26057852
    {'ambient': '256.18790', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.i1.a1', '4.s1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.p1.a1', '16.p1.b1', '16.x1.a1', '16.bp1.a1', '16.bq1.a1', '16.cm1.a1', '16.cn1.a1', '16.dg1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3188, 3947, 4637, 5759, 3195, 3958, 4630, 5815], 'generators': [7, 216, 16, 64], 'label': '256.18790.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.i1.a1', '4.s1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.a1.a1', '16.p1.b1', '16.p1.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: 26057853
    {'ambient': '256.18790', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.j1.a1', '4.n1.a1', '4.s1.a1', '4.x1.a1', '4.y1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.y1.a1', '16.bs1.a1', '16.bt1.a1', '16.co1.a1', '16.cp1.a1', '16.dh1.a1', '16.di1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2772, 6600, 8795, 5054, 2779, 6620, 8783, 5085], 'generators': [3, 216, 16, 64], 'label': '256.18790.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.j1.a1', '4.s1.a1', '4.n1.a1', '4.x1.a1', '4.y1.a1', '4.z1.a1'], 'normal_contains': ['16.a1.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: 26057854
    {'ambient': '256.18790', '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': '4.bc1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.k1.a1', '4.o1.a1', '4.s1.a1', '4.ba1.a1', '4.bb1.a1', '4.bc1.a1'], 'contains': ['16.a1.a1', '16.s1.a1', '16.s1.b1', '16.z1.a1', '16.dj1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2380, 7108, 9539, 3753, 2386, 7129, 9526, 3776], 'generators': [4, 16, 64], 'label': '256.18790.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.d1.a1', '4.k1.a1', '4.s1.a1', '4.o1.a1', '4.ba1.a1', '4.bb1.a1', '4.bc1.a1'], 'normal_contains': ['16.a1.a1', '16.s1.b1', '16.s1.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: 26057855
    {'ambient': '256.18790', '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': '16.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.p1.a1', '4.t1.a1', '4.ba1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.j1.b1', '16.ba1.a1', '16.bu1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [897, 4634, 8661, 4513, 899, 4648, 8650, 4541], 'generators': [1, 216, 64], 'label': '256.18790.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.e1.a1', '4.j1.a1', '4.t1.a1', '4.p1.a1', '4.ba1.a1', '4.bd1.a1', '4.be1.a1'], 'normal_contains': ['16.a1.a1', '16.j1.a1', '16.j1.b1'], '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: 26057856
    {'ambient': '256.18790', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.q1.a1', '4.u1.a1', '4.x1.a1', '4.bb1.a1', '4.bd1.a1', '4.bf1.a1'], 'contains': ['16.a1.a1', '16.q1.a1', '16.q1.b1', '16.bb1.a1', '16.bv1.a1', '16.bz1.a1', '16.cq1.a1', '16.cu1.a1', '16.dn1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5321, 4167, 5786, 5978, 5333, 4179, 5778, 6036], 'generators': [39, 216, 16, 64], 'label': '256.18790.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.a1.a1', '4.u1.a1', '4.q1.a1', '4.x1.a1', '4.bb1.a1', '4.bd1.a1', '4.bf1.a1'], 'normal_contains': ['16.a1.a1', '16.q1.a1', '16.q1.b1'], '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}