Abstract group data - 40320.a

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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': '2.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 840, 'aut_gen_orders': [8, 2], 'aut_gens': [[5913, 5040], [24151, 3752], [6201, 5040]], 'aut_group': '40320.a', 'aut_hash': 6644662513446815922, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 40320, 'aut_permdeg': 28, 'aut_perms': [277321134931820842725130040744, 186848318957116539924564770], 'aut_phi_ratio': 4.375, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 28, 1, 1], [2, 105, 1, 1], [2, 210, 1, 1], [2, 420, 1, 1], [3, 112, 1, 1], [3, 1120, 1, 1], [4, 420, 1, 1], [4, 1260, 1, 2], [4, 2520, 1, 1], [5, 1344, 1, 1], [6, 1120, 1, 2], [6, 1680, 1, 1], [6, 3360, 1, 2], [7, 5760, 1, 1], [8, 5040, 1, 1], [10, 4032, 1, 1], [12, 3360, 1, 1], [15, 2688, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_8', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 840, 'autcentquo_group': '40320.a', 'autcentquo_hash': 6644662513446815922, 'autcentquo_nilpotent': False, 'autcentquo_order': 40320, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_8', 'cc_stats': [[1, 1, 1], [2, 28, 1], [2, 105, 1], [2, 210, 1], [2, 420, 1], [3, 112, 1], [3, 1120, 1], [4, 420, 1], [4, 1260, 2], [4, 2520, 1], [5, 1344, 1], [6, 1120, 2], [6, 1680, 1], [6, 3360, 2], [7, 5760, 1], [8, 5040, 1], [10, 4032, 1], [12, 3360, 1], [15, 2688, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '40320.a', 'commutator_count': 1, 'commutator_label': '20160.a', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '20160.a'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 28, 1, 1], [2, 105, 1, 1], [2, 210, 1, 1], [2, 420, 1, 1], [3, 112, 1, 1], [3, 1120, 1, 1], [4, 420, 1, 1], [4, 1260, 1, 2], [4, 2520, 1, 1], [5, 1344, 1, 1], [6, 1120, 1, 2], [6, 1680, 1, 1], [6, 3360, 1, 2], [7, 5760, 1, 1], [8, 5040, 1, 1], [10, 4032, 1, 1], [12, 3360, 1, 1], [15, 2688, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 24666, 'exponent': 840, 'exponents_of_order': [7, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[7, 1, 2], [14, 1, 2], [20, 1, 2], [21, 1, 2], [28, 1, 2], [35, 1, 2], [42, 1, 1], [56, 1, 2], [64, 1, 2], [70, 1, 2], [90, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '40320.a', 'hash': 6644662513446815922, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 840, 'inner_gen_orders': [8, 2], 'inner_gens': [[5913, 720], [10233, 5040]], 'inner_hash': 6644662513446815922, 'inner_nilpotent': False, 'inner_order': 40320, 'inner_split': True, 'inner_tex': 'S_8', 'inner_used': [1, 2], 'irrC_degree': 7, 'irrQ_degree': 7, 'irrQ_dim': 7, 'irrR_degree': 7, 'irrep_stats': [[1, 2], [7, 2], [14, 2], [20, 2], [21, 2], [28, 2], [35, 2], [42, 1], [56, 2], [64, 2], [70, 2], [90, 1]], 'label': '40320.a', 'linC_count': 2, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 2, 'linQ_dim': 7, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S8', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 22, 'number_divisions': 22, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 296, 'number_subgroup_classes': 296, 'number_subgroups': 151221, 'old_label': None, 'order': 40320, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 763], [3, 1232], [4, 5460], [5, 1344], [6, 10640], [7, 5760], [8, 5040], [10, 4032], [12, 3360], [15, 2688]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 8, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [7, 2], [14, 2], [20, 2], [21, 2], [28, 2], [35, 2], [42, 1], [56, 2], [64, 2], [70, 2], [90, 1]], 'representations': {'Lie': [{'d': 6, 'q': 2, 'gens': [34630353537, 1344290976, 17197729794], 'family': 'SOPlus'}, {'d': 6, 'q': 2, 'family': 'GOPlus'}, {'d': 6, 'q': 2, 'family': 'PSOPlus'}, {'d': 6, 'q': 2, 'family': 'PGOPlus'}, {'d': 6, 'q': 2, 'family': 'CSOPlus'}, {'d': 6, 'q': 2, 'family': 'COPlus'}], 'Perm': {'d': 8, 'gens': [5913, 5040]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_8', 'transitive_degree': 8, '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: 110126399
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 40320, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 110126410
    {'aut_label': '2A', 'centralizer': '28.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 40320, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 1, 'size': 28}
  • id: 110126414
    {'aut_label': '2B', 'centralizer': '105.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 40320, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 27882, 'size': 105}
  • id: 110126415
    {'aut_label': '2C', 'centralizer': '210.b1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 40320, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 741, 'size': 210}
  • id: 110126416
    {'aut_label': '2D', 'centralizer': '420.c1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 40320, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 1934, 'size': 420}
  • id: 110126417
    {'aut_label': '3A', 'centralizer': '112.b1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 40320, 'label': '3A', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 240, 'size': 112}
  • id: 110126418
    {'aut_label': '3B', 'centralizer': '1120.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 40320, 'label': '3B', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 35481, 'size': 1120}
  • id: 110126419
    {'aut_label': '4A', 'centralizer': '420.d1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 40320, 'label': '4A', 'order': 4, 'powers': [4, 8, 8, 8], 'representative': 2817, 'size': 420}
  • id: 110126420
    {'aut_label': '4B', 'centralizer': '1260.i1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 40320, 'label': '4B', 'order': 4, 'powers': [3, 9, 9, 9], 'representative': 38314, 'size': 1260}
  • id: 110126400
    {'aut_label': '4C', 'centralizer': '1260.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 40320, 'label': '4C', 'order': 4, 'powers': [4, 10, 10, 10], 'representative': 5247, 'size': 1260}
  • id: 110126401
    {'aut_label': '4D', 'centralizer': '2520.c1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 40320, 'label': '4D', 'order': 4, 'powers': [4, 11, 11, 11], 'representative': 28104, 'size': 2520}
  • id: 110126402
    {'aut_label': '5A', 'centralizer': '1344.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 40320, 'label': '5A', 'order': 5, 'powers': [12, 12, 1, 12], 'representative': 1599, 'size': 1344}
  • id: 110126403
    {'aut_label': '6A', 'centralizer': '1120.d1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 40320, 'label': '6A', 'order': 6, 'powers': [6, 2, 13, 13], 'representative': 145, 'size': 1120}
  • id: 110126404
    {'aut_label': '6B', 'centralizer': '1120.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 40320, 'label': '6B', 'order': 6, 'powers': [7, 2, 14, 14], 'representative': 5248, 'size': 1120}
  • id: 110126405
    {'aut_label': '6C', 'centralizer': '1680.e1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 40320, 'label': '6C', 'order': 6, 'powers': [6, 4, 15, 15], 'representative': 31822, 'size': 1680}
  • id: 110126406
    {'aut_label': '6D', 'centralizer': '3360.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 40320, 'label': '6D', 'order': 6, 'powers': [7, 3, 16, 16], 'representative': 17856, 'size': 3360}
  • id: 110126407
    {'aut_label': '6E', 'centralizer': '3360.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 40320, 'label': '6E', 'order': 6, 'powers': [7, 5, 17, 17], 'representative': 3984, 'size': 3360}
  • id: 110126408
    {'aut_label': '7A', 'centralizer': '5760.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 40320, 'label': '7A', 'order': 7, 'powers': [18, 18, 18, 1], 'representative': 24495, 'size': 5760}
  • id: 110126409
    {'aut_label': '8A', 'centralizer': '5040.q1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 40320, 'label': '8A', 'order': 8, 'powers': [9, 19, 19, 19], 'representative': 9476, 'size': 5040}
  • id: 110126411
    {'aut_label': '10A', 'centralizer': '4032.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 40320, 'label': '10A', 'order': 10, 'powers': [12, 20, 2, 20], 'representative': 4100, 'size': 4032}
  • id: 110126412
    {'aut_label': '12A', 'centralizer': '3360.m1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 40320, 'label': '12A', 'order': 12, 'powers': [15, 8, 21, 21], 'representative': 19906, 'size': 3360}
  • id: 110126413
    {'aut_label': '15A', 'centralizer': '2688.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 40320, 'label': '15A', 'order': 15, 'powers': [22, 12, 6, 22], 'representative': 12690, 'size': 2688}
• 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: 4527408
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.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], 'schur_index': 1}
  • id: 4527419
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.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], 'schur_index': 1}
  • id: 4527423
    {'cdim': 7, 'counter': 3, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.7a', 'multiplicity': 1, 'nt': [8, 50], 'qdim': 7, 'qvalues': [7, 5, -1, 3, 1, 4, 1, 3, -1, -1, 1, 2, 2, -1, 0, -1, 1, 0, -1, 0, 0, -1], 'schur_index': 1}
  • id: 4527424
    {'cdim': 7, 'counter': 4, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.7b', 'multiplicity': 1, 'nt': [16, 1838], 'qdim': 7, 'qvalues': [7, -5, -1, 3, -1, 4, 1, -3, -1, 1, 1, 2, -2, 1, 0, -1, -1, 0, 1, 0, 0, -1], 'schur_index': 1}
  • id: 4527425
    {'cdim': 14, 'counter': 5, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.14a', 'multiplicity': 1, 'nt': [30, 1153], 'qdim': 14, 'qvalues': [14, -4, 6, 2, 0, -1, 2, 2, 2, -2, 0, -1, -1, 2, -1, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
  • id: 4527426
    {'cdim': 14, 'counter': 6, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.14b', 'multiplicity': 1, 'nt': [30, 1153], 'qdim': 14, 'qvalues': [14, 4, 6, 2, 0, -1, 2, -2, 2, 2, 0, -1, 1, -2, -1, 0, 0, 0, 0, -1, 1, -1], 'schur_index': 1}
  • id: 4527427
    {'cdim': 20, 'counter': 7, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.20a', 'multiplicity': 1, 'nt': [28, 502], 'qdim': 20, 'qvalues': [20, 10, 4, 4, 2, 5, -1, 2, 0, 2, 0, 0, 1, 1, 1, 1, -1, -1, 0, 0, -1, 0], 'schur_index': 1}
  • id: 4527428
    {'cdim': 20, 'counter': 8, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.20b', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 20, 'qvalues': [20, -10, 4, 4, -2, 5, -1, -2, 0, -2, 0, 0, -1, -1, 1, 1, 1, -1, 0, 0, 1, 0], 'schur_index': 1}
  • id: 4527429
    {'cdim': 21, 'counter': 9, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.21a', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, -9, -3, 1, 3, 6, 0, -3, 1, 1, -1, 1, 0, 0, -2, 0, 0, 0, -1, 1, 0, 1], 'schur_index': 1}
  • id: 4527409
    {'cdim': 21, 'counter': 10, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.21b', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, 9, -3, 1, -3, 6, 0, 3, 1, -1, -1, 1, 0, 0, -2, 0, 0, 0, 1, -1, 0, 1], 'schur_index': 1}
  • id: 4527410
    {'cdim': 28, 'counter': 11, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.28a', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 28, 'qvalues': [28, 10, -4, 4, 2, 1, 1, -2, 0, -2, 0, -2, 1, 1, 1, -1, -1, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4527411
    {'cdim': 28, 'counter': 12, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.28b', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 28, 'qvalues': [28, -10, -4, 4, -2, 1, 1, 2, 0, 2, 0, -2, -1, -1, 1, -1, 1, 0, 0, 0, -1, 1], 'schur_index': 1}
  • id: 4527412
    {'cdim': 35, 'counter': 13, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.35a', 'multiplicity': 1, 'nt': [112, 0], 'qdim': 35, 'qvalues': [35, -5, 3, -5, 3, 5, 2, -1, -1, -1, -1, 0, 1, -2, 1, 0, 0, 0, 1, 0, -1, 0], 'schur_index': 1}
  • id: 4527413
    {'cdim': 35, 'counter': 14, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.35b', 'multiplicity': 1, 'nt': [112, 0], 'qdim': 35, 'qvalues': [35, 5, 3, -5, -3, 5, 2, 1, -1, 1, -1, 0, -1, 2, 1, 0, 0, 0, -1, 0, 1, 0], 'schur_index': 1}
  • id: 4527414
    {'cdim': 42, 'counter': 15, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.42a', 'multiplicity': 1, 'nt': [336, 0], 'qdim': 42, 'qvalues': [42, 0, -6, 2, 0, -6, 0, 0, 2, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1], 'schur_index': 1}
  • id: 4527415
    {'cdim': 56, 'counter': 16, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.56a', 'multiplicity': 1, 'nt': [105, 0], 'qdim': 56, 'qvalues': [56, 4, 8, 0, 4, -4, -1, 0, 0, 0, 0, 1, -2, 1, 0, -1, 1, 0, 0, -1, 0, 1], 'schur_index': 1}
  • id: 4527416
    {'cdim': 56, 'counter': 17, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.56b', 'multiplicity': 1, 'nt': [210, 0], 'qdim': 56, 'qvalues': [56, -4, 8, 0, -4, -4, -1, 0, 0, 0, 0, 1, 2, -1, 0, -1, -1, 0, 0, 1, 0, 1], 'schur_index': 1}
  • id: 4527417
    {'cdim': 64, 'counter': 18, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.64a', 'multiplicity': 1, 'nt': [168, 0], 'qdim': 64, 'qvalues': [64, 16, 0, 0, 0, 4, -2, 0, 0, 0, 0, -1, -2, -2, 0, 0, 0, 1, 0, 1, 0, -1], 'schur_index': 1}
  • id: 4527418
    {'cdim': 64, 'counter': 19, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.64b', 'multiplicity': 1, 'nt': [336, 0], 'qdim': 64, 'qvalues': [64, -16, 0, 0, 0, 4, -2, 0, 0, 0, 0, -1, 2, 2, 0, 0, 0, 1, 0, -1, 0, -1], 'schur_index': 1}
  • id: 4527420
    {'cdim': 70, 'counter': 20, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.70a', 'multiplicity': 1, 'nt': [168, 0], 'qdim': 70, 'qvalues': [70, -10, -2, 2, 2, -5, 1, 4, -2, 0, 0, 0, -1, -1, -1, 1, -1, 0, 0, 0, 1, 0], 'schur_index': 1}
  • id: 4527421
    {'cdim': 70, 'counter': 21, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.70b', 'multiplicity': 1, 'nt': [210, 0], 'qdim': 70, 'qvalues': [70, 10, -2, 2, -2, -5, 1, -4, -2, 0, 0, 0, 1, 1, -1, 1, 1, 0, 0, 0, -1, 0], 'schur_index': 1}
  • id: 4527422
    {'cdim': 90, 'counter': 22, 'faithful': True, 'group': '40320.a', 'group_order': 40320, 'image': None, 'label': '40320.a.90a', 'multiplicity': 1, 'nt': [336, 0], 'qdim': 90, 'qvalues': [90, 0, -6, -6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -1, 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: 7033858
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 40320, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 40320, 'label': '40320.a.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]]]}
  • id: 7033869
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 40320, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 20160, 'label': '40320.a.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]]]}
  • id: 7033873
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 1, 'dim': 7, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.7a', 'nt': [8, 50], 'q_character': None, 'values': [[[7, 0]], [[5, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7033874
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 1, 'dim': 7, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.7b', 'nt': [16, 1838], 'q_character': None, 'values': [[[7, 0]], [[-5, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[4, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7033875
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.14a', 'nt': [30, 1153], 'q_character': None, 'values': [[[14, 0]], [[-4, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7033876
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.14b', 'nt': [30, 1153], 'q_character': None, 'values': [[[14, 0]], [[4, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 7033877
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.20a', 'nt': [28, 502], 'q_character': None, 'values': [[[20, 0]], [[10, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[5, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 7033878
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.20b', 'nt': [56, 0], 'q_character': None, 'values': [[[20, 0]], [[-10, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[5, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 7033879
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 1, 'dim': 21, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.21a', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[-9, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 7033859
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 1, 'dim': 21, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.21b', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[9, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 7033860
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 1, 'dim': 28, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.28a', 'nt': [56, 0], 'q_character': None, 'values': [[[28, 0]], [[10, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7033861
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 1, 'dim': 28, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.28b', 'nt': [70, 0], 'q_character': None, 'values': [[[28, 0]], [[-10, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 7033862
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 1, 'dim': 35, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.35a', 'nt': [112, 0], 'q_character': None, 'values': [[[35, 0]], [[-5, 0]], [[3, 0]], [[-5, 0]], [[3, 0]], [[5, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 7033863
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 1, 'dim': 35, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.35b', 'nt': [112, 0], 'q_character': None, 'values': [[[35, 0]], [[5, 0]], [[3, 0]], [[-5, 0]], [[-3, 0]], [[5, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 7033864
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 1, 'dim': 42, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.42a', 'nt': [336, 0], 'q_character': None, 'values': [[[42, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7033865
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 1, 'dim': 56, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.56a', 'nt': [105, 0], 'q_character': None, 'values': [[[56, 0]], [[4, 0]], [[8, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 7033866
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 1, 'dim': 56, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.56b', 'nt': [210, 0], 'q_character': None, 'values': [[[56, 0]], [[-4, 0]], [[8, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 7033867
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 64, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.64a', 'nt': [168, 0], 'q_character': None, 'values': [[[64, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7033868
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 1, 'dim': 64, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.64b', 'nt': [336, 0], 'q_character': None, 'values': [[[64, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 7033870
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 1, 'dim': 70, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.70a', 'nt': [168, 0], 'q_character': None, 'values': [[[70, 0]], [[-10, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-5, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 7033871
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 1, 'dim': 70, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.70b', 'nt': [210, 0], 'q_character': None, 'values': [[[70, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-5, 0]], [[1, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 7033872
    {'center': '40320.a1.a1', 'center_index': 40320, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 1, 'dim': 90, 'faithful': True, 'field': [0, 1], 'group': '40320.a', 'group_counter': 1, 'group_order': 40320, 'image': None, 'image_isoclass': '40320.a', 'image_order': 40320, 'indicator': 1, 'kernel': '40320.a1.a1', 'kernel_order': 1, 'label': '40320.a.90a', 'nt': [336, 0], 'q_character': None, 'values': [[[90, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 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: 66394025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 40320, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 210, 'label': '40320.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40320.a', 'subgroup_hash': 6644662513446815922, 'subgroup_order': 40320, 'subgroup_tex': 'S_8', 'supersolvable': False, 'sylow': 0}
  • id: 66394136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 20160, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '40320.a.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L1', 'D1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20160.a', 'subgroup_hash': 3764836782182912467, 'subgroup_order': 20160, 'subgroup_tex': 'A_8', 'supersolvable': False, 'sylow': 0}
  • id: 66394244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.8.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5040.w', 'subgroup_hash': 6283920599749723413, 'subgroup_order': 5040, 'subgroup_tex': 'S_7', 'supersolvable': False, 'sylow': 0}
  • id: 66394255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2520.a', 'subgroup_hash': 1290983011404564636, 'subgroup_order': 2520, 'subgroup_tex': 'A_7', 'supersolvable': False, 'sylow': 0}
  • id: 66394266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.28.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
  • id: 66394277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1344.11686', 'subgroup_hash': 11686, 'subgroup_order': 1344, 'subgroup_tex': 'C_2^3:\\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66394288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '40320.a.35.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '35.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 35, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157849', 'subgroup_hash': 5496387407741636925, 'subgroup_order': 1152, 'subgroup_tex': 'S_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 66394299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.766', 'subgroup_hash': 766, 'subgroup_order': 720, 'subgroup_tex': 'C_2\\times A_6', 'supersolvable': False, 'sylow': 0}
  • id: 66394310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.56.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.767', 'subgroup_hash': 767, 'subgroup_order': 720, 'subgroup_tex': 'S_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
  • id: 66394037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
  • id: 66394048
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.70.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8653', 'subgroup_hash': 8653, 'subgroup_order': 576, 'subgroup_tex': 'S_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 66394059
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.70.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8652', 'subgroup_hash': 8652, 'subgroup_order': 576, 'subgroup_tex': 'A_4^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.70.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.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': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8654', 'subgroup_hash': 8654, 'subgroup_order': 576, 'subgroup_tex': '\\POPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66394081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.105.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '105.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 105, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5602', 'subgroup_hash': 5602, 'subgroup_order': 384, 'subgroup_tex': 'C_2\\wr S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.121', 'subgroup_hash': 121, 'subgroup_order': 360, 'subgroup_tex': 'S_3\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.119', 'subgroup_hash': 119, 'subgroup_order': 360, 'subgroup_tex': 'C_3\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.120', 'subgroup_hash': 120, 'subgroup_order': 360, 'subgroup_tex': 'C_3:S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.d1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.118', 'subgroup_hash': 118, 'subgroup_order': 360, 'subgroup_tex': 'A_6', 'supersolvable': False, 'sylow': 0}
  • id: 66394137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.120.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.208', 'subgroup_hash': 208, 'subgroup_order': 336, 'subgroup_tex': '\\PGL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 66394148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.140.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1024', 'subgroup_hash': 1024, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.140.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1026', 'subgroup_hash': 1026, 'subgroup_order': 288, 'subgroup_tex': '\\PSOPlus(4,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66394170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.140.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.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': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1025', 'subgroup_hash': 1025, 'subgroup_order': 288, 'subgroup_tex': 'A_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 66394181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.201', 'subgroup_hash': 201, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.210.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1472', 'subgroup_hash': 1472, 'subgroup_order': 192, 'subgroup_tex': 'D_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.210.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.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': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1494', 'subgroup_hash': 1494, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.210.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.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': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.955', 'subgroup_hash': 955, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.210.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.d2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1493', 'subgroup_hash': 1493, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.19', 'subgroup_hash': 19, 'subgroup_order': 180, 'subgroup_tex': '\\GL(2,4)', 'supersolvable': False, 'sylow': 0}
  • id: 66394247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.43', 'subgroup_hash': 43, 'subgroup_order': 168, 'subgroup_tex': 'F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 66394248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.42', 'subgroup_hash': 42, 'subgroup_order': 168, 'subgroup_tex': '\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 66394249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.42', 'subgroup_hash': 42, 'subgroup_order': 168, 'subgroup_tex': '\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 66394250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.280.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 66394251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.280.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.280.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.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': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.184', 'subgroup_hash': 184, 'subgroup_order': 144, 'subgroup_tex': 'A_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 66394253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '40320.a.315.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '315.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 315, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.928', 'subgroup_hash': 928, 'subgroup_order': 128, 'subgroup_tex': 'C_2\\wr D_4', 'supersolvable': True, 'sylow': 2}
  • id: 66394254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 66394263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.187', 'subgroup_hash': 187, 'subgroup_order': 96, 'subgroup_tex': 'C_4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.195', 'subgroup_hash': 195, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
  • id: 66394271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.70', 'subgroup_hash': 70, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.j2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.j2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.204', 'subgroup_hash': 204, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.420.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.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': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66394280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66394282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66394284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66394285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.560.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.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': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.226', 'subgroup_hash': 226, 'subgroup_order': 64, 'subgroup_tex': 'D_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.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': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.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': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.34', 'subgroup_hash': 34, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.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': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.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': 630, 'quotient_simple': 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: 66394293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.630.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.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': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394295
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394296
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.d1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.e1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 66394300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
  • id: 66394301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66394314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.840.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.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': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394028
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
  • id: 66394029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1008.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.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': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66394043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, '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: 66394045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394055
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394058
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.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': 1260, 'quotient_simple': None, '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: 66394061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1260.p2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.p2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, '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: 66394062
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394063
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1344.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1344.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394064
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1344.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1344.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': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 66394065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 66394078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394086
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66394088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.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': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1680.x2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.x2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394093
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.1920.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1920.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1920, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2016.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66394095
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2016.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394096
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2016.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.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': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.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': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.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': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.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': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2240.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': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': None, '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: 66394106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': None, '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: 66394107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.y2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.y2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': None, '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: 66394133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394139
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2520.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.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': 2520, 'quotient_simple': None, '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: 66394140
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.2688.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2688.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2688, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 66394141
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.2880.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 66394142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394146
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.3360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66394156
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66394157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394158
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.r2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.r2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 66394163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.3360.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.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': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394164
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.4032.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4032.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4032, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 66394165
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.4032.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4032.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4032, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394166
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.4032.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4032.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': 4032, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 66394167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '40320.a.4480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 66394168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': None, '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: 66394169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': None, '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: 66394171
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.d2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': None, '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: 66394174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394187
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.5040.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394194
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394196
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394198
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.bd2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.bd2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': None, '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: 66394204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.5040.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.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': 5040, 'quotient_simple': None, '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: 66394205
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '40320.a.5760.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5760.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5760, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 66394206
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.6720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394207
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.6720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394208
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394209
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.6720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394210
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394211
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.6720.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394212
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394213
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394215
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.6720.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66394216
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394217
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.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': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394218
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.6720.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6720.k2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394219
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '40320.a.8064.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8064.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8064, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 66394220
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, 'quotient_simple': 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: 66394221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, 'quotient_simple': 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: 66394222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394226
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.10080.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.i2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, 'quotient_simple': 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: 66394231
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.10080.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394232
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.10080.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394233
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.10080.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.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': 10080, 'quotient_simple': 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: 66394235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '40320.a.10080.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.m2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, 'quotient_simple': 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: 66394237
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.13440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13440.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13440, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394238
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.13440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13440.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13440, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66394239
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 1440, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.20160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20160, '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: 66394240
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.20160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20160, '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: 66394241
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.20160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20160.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': 20160, '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: 66394242
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '40320.a.20160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20160.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': 20160, '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: 66394243
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '40320.a', 'ambient_counter': 1, 'ambient_order': 40320, 'ambient_tex': 'S_8', 'central': True, 'central_factor': False, 'centralizer_order': 40320, 'characteristic': True, 'core_order': 1, 'counter': 296, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '40320.a.40320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40320.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '40320.a', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6644662513446815922, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40320, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_8', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C2'], '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: 66394038
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '280.c1.a1', '560.c1.a1', '560.e1.a1', '560.j1.a1'], 'contains': ['3360.p1.a1', '3360.q1.a1', '3360.r2.a1', '4480.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3022, -1, 7645, -1, 8117, -1, 2215, -1], 'generators': [8070, 27630, 15, 18246], 'label': '40320.a.1120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '1120.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394039
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.a1.a1', '560.f1.a1', '560.i1.a1'], 'contains': ['2240.e1.a1', '2240.f1.a1', '3360.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [7655, -1, 2312, -1, 6742, -1, 3088, -1], 'generators': [316, 639, 233, 237], 'label': '40320.a.1120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394040
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.b1.a1', '560.b1.a1', '560.d1.a1', '560.i1.a1'], 'contains': ['2240.e1.a1', '10080.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3841, -1, 5915, -1, 5857, -1, 4181, -1], 'generators': [39062, 34023, 39183, 25769], 'label': '40320.a.1120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394041
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '560.b1.a1', '560.f1.a1', '560.h1.a1'], 'contains': ['2240.e1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4202, -1, 6046, -1, 5977, -1, 3722, -1], 'generators': [3753, 26046, 35508, 29821], 'label': '40320.a.1120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394042
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '560.g1.a1', '560.h1.a1', '560.i1.a1'], 'contains': ['2240.d1.a1', '2240.e1.a1', '3360.s1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [2413, -1, 8279, -1, 8744, -1, 1500, -1], 'generators': [21045, 3766, 141, 3032], 'label': '40320.a.1120.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394043
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.d1.a1', '630.b1.a1'], 'contains': ['2520.c1.a1', '2520.d1.a1', '2520.f1.a1', '2520.n1.a1', '2520.o1.a1', '2520.u1.a1', '2520.v1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4421, -1, 5128, -1, 2129, -1, 7930, -1], 'generators': [4527, 3109, 21410, 11102, 54], 'label': '40320.a.1260.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '1260.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394044
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.a1.a1', '630.b1.a1'], 'contains': ['2520.d1.a1', '2520.e1.a1', '2520.g1.a1', '2520.l1.a1', '2520.m1.a1', '2520.t1.a1', '2520.v1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6181, -1, 3996, -1, 2282, -1, 7533, -1], 'generators': [31400, 4527, 3109, 21410, 11102], 'label': '40320.a.1260.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '1260.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66394045
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.b1.a1'], 'contains': ['2520.c1.a1', '2520.e1.a1', '2520.h1.a1', '2520.l1.a1', '2520.n1.a1', '2520.x1.a1', '2520.z1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5575, -1, 4953, -1, 2424, -1, 7391, -1], 'generators': [4527, 21410, 11102, 54, 34430], 'label': '40320.a.1260.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '1260.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66394046
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.b1.a1', '420.e1.a1', '630.b1.a1'], 'contains': ['2520.f1.a1', '2520.g1.a1', '2520.h1.a1', '2520.t1.a1', '2520.u1.a1', '2520.x1.a1', '2520.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [5754, -1, 4558, -1, 2912, -1, 7146, -1], 'generators': [4527, 3109, 31376, 54, 10814], 'label': '40320.a.1260.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '1260.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 66394047
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.c1.a1', '420.f1.a1', '630.b1.a1'], 'contains': ['2520.a1.a1', '2520.b1.a1', '2520.c1.a1', '2520.e1.a1', '2520.f1.a1', '2520.g1.a1', '2520.i1.a1', '2520.j1.a1', '2520.k1.a1', '2520.q1.a1', '2520.w1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4826, -1, 5570, -1, 3601, -1, 6399, -1], 'generators': [36875, 722, 14435, 36873, 24], 'label': '40320.a.1260.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '1260.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394048
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '70.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1.a1'], 'contains': ['140.a1.a1', '140.b1.a1', '210.b1.a1', '280.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [2418, -1, 7918, -1, 6658, -1, 3549, -1], 'generators': [10814, 4527, 31376, 3109, 21048, 31106, 103, 54], 'label': '40320.a.70.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394049
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.a1.a1', '630.b1.a1', '630.c1.a1'], 'contains': ['2520.d1.a1', '2520.h1.a1', '2520.k1.a1', '2520.r1.a1', '2520.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6008, -1, 4137, -1, 1805, -1, 8254, -1], 'generators': [4527, 60, 54, 6479, 10814], 'label': '40320.a.1260.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394050
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.g1.a1', '630.b1.a1'], 'contains': ['2520.l1.a1', '2520.n1.a1', '2520.q1.a1', '2520.r1.a1', '2520.t1.a1', '2520.u1.a1', '2520.w1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5019, -1, 4675, -1, 2535, -1, 7280, -1], 'generators': [31400, 4527, 21048, 3109, 21410], 'label': '40320.a.1260.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '1260.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66394052
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.f1.a1'], 'contains': ['2520.o1.a1', '2520.p1.a1', '2520.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9056, -1, 999, -1, 328, -1, 9730, -1], 'generators': [34348, 4527, 3011, 7812, 10814], 'label': '40320.a.1260.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '1260.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394051
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.f1.a1'], 'contains': ['2520.m1.a1', '2520.p1.a1', '2520.s1.a1', '2520.y1.a1', '2520.bb1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9721, -1, 396, -1, 197, -1, 9861, -1], 'generators': [34348, 31400, 4527, 7812, 10814], 'label': '40320.a.1260.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '1260.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394037
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '28.a1.a1'], 'contains': ['112.d1.a1', '336.e1.a1', '336.g1.a1', '560.h1.a1', '840.p1.a1', '840.q1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4906, -1, 5405, -1, 5658, -1, 4441, -1], 'generators': [122, 35425], 'label': '40320.a.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 66394025
    {'ambient': '40320.a', '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': '40320.a1.a1', 'complements': ['40320.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '8.a1.a1', '28.a1.a1', '35.a1.a1', '56.b1.a1', '105.a1.a1', '120.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7191, 5000, 3339, 5000, 5658, 5000, 4441, 5000], 'generators': [5040, 33241], 'label': '40320.a.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '40320.a', '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': '40320.a'}
  • id: 66394026
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1'], 'contains': ['112.d1.a1', '336.d1.a1', '336.f1.a1', '560.f1.a1', '840.f1.a1', '840.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4738, -1, 6991, -1, 6778, -1, 3446, -1], 'generators': [115, 289], 'label': '40320.a.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 66394027
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.d1.a1', '210.d2.a1'], 'contains': ['1680.n1.a1', '1680.p1.a1', '1680.q1.a1', '2520.bc1.a1', '3360.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9196, -1, 837, -1, 1488, -1, 8609, -1], 'generators': [36654, 21769, 32924, 19342, 33046], 'label': '40320.a.840.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.t1.a1', 'old_label': '840.t1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394028
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '120.a1.a1'], 'contains': ['1920.a1.a1', '2880.a1.a1', '6720.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 960, 'diagramx': [8961, -1, 643, -1, 4478, -1, 5341, -1], 'generators': [4746, 2569, 4811], 'label': '40320.a.960.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '960.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 66394029
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1008.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.a1.a1', '168.b1.a1', '336.c1.a1'], 'contains': ['2016.a1.a1', '2016.b1.a1', '2016.c1.a1', '5040.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [2434, -1, 6833, -1, 7875, -1, 1993, -1], 'generators': [1507, 3150, 1884, 21], 'label': '40320.a.1008.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1008.a1.a1', 'old_label': '1008.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394030
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.a1.a1'], 'contains': ['2240.a1.a1', '2240.c1.a1', '2240.f1.a1', '3360.a1.a1', '3360.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [7909, -1, 2101, -1, 6411, -1, 3515, -1], 'generators': [13504, 5675, 33905, 24], 'label': '40320.a.1120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '1120.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394031
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.a1.a1', '560.b1.a1', '560.g1.a1'], 'contains': ['2240.a1.a1', '2240.e1.a1', '2240.g1.a1', '3360.c1.a1', '3360.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3990, -1, 5769, -1, 8941, -1, 1378, -1], 'generators': [39062, 34023, 39183, 24], 'label': '40320.a.1120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394032
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '560.g1.a1'], 'contains': ['2240.b1.a1', '2240.d1.a1', '2240.g1.a1', '3360.c1.a1', '3360.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [1511, -1, 7527, -1, 9611, -1, 389, -1], 'generators': [29, 13504, 33905, 34166], 'label': '40320.a.1120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '1120.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66394033
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '560.g1.a1'], 'contains': ['2240.a1.a1', '2240.b1.a1', '2240.d1.a1', '3360.e1.a1', '3360.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [424, -1, 9083, -1, 9505, -1, 534, -1], 'generators': [13504, 33905, 24, 5], 'label': '40320.a.1120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '1120.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394034
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.b1.a1', '560.d1.a1', '560.f1.a1', '560.g1.a1'], 'contains': ['2240.b1.a1', '2240.e1.a1', '3360.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [980, -1, 8624, -1, 9399, -1, 786, -1], 'generators': [639, 233, 120, 237], 'label': '40320.a.1120.e1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394035
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.a1.a1'], 'contains': ['2240.c1.a1', '2240.f1.a1', '2240.g1.a1', '3360.h1.a1', '3360.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [8341, -1, 1557, -1, 6305, -1, 3621, -1], 'generators': [5699, 13504, 33905, 34166], 'label': '40320.a.1120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '1120.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66394036
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.c1.a1', '560.a1.a1', '560.d1.a1', '560.h1.a1'], 'contains': ['2240.c1.a1', '2240.e1.a1', '3360.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [8125, -1, 1857, -1, 4248, -1, 5753, -1], 'generators': [21045, 34990, 3766, 3032], 'label': '40320.a.1120.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '1120.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394053
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.b1.a1', '630.d1.a1', '630.f1.a1'], 'contains': ['2520.m1.a1', '2520.o1.a1', '2520.q1.a1', '2520.x1.a1', '2520.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6649, -1, 3533, -1, 1301, -1, 8758, -1], 'generators': [31400, 4527, 21048, 21410, 34430], 'label': '40320.a.1260.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394054
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.c1.a1', '630.d1.a1', '630.e1.a1'], 'contains': ['2520.r1.a1', '2520.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6794, -1, 3154, -1, 768, -1, 9067, -1], 'generators': [4527, 60, 34354, 6479, 10814], 'label': '40320.a.1260.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.k1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394055
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.a1.a1', '630.e1.a1', '630.f1.a1'], 'contains': ['2520.p1.a1', '2520.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8558, -1, 1651, -1, 546, -1, 9512, -1], 'generators': [4527, 60, 7812, 34430, 10814], 'label': '40320.a.1260.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.l1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394056
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.a1.a1', '630.d1.a1', '630.g1.a1'], 'contains': ['2520.y2.a1', '2520.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8249, -1, 1742, -1, 657, -1, 9401, -1], 'generators': [15824, 32924, 19342, 39541, 32672], 'label': '40320.a.1260.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.m1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394057
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['630.g1.a1'], 'contains': ['2520.y2.a1', '2520.z1.a1', '2520.bc1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8853, -1, 1169, -1, 1029, -1, 9179, -1], 'generators': [28662, 32924, 19342, 39541, 32672], 'label': '40320.a.1260.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.g1.a1', 'old_label': '1260.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394058
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.h1.a1', '420.i1.a1', '630.b1.a1', '630.e1.a1', '630.g1.a1'], 'contains': ['2520.v1.a1', '2520.w1.a1', '2520.z1.a1', '2520.ba1.a1', '2520.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6510, -1, 3425, -1, 1976, -1, 8083, -1], 'generators': [15824, 32924, 19342, 32672, 33046], 'label': '40320.a.1260.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '1260.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394059
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '70.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1.a1'], 'contains': ['140.b1.a1', '630.e1.a1', '1120.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [4073, -1, 4571, -1, 5324, -1, 4665, -1], 'generators': [10814, 6479, 4527, 31376, 3109, 21048, 31106, 103], 'label': '40320.a.70.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394060
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.j1.a1', '420.k1.a1', '630.g1.a1'], 'contains': ['2520.y2.a1', '2520.bc1.a1', '2520.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8706, -1, 1317, -1, 1170, -1, 8888, -1], 'generators': [28662, 32924, 19342, 32672, 33046], 'label': '40320.a.1260.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.d1.a1', 'old_label': '1260.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394061
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1260.p2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.j2.a1', '630.c1.a1', '630.f1.a1', '630.g1.a1'], 'contains': ['2520.y1.a1', '2520.ba1.a1', '2520.bc1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [9412, -1, 520, -1, 879, -1, 9290, -1], 'generators': [28662, 21769, 32924, 19342, 39024], 'label': '40320.a.1260.p2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '1260.p2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.p2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394062
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1344.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8064.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.a1.a1'], 'contains': ['2688.a1.a1', '4032.a1.a1', '6720.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [48, -1, 9978, -1, 9445, -1, 595, -1], 'generators': [30, 24, 34672], 'label': '40320.a.1344.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '1344.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 66394063
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1344.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1'], 'contains': ['2688.a1.a1', '4032.b1.a1', '6720.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [159, -1, 9804, -1, 8578, -1, 1461, -1], 'generators': [3750, 15981, 40093], 'label': '40320.a.1344.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '1344.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 66394064
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1344.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.a1.a1'], 'contains': ['2688.a1.a1', '4032.c1.a1', '6720.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [2867, -1, 7079, -1, 9335, -1, 705, -1], 'generators': [30, 5009, 34672], 'label': '40320.a.1344.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '1344.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 66394065
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.a1.a1', '420.c1.a1', '560.a1.a1'], 'contains': ['3360.a1.a1', '3360.b1.a1', '3360.d1.a1', '3360.h1.a1', '3360.i1.a1', '3360.k1.a1', '3360.o1.a1', '5040.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8035, -1, 1897, -1, 6151, -1, 4008, -1], 'generators': [29490, 40295, 24, 15062], 'label': '40320.a.1680.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '1680.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394066
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1.a1', '560.c1.a1', '840.b1.a1', '840.d1.a1', '840.j1.a1'], 'contains': ['3360.q1.a1', '5040.d1.a1', '6720.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1037, -1, 9490, -1, 8600, -1, 1121, -1], 'generators': [289, 285, 572, 693], 'label': '40320.a.1680.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.f1.a1', 'old_label': '1680.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394067
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.b1.a1', '840.a1.a1', '840.c1.a1', '840.g1.a1'], 'contains': ['3360.r1.a1', '5040.d2.a1', '6720.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [5336, -1, 3524, -1, 5510, -1, 4454, -1], 'generators': [3031, 29704, 24, 10801], 'label': '40320.a.1680.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394068
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.a1.a1', '840.h1.a1'], 'contains': ['3360.e1.a1', '3360.l1.a1', '3360.n1.a1', '5040.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2954, -1, 7951, -1, 7089, -1, 2870, -1], 'generators': [1640, 719, 403, 21], 'label': '40320.a.1680.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 66394069
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.b1.a1', '560.e1.a1', '840.h1.a1'], 'contains': ['3360.e1.a1', '3360.m1.a1', '3360.p1.a1', '5040.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1767, -1, 9084, -1, 7334, -1, 2666, -1], 'generators': [1640, 639, 403, 21], 'label': '40320.a.1680.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394070
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '70.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '35.a1.a1'], 'contains': ['140.b1.a1', '140.c1.a1', '210.d1.a1', '1120.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7283, -1, 2910, -1, 4594, -1, 5472, -1], 'generators': [721, 15966, 1232, 35617, 4264, 21048, 566, 48], 'label': '40320.a.70.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '70.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394071
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.c1.a1', '420.d1.a1', '840.h1.a1'], 'contains': ['3360.f1.a1', '3360.m1.a1', '3360.n1.a1', '5040.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2664, -1, 8496, -1, 7201, -1, 3270, -1], 'generators': [1640, 625, 80, 403], 'label': '40320.a.1680.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394072
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.e1.a1', '840.f1.a1', '840.g1.a1'], 'contains': ['3360.r1.a1', '5040.i1.a1', '6720.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7267, -1, 2730, -1, 5339, -1, 4733, -1], 'generators': [289, 443, 55, 265], 'label': '40320.a.1680.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394073
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.e1.a1', '560.c1.a1', '840.h1.a1'], 'contains': ['3360.f1.a1', '3360.l1.a1', '3360.p1.a1', '5040.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1992, -1, 7075, -1, 7605, -1, 2396, -1], 'generators': [1640, 639, 80, 403], 'label': '40320.a.1680.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '1680.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66394074
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.b1.a1', '420.f1.a1', '560.g1.a1', '840.h1.a1'], 'contains': ['3360.c1.a1', '3360.e1.a1', '3360.f1.a1', '3360.g1.a1', '3360.s1.a1', '5040.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1616, -1, 8051, -1, 9099, -1, 940, -1], 'generators': [3632, 67, 526, 21], 'label': '40320.a.1680.i1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394075
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.d1.a1', '560.e1.a1', '840.i1.a1', '840.j1.a1'], 'contains': ['3360.q1.a1', '5040.h1.a1', '6720.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [649, -1, 9722, -1, 8497, -1, 1224, -1], 'generators': [384, 288, 126, 264], 'label': '40320.a.1680.j1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '1680.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394076
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.j2.a1', '840.g1.a1', '840.k1.a1', '840.q1.a1'], 'contains': ['3360.r1.a1', '5040.o1.a1', '6720.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7576, -1, 2369, -1, 3786, -1, 6177, -1], 'generators': [1581, 34378, 32924, 32672], 'label': '40320.a.1680.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394077
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.j2.a1', '840.l1.a1'], 'contains': ['5040.r1.a1', '6720.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9895, -1, 161, -1, 389, -1, 9611, -1], 'generators': [34378, 15824, 32924, 39024], 'label': '40320.a.1680.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.l1.a1', 'old_label': '1680.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394078
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.d1.a1', '840.i1.a1', '840.m1.a1', '840.n1.a1', '840.o1.a1', '840.p1.a1', '840.r1.a1'], 'contains': ['3360.q1.a1', '5040.w1.a1', '6720.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1188, -1, 9288, -1, 6977, -1, 2982, -1], 'generators': [35433, 38457, 122, 5061], 'label': '40320.a.1680.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '1680.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394079
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.i1.a1', '840.t1.a1'], 'contains': ['3360.j1.a1', '5040.v1.a1', '6720.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9132, -1, 1055, -1, 1267, -1, 8733, -1], 'generators': [30235, 36654, 39541, 5356], 'label': '40320.a.1680.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.t1.a1', 'old_label': '1680.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.n1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394080
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.e1.a1', '840.a1.a1', '840.e1.a1', '840.q1.a1'], 'contains': ['3360.r1.a1', '5040.u1.a1', '6720.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7492, -1, 2453, -1, 3925, -1, 6038, -1], 'generators': [1581, 1401, 403, 33046], 'label': '40320.a.1680.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394081
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '105.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['210.a1.a1', '210.c1.a1', '210.d2.a1', '315.a1.a1', '420.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7505, -1, 2501, -1, 1489, -1, 8455, -1], 'generators': [26, 14493, 3823, 4527, 60, 36899, 54, 23616], 'label': '40320.a.105.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '105.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '105.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394082
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '420.j1.a1', '420.j2.a1', '840.t1.a1'], 'contains': ['3360.j1.a1', '5040.ba1.a1', '6720.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9619, -1, 758, -1, 1095, -1, 8905, -1], 'generators': [34378, 21769, 32924, 19342], 'label': '40320.a.1680.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.t1.a1', 'old_label': '1680.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394083
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '420.k1.a1', '840.t1.a1'], 'contains': ['3360.j1.a1', '5040.z1.a1', '6720.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9284, -1, 842, -1, 1197, -1, 8804, -1], 'generators': [30235, 36654, 5356, 33046], 'label': '40320.a.1680.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.t1.a1', 'old_label': '1680.q1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394084
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.b1.a1', '840.i1.a1', '840.m1.a1'], 'contains': ['3360.q1.a1', '5040.bd2.a1', '6720.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3281, -1, 7363, -1, 8014, -1, 1816, -1], 'generators': [36689, 2910, 3420, 4142], 'label': '40320.a.1680.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '1680.r1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394085
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.f1.a1', '840.a1.a1', '840.f1.a1', '840.k1.a1'], 'contains': ['3360.r1.a1', '5040.bc1.a1', '6720.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6904, -1, 2853, -1, 4810, -1, 4943, -1], 'generators': [348, 647, 687, 572], 'label': '40320.a.1680.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.s1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.s1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394086
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.c1.a1', '840.e1.a1', '840.k1.a1'], 'contains': ['3360.r1.a1', '5040.bd1.a1', '6720.k2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7182, -1, 2608, -1, 4669, -1, 5295, -1], 'generators': [3444, 25741, 4142, 39905], 'label': '40320.a.1680.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.t1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394087
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.g1.a1', '840.h1.a1'], 'contains': ['3360.l1.a1', '3360.m1.a1', '3360.s1.a1', '5040.bc1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2202, -1, 7798, -1, 7484, -1, 2517, -1], 'generators': [1640, 625, 719, 403], 'label': '40320.a.1680.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.u1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 66394088
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.h1.a1', '560.j1.a1', '840.h1.a1'], 'contains': ['3360.n1.a1', '3360.p1.a1', '3360.s1.a1', '5040.be1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2503, -1, 8590, -1, 6828, -1, 2779, -1], 'generators': [27630, 15961, 15, 18246], 'label': '40320.a.1680.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '1680.v1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 66394089
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '336.g1.a1', '560.j1.a1', '840.b1.a1', '840.j1.a1', '840.p1.a1'], 'contains': ['3360.q1.a1', '5040.be1.a1', '6720.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2436, -1, 8145, -1, 8294, -1, 1745, -1], 'generators': [31113, 31192, 36233, 39183], 'label': '40320.a.1680.w1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.f1.a1', 'old_label': '1680.w1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394090
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '240.c1.a1', '840.c1.a1', '840.f1.a1', '840.q1.a1'], 'contains': ['3360.r1.a1', '5040.be1.a1', '6720.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7121, -1, 3069, -1, 4740, -1, 5014, -1], 'generators': [5045, 36233, 39183, 19764], 'label': '40320.a.1680.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '1680.x1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394091
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1680.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '420.i1.a1', '560.j1.a1'], 'contains': ['3360.r2.a1', '5040.be1.a1', '6720.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [4569, -1, 5315, -1, 4919, -1, 4872, -1], 'generators': [5054, 36186, 5045, 29821], 'label': '40320.a.1680.x2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.x2.a1', 'old_label': '1680.x2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.x2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394092
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1'], 'contains': ['224.a1.a1', '336.a1.a1', '560.c1.a1', '672.a1.a1', '1120.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1056, -1, 7485, -1, 9379, -1, 562, -1], 'generators': [4401, 30, 24, 39935], 'label': '40320.a.112.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '112.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 66394093
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '1920.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '240.b1.a1', '240.c1.a1', '960.a1.a1'], 'contains': ['5760.a1.a1', '13440.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 960, 'diagramx': [9505, -1, 251, -1, 3340, -1, 6930, -1], 'generators': [9562, 19045], 'label': '40320.a.1920.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '960.a1.a1', 'old_label': '1920.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1920.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 66394094
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2016.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1.a1', '336.b1.a1', '672.a1.a1', '1008.a1.a1'], 'contains': ['4032.a1.a1', '4032.b1.a1', '4032.c1.a1', '10080.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [869, -1, 6700, -1, 9247, -1, 792, -1], 'generators': [1950, 566, 21], 'label': '40320.a.2016.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1008.a1.a1', 'old_label': '2016.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394095
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2016.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.d1.a1', '336.f1.a1', '672.b1.a1', '1008.a1.a1'], 'contains': ['4032.b1.a1', '10080.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [1236, -1, 7215, -1, 7794, -1, 2209, -1], 'generators': [246, 414, 601], 'label': '40320.a.2016.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '2016.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394096
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2016.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.e1.a1', '336.g1.a1', '672.c1.a1', '1008.a1.a1'], 'contains': ['4032.b1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [2780, -1, 6796, -1, 7632, -1, 2408, -1], 'generators': [26, 112, 5102], 'label': '40320.a.2016.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1008.a1.a1', 'old_label': '2016.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394097
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.a1.a1', '1120.b1.a1', '1120.d1.a1'], 'contains': ['4480.a1.a1', '6720.a1.a1', '6720.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3769, -1, 6424, -1, 8335, -1, 1704, -1], 'generators': [39062, 34023, 24], 'label': '40320.a.2240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '2240.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394098
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.c1.a1', '560.e1.a1', '1120.c1.a1', '1120.d1.a1', '1120.e1.a1'], 'contains': ['4480.a1.a1', '6720.a1.a1', '6720.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [345, -1, 9576, -1, 9138, -1, 902, -1], 'generators': [233, 120, 237], 'label': '40320.a.2240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '2240.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394099
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.c1.a1', '1120.a1.a1', '1120.f1.a1', '1120.g1.a1'], 'contains': ['4480.a1.a1', '6720.d1.a1', '6720.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [8546, -1, 1500, -1, 4696, -1, 5391, -1], 'generators': [21045, 34990, 3032], 'label': '40320.a.2240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '2240.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394100
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '1120.c1.a1', '1120.d1.a1', '1120.l1.a1'], 'contains': ['4480.a1.a1', '6720.f1.a1', '6720.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [1105, -1, 8541, -1, 8825, -1, 1289, -1], 'generators': [21045, 141, 3032], 'label': '40320.a.2240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '2240.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394101
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.j1.a1', '1120.b1.a1', '1120.e1.a1', '1120.g1.a1', '1120.i1.a1', '1120.j1.a1', '1120.k1.a1', '1120.l1.a1'], 'contains': ['4480.a1.a1', '6720.g1.a1', '6720.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3661, -1, 6070, -1, 7713, -1, 2327, -1], 'generators': [3753, 26046, 29821], 'label': '40320.a.2240.e1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '2240.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394102
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.a1.a1', '1120.f1.a1', '1120.i1.a1'], 'contains': ['4480.a1.a1', '6720.i1.a1', '6720.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [7786, -1, 2165, -1, 6358, -1, 3568, -1], 'generators': [316, 233, 237], 'label': '40320.a.2240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '2240.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394103
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1'], 'contains': ['224.a1.a1', '336.d1.a1', '560.e1.a1', '672.b1.a1', '1120.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [731, -1, 9457, -1, 8954, -1, 816, -1], 'generators': [30, 15094, 5088], 'label': '40320.a.112.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '112.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 66394104
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.b1.a1', '1120.c1.a1', '1120.f1.a1'], 'contains': ['4480.a1.a1', '6720.j1.a1', '6720.k2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3945, -1, 5646, -1, 8186, -1, 1853, -1], 'generators': [39207, 39062, 34023], 'label': '40320.a.2240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '2240.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394105
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.a1.a1', '1260.e1.a1'], 'contains': ['5040.a1.a1', '5040.b1.a1', '5040.d2.a1', '5040.s1.a1', '5040.u1.a1', '5040.bb1.a1', '5040.bc1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [5240, -1, 4181, -1, 4394, -1, 5570, -1], 'generators': [40295, 3420, 24, 39183], 'label': '40320.a.2520.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '2520.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394106
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.b1.a1', '840.c1.a1', '1260.e1.a1'], 'contains': ['5040.c1.a1', '5040.d1.a1', '5040.d2.a1', '5040.bb1.a1', '5040.bd1.a1', '5040.bd2.a1', '5040.be1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4155, -1, 5980, -1, 4528, -1, 5435, -1], 'generators': [3420, 24, 4142, 39905], 'label': '40320.a.2520.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '2520.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394107
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.a1.a1', '1260.c1.a1', '1260.e1.a1'], 'contains': ['5040.b1.a1', '5040.c1.a1', '5040.e1.a1', '5040.k1.a1', '5040.n1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4423, -1, 6451, -1, 2813, -1, 7187, -1], 'generators': [36875, 9393, 36873, 24], 'label': '40320.a.2520.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394108
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.a1.a1', '1260.b1.a1', '1260.f1.a1'], 'contains': ['5040.e1.a1', '5040.l1.a1', '5040.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5939, -1, 4427, -1, 1652, -1, 8311, -1], 'generators': [14493, 60, 54, 6479], 'label': '40320.a.2520.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394109
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.b1.a1', '1260.c1.a1', '1260.e1.a1'], 'contains': ['5040.e1.a1', '5040.g1.a1', '5040.j1.a1', '5040.n1.a1', '5040.bb1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5831, -1, 5261, -1, 2957, -1, 6817, -1], 'generators': [14435, 36873, 36899, 746], 'label': '40320.a.2520.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394110
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.i1.a1', '1260.a1.a1', '1260.d1.a1', '1260.e1.a1'], 'contains': ['5040.e1.a1', '5040.f1.a1', '5040.h1.a1', '5040.k1.a1', '5040.s1.a1', '5040.w1.a1', '5040.bd2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3910, -1, 6092, -1, 3453, -1, 6548, -1], 'generators': [36873, 36899, 746, 14459], 'label': '40320.a.2520.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394111
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.d1.a1', '1260.b1.a1', '1260.d1.a1', '1260.e1.a1'], 'contains': ['5040.a1.a1', '5040.d1.a1', '5040.e1.a1', '5040.j1.a1', '5040.w1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [6546, -1, 3656, -1, 3561, -1, 6440, -1], 'generators': [36875, 14435, 36873, 24], 'label': '40320.a.2520.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '2520.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394112
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.c1.a1', '1260.d1.a1', '1260.f1.a1'], 'contains': ['5040.e1.a1', '5040.f1.a1', '5040.m1.a1', '5040.t1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6059, -1, 4649, -1, 2380, -1, 7621, -1], 'generators': [14493, 36945, 60, 54], 'label': '40320.a.2520.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394113
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.a1.a1', '840.e1.a1', '1260.e1.a1'], 'contains': ['5040.a1.a1', '5040.c1.a1', '5040.f1.a1', '5040.g1.a1', '5040.i1.a1', '5040.u1.a1', '5040.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4034, -1, 5578, -1, 4103, -1, 5860, -1], 'generators': [5675, 514, 24, 5], 'label': '40320.a.2520.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '2520.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394114
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '56.b1.a1'], 'contains': ['224.a1.a1', '336.g1.a1', '560.j1.a1', '672.c1.a1', '1120.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2705, -1, 8285, -1, 8628, -1, 1334, -1], 'generators': [3750, 18607, 122], 'label': '40320.a.112.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '112.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 66394115
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.f1.a1', '840.h1.a1', '840.j1.a1', '1260.e1.a1'], 'contains': ['5040.b1.a1', '5040.d1.a1', '5040.g1.a1', '5040.h1.a1', '5040.i1.a1', '5040.bc1.a1', '5040.be1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3023, -1, 7380, -1, 5092, -1, 5192, -1], 'generators': [289, 341, 55, 265], 'label': '40320.a.2520.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '2520.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394116
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.g1.a1', '1260.e1.a1', '1260.f1.a1'], 'contains': ['5040.d2.a1', '5040.e1.a1', '5040.i1.a1', '5040.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5649, -1, 4520, -1, 3641, -1, 6359, -1], 'generators': [36875, 722, 36873, 24], 'label': '40320.a.2520.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '2520.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394117
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.b1.a1', '1260.c1.a1', '1260.g1.a1'], 'contains': ['5040.j1.a1', '5040.m1.a1', '5040.n1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5433, -1, 4875, -1, 2041, -1, 7879, -1], 'generators': [31400, 4527, 21410, 23309], 'label': '40320.a.2520.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 66394118
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.b1.a1', '1260.h1.a1', '1260.j1.a1'], 'contains': ['5040.j1.a1', '5040.l1.a1', '5040.p1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8392, -1, 2113, -1, 745, -1, 9256, -1], 'generators': [13360, 31400, 4527, 21410], 'label': '40320.a.2520.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '2520.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394119
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.a1.a1', '1260.c1.a1', '1260.g1.a1'], 'contains': ['5040.k1.a1', '5040.m1.a1', '5040.n1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4895, -1, 5412, -1, 1902, -1, 7980, -1], 'generators': [4527, 21410, 34354, 23309], 'label': '40320.a.2520.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394120
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.a1.a1', '1260.i1.a1', '1260.j1.a1'], 'contains': ['5040.k1.a1', '5040.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6892, -1, 3154, -1, 987, -1, 9013, -1], 'generators': [13360, 4527, 3011, 21410], 'label': '40320.a.2520.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '2520.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394121
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.h1.a1', '1260.i1.a1', '1260.l1.a1'], 'contains': ['5040.l1.a1', '5040.q1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9075, -1, 930, -1, 207, -1, 9793, -1], 'generators': [34348, 4527, 7812, 10814], 'label': '40320.a.2520.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '2520.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394122
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.k1.a1', '1260.e1.a1', '1260.g1.a1', '1260.j1.a1'], 'contains': ['5040.j1.a1', '5040.k1.a1', '5040.o1.a1', '5040.bc1.a1', '5040.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4988, -1, 3891, -1, 3092, -1, 7043, -1], 'generators': [722, 14435, 36873, 36899], 'label': '40320.a.2520.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.q1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394123
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.f1.a1', '1260.g1.a1', '1260.k1.a1'], 'contains': ['5040.m1.a1', '5040.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5729, -1, 3387, -1, 1541, -1, 8422, -1], 'generators': [4527, 21048, 21410, 34354], 'label': '40320.a.2520.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '2520.r1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394124
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.l1.a1', '1260.h1.a1'], 'contains': ['5040.p1.a1', '5040.q1.a1', '5040.r1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9937, -1, 132, -1, 110, -1, 9890, -1], 'generators': [14493, 31400, 7812, 32856], 'label': '40320.a.2520.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.h1.a1', 'old_label': '2520.s1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394125
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.c1.a1', '56.d1.a1'], 'contains': ['672.d1.a1', '672.e1.a1', '1120.k1.a1', '1680.w1.a1', '1680.x1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4676, -1, 6863, -1, 6797, -1, 3463, -1], 'generators': [27607, 39183], 'label': '40320.a.112.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 66394126
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.m1.a1', '1260.b1.a1', '1260.d1.a1', '1260.g1.a1'], 'contains': ['5040.j1.a1', '5040.m1.a1', '5040.t1.a1', '5040.w1.a1', '5040.bd2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6198, -1, 4326, -1, 2669, -1, 7332, -1], 'generators': [31400, 4527, 3109, 10814], 'label': '40320.a.2520.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.t1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394127
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.n1.a1', '1260.a1.a1', '1260.d1.a1', '1260.g1.a1'], 'contains': ['5040.k1.a1', '5040.m1.a1', '5040.w1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [4551, -1, 5106, -1, 2524, -1, 7477, -1], 'generators': [4527, 3011, 31376, 10814], 'label': '40320.a.2520.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '2520.u1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394128
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.o1.a1', '1260.a1.a1', '1260.b1.a1', '1260.o1.a1'], 'contains': ['5040.l1.a1', '5040.n1.a1', '5040.w1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6689, -1, 3295, -1, 1801, -1, 8081, -1], 'generators': [15824, 32924, 32672, 33046], 'label': '40320.a.2520.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.v1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394129
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.p1.a1', '840.q1.a1', '1260.e1.a1', '1260.g1.a1', '1260.o1.a1'], 'contains': ['5040.n1.a1', '5040.o1.a1', '5040.u1.a1', '5040.w1.a1', '5040.be1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5551, -1, 3780, -1, 3227, -1, 6683, -1], 'generators': [1581, 32924, 32672, 33046], 'label': '40320.a.2520.w1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.w1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394130
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.c1.a1', '1260.d1.a1', '1260.j1.a1'], 'contains': ['5040.j1.a1', '5040.k1.a1', '5040.s1.a1', '5040.t1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6457, -1, 4036, -1, 2163, -1, 7756, -1], 'generators': [31400, 4527, 21410, 34430], 'label': '40320.a.2520.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '2520.x1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 66394131
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.h1.a1', '1260.i1.a1', '1260.p2.a1'], 'contains': ['5040.l1.a1', '5040.r1.a1', '5040.v1.a1', '5040.x1.a1', '5040.z1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9556, -1, 509, -1, 302, -1, 9699, -1], 'generators': [28662, 21769, 32924, 39024], 'label': '40320.a.2520.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '2520.y1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394132
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.m1.a1', '1260.n1.a1', '1260.p1.a1'], 'contains': ['5040.x1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8834, -1, 1275, -1, 487, -1, 9512, -1], 'generators': [32924, 19342, 39024, 33046], 'label': '40320.a.2520.y2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.g1.a1', 'old_label': '2520.y2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.y2.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394133
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.c1.a1', '1260.n1.a1', '1260.o1.a1'], 'contains': ['5040.n1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7121, -1, 3074, -1, 1430, -1, 8533, -1], 'generators': [32924, 19342, 2041, 32672], 'label': '40320.a.2520.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '2520.z1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394134
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1260.f1.a1', '1260.j1.a1', '1260.k1.a1', '1260.l1.a1', '1260.m1.a1', '1260.o1.a1', '1260.p2.a1'], 'contains': ['5040.l1.a1', '5040.o1.a1', '5040.v1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7909, -1, 2224, -1, 879, -1, 9120, -1], 'generators': [21769, 32924, 39024, 23199], 'label': '40320.a.2520.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '2520.ba1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394135
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '1260.h1.a1'], 'contains': ['5040.p1.a1', '5040.q1.a1', '5040.z1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9844, -1, 201, -1, 27, -1, 9974, -1], 'generators': [38286, 14493, 31400, 32856], 'label': '40320.a.2520.bb1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.h1.a1', 'old_label': '2520.bb1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394136
    {'ambient': '40320.a', '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': '40320.a1.a1', 'complements': ['20160.a1.a1', '20160.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16.a1.a1', '30.a1.a1', '56.d1.a1', '70.c1.a1', '112.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7244, 5000, 3339, 5000, 5658, 5000, 4441, 5000], 'generators': [11023, 36899], 'label': '40320.a.2.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['40320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40320.a'}
  • id: 66394137
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['240.b1.a1', '960.a1.a1', '2520.bb1.a1', '3360.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9621, -1, 769, -1, 3980, -1, 5579, -1], 'generators': [37981, 12316], 'label': '40320.a.120.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '336.208'}
  • id: 66394138
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.t1.a1', '1260.n1.a1', '1260.p1.a1', '1260.p2.a1'], 'contains': ['5040.v1.a1', '5040.x1.a1', '5040.y1.a1', '5040.z1.a1', '5040.ba1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9326, -1, 648, -1, 610, -1, 9390, -1], 'generators': [28662, 21769, 32924, 12829], 'label': '40320.a.2520.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.g1.a1', 'old_label': '2520.bc1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 66394139
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2520.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.r1.a1', '840.s1.a1', '1260.d1.a1', '1260.o1.a1', '1260.p1.a1'], 'contains': ['5040.w1.a1', '5040.y1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7449, -1, 2964, -1, 2272, -1, 8177, -1], 'generators': [32924, 19342, 32672, 33046], 'label': '40320.a.2520.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '2520.bd1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394140
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2688.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2688.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.a1.a1', '1344.b1.a1', '1344.c1.a1'], 'contains': ['8064.a1.a1', '13440.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [55, -1, 9916, -1, 8987, -1, 957, -1], 'generators': [3750, 40093], 'label': '40320.a.2688.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '2688.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2688.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 66394141
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '2880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1.a1'], 'contains': ['5760.a1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 960, 'diagramx': [9150, -1, 769, -1, 4989, -1, 4593, -1], 'generators': [2569, 4811], 'label': '40320.a.2880.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '960.a1.a1', 'old_label': '2880.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 66394142
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.g1.a1', '1120.a1.a1', '1680.a1.a1'], 'contains': ['6720.b1.a1', '6720.d1.a1', '6720.i1.a1', '10080.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8230, -1, 1765, -1, 6097, -1, 4135, -1], 'generators': [40295, 24, 15062], 'label': '40320.a.3360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394143
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.a1.a1', '1120.a1.a1', '1680.a1.a1'], 'contains': ['6720.b1.a1', '6720.e1.a1', '6720.k1.a1', '10080.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [7961, -1, 1944, -1, 5887, -1, 3996, -1], 'generators': [27304, 40295, 24], 'label': '40320.a.3360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '3360.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394144
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1.a1', '840.b1.a1', '1120.b1.a1', '1120.c1.a1', '1680.i1.a1'], 'contains': ['6720.a1.a1', '6720.g1.a1', '6720.j1.a1', '10080.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [2285, -1, 7853, -1, 8927, -1, 1187, -1], 'generators': [122, 3032, 21], 'label': '40320.a.3360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.i1.a1', 'old_label': '3360.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394145
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.b1.a1', '840.c1.a1', '1120.b1.a1', '1680.a1.a1'], 'contains': ['6720.b1.a1', '6720.h1.a1', '6720.k2.a1', '10080.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [7079, -1, 4721, -1, 6200, -1, 3780, -1], 'generators': [9905, 5552, 24], 'label': '40320.a.3360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394146
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.d1.a1', '1120.d1.a1', '1680.d1.a1', '1680.e1.a1', '1680.i1.a1'], 'contains': ['6720.a1.a1', '6720.f1.a1', '10080.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [970, -1, 9519, -1, 8074, -1, 2036, -1], 'generators': [3632, 67, 21], 'label': '40320.a.3360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394147
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.a1.a1', '840.i1.a1', '1120.c1.a1', '1680.f1.a1', '1680.h1.a1', '1680.i1.a1'], 'contains': ['6720.c1.a1', '6720.f1.a1', '6720.j1.a1', '10080.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1329, -1, 7992, -1, 8438, -1, 1564, -1], 'generators': [3632, 67, 512], 'label': '40320.a.3360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394148
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '140.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.a1.a1'], 'contains': ['280.c1.a1', '420.b1.a1', '420.e1.a1', '560.c1.a1', '560.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1952, -1, 8703, -1, 6880, -1, 3345, -1], 'generators': [10814, 4527, 31376, 3109, 31106, 103, 54], 'label': '40320.a.140.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '140.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.a1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8653'}
  • id: 66394149
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.d1.a1', '840.j1.a1', '1120.d1.a1', '1120.e1.a1', '1680.i1.a1'], 'contains': ['6720.a1.a1', '6720.c1.a1', '6720.g1.a1', '10080.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [698, -1, 8748, -1, 9035, -1, 1004, -1], 'generators': [103, 5, 264], 'label': '40320.a.3360.g1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '3360.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394150
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.k1.a1', '840.l1.a1', '1120.f1.a1', '1680.a1.a1'], 'contains': ['6720.d1.a1', '6720.k1.a1', '6720.k2.a1', '10080.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8846, -1, 1161, -1, 5708, -1, 4458, -1], 'generators': [40319, 29490, 15062], 'label': '40320.a.3360.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394151
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '840.e1.a1', '1120.f1.a1', '1680.a1.a1'], 'contains': ['6720.e1.a1', '6720.i1.a1', '6720.k2.a1', '10080.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8597, -1, 1419, -1, 5779, -1, 4275, -1], 'generators': [29514, 40295, 15062], 'label': '40320.a.3360.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394152
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.s1.a1', '1680.n1.a1', '1680.p1.a1', '1680.q1.a1'], 'contains': ['10080.h1.a1', '13440.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9181, -1, 1048, -1, 1415, -1, 8747, -1], 'generators': [1401, 21769, 19342], 'label': '40320.a.3360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.t1.a1', 'old_label': '3360.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394153
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.e1.a1', '840.q1.a1', '840.t1.a1', '1120.g1.a1', '1680.a1.a1'], 'contains': ['6720.d1.a1', '6720.e1.a1', '6720.h1.a1', '10080.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8505, -1, 1557, -1, 3871, -1, 6146, -1], 'generators': [36654, 32924, 33046], 'label': '40320.a.3360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394154
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.m1.a1', '1680.d1.a1', '1680.h1.a1', '1680.u1.a1'], 'contains': ['6720.f1.a1', '6720.j1.a1', '10080.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2611, -1, 7160, -1, 7484, -1, 2517, -1], 'generators': [1640, 719, 403], 'label': '40320.a.3360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394155
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.b1.a1', '840.n1.a1', '1680.e1.a1', '1680.f1.a1', '1680.u1.a1'], 'contains': ['6720.f1.a1', '10080.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1776, -1, 9009, -1, 7370, -1, 2753, -1], 'generators': [1640, 625, 403], 'label': '40320.a.3360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394156
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.c1.a1', '840.o1.a1', '1680.d1.a1', '1680.f1.a1', '1680.v1.a1'], 'contains': ['6720.f1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2519, -1, 8594, -1, 7089, -1, 2870, -1], 'generators': [6655, 15, 18246], 'label': '40320.a.3360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394157
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.f1.a1', '840.f1.a1', '1120.i1.a1', '1680.a1.a1'], 'contains': ['6720.h1.a1', '6720.i1.a1', '6720.k1.a1', '10080.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [7731, -1, 2329, -1, 5958, -1, 3850, -1], 'generators': [617, 450, 572], 'label': '40320.a.3360.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '3360.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394158
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.r1.a1', '1120.h1.a1', '1680.e1.a1', '1680.h1.a1', '1680.v1.a1'], 'contains': ['6720.f1.a1', '10080.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1653, -1, 8887, -1, 7259, -1, 2643, -1], 'generators': [27630, 15, 18246], 'label': '40320.a.3360.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '3360.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394159
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '140.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.a1.a1', '70.b1.a1', '70.c1.a1'], 'contains': ['280.c1.a1', '420.h1.a1', '420.i1.a1', '560.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3170, -1, 7073, -1, 5785, -1, 4314, -1], 'generators': [721, 15966, 1232, 21048, 4264, 566, 48], 'label': '40320.a.140.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '140.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394160
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.d1.a1', '1120.h1.a1', '1680.b1.a1', '1680.j1.a1', '1680.m1.a1', '1680.r1.a1', '1680.w1.a1'], 'contains': ['10080.m1.a1', '13440.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [1054, -1, 9334, -1, 7972, -1, 1934, -1], 'generators': [82, 55, 104], 'label': '40320.a.3360.q1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '3360.q1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394161
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.e1.a1', '1680.c1.a1', '1680.g1.a1', '1680.k1.a1', '1680.o1.a1', '1680.s1.a1', '1680.t1.a1', '1680.x1.a1'], 'contains': ['10080.m2.a1', '13440.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7281, -1, 2548, -1, 4396, -1, 5218, -1], 'generators': [39876, 5094, 5041], 'label': '40320.a.3360.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '3360.r1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394162
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.s1.a1', '1120.h1.a1', '1680.x2.a1'], 'contains': ['10080.m1.a1', '13440.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [4638, -1, 5398, -1, 5182, -1, 4603, -1], 'generators': [36186, 5045, 29821], 'label': '40320.a.3360.r2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.j1.a1', 'old_label': '3360.r2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.r2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394163
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '3360.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.g1.a1', '840.p1.a1', '1120.l1.a1', '1680.i1.a1', '1680.u1.a1', '1680.v1.a1'], 'contains': ['6720.f1.a1', '6720.g1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2024, -1, 8316, -1, 7864, -1, 2138, -1], 'generators': [5094, 5061, 15], 'label': '40320.a.3360.s1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '3360.s1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66394164
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '4032.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4032.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.a1.a1', '2016.a1.a1'], 'contains': ['8064.a1.a1', '20160.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [147, -1, 9231, -1, 9160, -1, 819, -1], 'generators': [1950, 21], 'label': '40320.a.4032.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1008.a1.a1', 'old_label': '4032.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 66394165
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '4032.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.d1.a1', '672.e1.a1', '1344.b1.a1', '2016.a1.a1', '2016.b1.a1', '2016.c1.a1'], 'contains': ['8064.a1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [361, -1, 6974, -1, 8050, -1, 1865, -1], 'generators': [4446, 4553], 'label': '40320.a.4032.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '4032.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394166
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '4032.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.c1.a1', '2016.a1.a1'], 'contains': ['8064.a1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1008, 'diagramx': [2412, -1, 6916, -1, 8908, -1, 1036, -1], 'generators': [1950, 572], 'label': '40320.a.4032.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1008.a1.a1', 'old_label': '4032.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 66394167
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '4480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2240.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.h1.a1', '2240.a1.a1', '2240.b1.a1', '2240.c1.a1', '2240.d1.a1', '2240.e1.a1', '2240.f1.a1', '2240.g1.a1'], 'contains': ['13440.a1.a1', '13440.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3459, -1, 5988, -1, 7936, -1, 2133, -1], 'generators': [3753, 26046], 'label': '40320.a.4480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '4480.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394168
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.a1.a1', '2520.a1.a1', '2520.g1.a1', '2520.i1.a1'], 'contains': ['10080.a1.a1', '10080.b1.a1', '10080.e1.a1', '10080.g1.a1', '10080.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6954, -1, 3069, -1, 4509, -1, 5579, -1], 'generators': [40295, 3420, 24], 'label': '40320.a.5040.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394169
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1008.a1.a1', '1680.f1.a1', '2520.a1.a1', '2520.c1.a1', '2520.j1.a1'], 'contains': ['10080.b1.a1', '10080.j1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3002, -1, 7060, -1, 5080, -1, 4857, -1], 'generators': [289, 55, 83], 'label': '40320.a.5040.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394170
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '140.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.c1.a1'], 'contains': ['280.c1.a1', '420.j1.a1', '420.k1.a1', '2240.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [8427, -1, 1573, -1, 3824, -1, 6263, -1], 'generators': [721, 15966, 1232, 35617, 4264, 21048, 48], 'label': '40320.a.140.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.c1.a1', 'old_label': '140.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.c1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 66394171
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.b1.a1', '2520.b1.a1', '2520.c1.a1', '2520.i1.a1'], 'contains': ['10080.b1.a1', '10080.k1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3771, -1, 6248, -1, 4152, -1, 5865, -1], 'generators': [25745, 39183, 24], 'label': '40320.a.5040.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394172
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.b1.a1', '1680.h1.a1', '2520.b1.a1', '2520.g1.a1', '2520.j1.a1'], 'contains': ['10080.b1.a1', '10080.i1.a1', '10080.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2853, -1, 6557, -1, 5403, -1, 4679, -1], 'generators': [289, 341, 55], 'label': '40320.a.5040.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.f1.a1', 'old_label': '5040.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394173
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.c1.a1', '2520.a1.a1', '2520.b1.a1', '2520.k1.a1'], 'contains': ['10080.b1.a1', '10080.i2.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [5021, -1, 4463, -1, 4589, -1, 5498, -1], 'generators': [3031, 24, 10801], 'label': '40320.a.5040.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '5040.d2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.d2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394174
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.c1.a1', '2520.d1.a1', '2520.e1.a1', '2520.f1.a1', '2520.g1.a1', '2520.h1.a1', '2520.k1.a1'], 'contains': ['10080.a1.a1', '10080.b1.a1', '10080.c1.a1', '10080.d1.a1', '10080.i2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5919, -1, 4987, -1, 3664, -1, 6399, -1], 'generators': [14435, 2, 24], 'label': '40320.a.5040.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394175
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.d1.a1', '2520.f1.a1', '2520.h1.a1', '2520.i1.a1'], 'contains': ['10080.c1.a1', '10080.g1.a1', '10080.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3687, -1, 5812, -1, 3763, -1, 6254, -1], 'generators': [5699, 514, 5], 'label': '40320.a.5040.f1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394176
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.f1.a1', '1680.d1.a1', '2520.e1.a1', '2520.i1.a1', '2520.j1.a1'], 'contains': ['10080.c1.a1', '10080.i1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3570, -1, 6962, -1, 4977, -1, 5148, -1], 'generators': [316, 134, 120], 'label': '40320.a.5040.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394177
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.e1.a1', '1680.j1.a1', '2520.f1.a1', '2520.j1.a1'], 'contains': ['10080.c1.a1', '10080.j1.a1', '10080.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2350, -1, 7915, -1, 5327, -1, 4754, -1], 'generators': [288, 126, 264], 'label': '40320.a.5040.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '5040.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394178
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.g1.a1', '1680.i1.a1', '2520.i1.a1', '2520.j1.a1', '2520.k1.a1'], 'contains': ['10080.b1.a1', '10080.c1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3236, -1, 5911, -1, 5483, -1, 5001, -1], 'generators': [289, 55, 265], 'label': '40320.a.5040.i1.a1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '5040.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394179
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.e1.a1', '2520.g1.a1', '2520.l1.a1', '2520.m1.a1', '2520.q1.a1', '2520.t1.a1', '2520.x1.a1'], 'contains': ['10080.d1.a1', '10080.e1.a1', '10080.i1.a1', '10080.i2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6474, -1, 3834, -1, 3038, -1, 7037, -1], 'generators': [36875, 36897, 14435], 'label': '40320.a.5040.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394180
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.c1.a1', '2520.f1.a1', '2520.n1.a1', '2520.o1.a1', '2520.q1.a1', '2520.u1.a1', '2520.x1.a1'], 'contains': ['10080.d1.a1', '10080.j1.a1', '10080.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4698, -1, 5560, -1, 2931, -1, 7144, -1], 'generators': [9393, 36873, 36899], 'label': '40320.a.5040.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394181
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.f1.a1', '840.a1.a1', '1008.a1.a1', '1680.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [6722, -1, 3121, -1, 5690, -1, 4387, -1], 'generators': [36875, 39574, 24], 'label': '40320.a.168.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394182
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.d1.a1', '2520.m1.a1', '2520.o1.a1', '2520.p1.a1', '2520.v1.a1', '2520.y1.a1', '2520.ba1.a1'], 'contains': ['10080.d1.a1', '10080.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8001, -1, 2246, -1, 933, -1, 9067, -1], 'generators': [32924, 39024, 23199], 'label': '40320.a.5040.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '5040.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394183
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.d1.a1', '2520.h1.a1', '2520.l1.a1', '2520.n1.a1', '2520.r1.a1', '2520.t1.a1', '2520.u1.a1'], 'contains': ['10080.d1.a1', '10080.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5394, -1, 4674, -1, 2380, -1, 7621, -1], 'generators': [4527, 34354, 10814], 'label': '40320.a.5040.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394184
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.c1.a1', '2520.e1.a1', '2520.l1.a1', '2520.n1.a1', '2520.v1.a1', '2520.w1.a1', '2520.z1.a1'], 'contains': ['10080.d1.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5734, -1, 5230, -1, 2727, -1, 7349, -1], 'generators': [32924, 2041, 32672], 'label': '40320.a.5040.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394185
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.k1.a1', '2520.k1.a1', '2520.q1.a1', '2520.r1.a1', '2520.w1.a1', '2520.ba1.a1'], 'contains': ['10080.d1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6206, -1, 3339, -1, 3145, -1, 6934, -1], 'generators': [1581, 32924, 32672], 'label': '40320.a.5040.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '5040.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394186
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.m1.a1', '2520.s1.a1', '2520.bb1.a1'], 'contains': ['10080.e1.a1', '10080.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9640, -1, 423, -1, 318, -1, 9682, -1], 'generators': [14447, 32502, 25181], 'label': '40320.a.5040.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.h1.a1', 'old_label': '5040.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394187
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.p1.a1', '2520.s1.a1', '2520.bb1.a1'], 'contains': ['10080.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9861, -1, 203, -1, 159, -1, 9841, -1], 'generators': [14493, 7812, 32856], 'label': '40320.a.5040.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.h1.a1', 'old_label': '5040.q1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394188
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.l1.a1', '2520.s1.a1', '2520.y1.a1'], 'contains': ['10080.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [9921, -1, 92, -1, 389, -1, 9611, -1], 'generators': [15824, 32924, 39024], 'label': '40320.a.5040.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.c1.a1', 'old_label': '5040.r1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394189
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.a1.a1', '2520.f1.a1', '2520.x1.a1'], 'contains': ['10080.g1.a1', '10080.i2.a1', '10080.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5560, -1, 4526, -1, 3588, -1, 6475, -1], 'generators': [40319, 39207, 3420], 'label': '40320.a.5040.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.s1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394190
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.h1.a1', '2520.t1.a1', '2520.x1.a1'], 'contains': ['10080.g1.a1', '10080.i2.a1', '10080.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6314, -1, 4585, -1, 2829, -1, 7247, -1], 'generators': [10860, 6479, 14433], 'label': '40320.a.5040.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.d1.a1', 'old_label': '5040.t1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394191
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.h1.a1', '1680.o1.a1', '2520.a1.a1', '2520.i1.a1', '2520.w1.a1'], 'contains': ['10080.g1.a1', '10080.l1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4915, -1, 3949, -1, 3979, -1, 6038, -1], 'generators': [1581, 403, 33046], 'label': '40320.a.5040.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.u1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394192
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.a1.a1', '56.b1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.g1.a1', '840.j1.a1', '1008.a1.a1', '1680.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1473, -1, 7945, -1, 8815, -1, 1184, -1], 'generators': [741, 3380, 21], 'label': '40320.a.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.b1.a1', 'old_label': '168.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394193
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.n1.a1', '2520.y1.a1', '2520.ba1.a1', '2520.bc1.a1'], 'contains': ['10080.d1.a1', '10080.f1.a1', '10080.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9238, -1, 837, -1, 794, -1, 9206, -1], 'generators': [5120, 21769, 5356], 'label': '40320.a.5040.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.p2.a1', 'old_label': '5040.v1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394194
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.m1.a1', '2520.f1.a1', '2520.g1.a1', '2520.t1.a1', '2520.u1.a1', '2520.v1.a1', '2520.w1.a1', '2520.bd1.a1'], 'contains': ['10080.d1.a1', '10080.g1.a1', '10080.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [6708, -1, 3564, -1, 3415, -1, 6683, -1], 'generators': [32924, 32672, 33046], 'label': '40320.a.5040.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '5040.w1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394195
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.y1.a1', '2520.y2.a1', '2520.bc1.a1'], 'contains': ['10080.f1.a1', '10080.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9399, -1, 643, -1, 508, -1, 9390, -1], 'generators': [28662, 32924, 39024], 'label': '40320.a.5040.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.g1.a1', 'old_label': '5040.x1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394196
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.h1.a1', '2520.x1.a1', '2520.y2.a1', '2520.z1.a1', '2520.ba1.a1', '2520.bc1.a1', '2520.bd1.a1'], 'contains': ['10080.d1.a1', '10080.g1.a1', '10080.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7527, -1, 2612, -1, 1302, -1, 8442, -1], 'generators': [32924, 19342, 33046], 'label': '40320.a.5040.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '5040.y1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394197
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.q1.a1', '2520.y1.a1', '2520.bb1.a1', '2520.bc1.a1'], 'contains': ['10080.f1.a1', '10080.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9549, -1, 352, -1, 610, -1, 9492, -1], 'generators': [21769, 5356, 33046], 'label': '40320.a.5040.z1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '5040.z1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66394198
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '1680.p1.a1', '2520.bc1.a1'], 'contains': ['10080.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [9487, -1, 554, -1, 1095, -1, 8905, -1], 'generators': [21769, 32924, 19342], 'label': '40320.a.5040.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '5040.ba1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 66394199
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2520.a1.a1', '2520.b1.a1', '2520.e1.a1'], 'contains': ['10080.i1.a1', '10080.i2.a1', '10080.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [5145, -1, 5395, -1, 4254, -1, 5692, -1], 'generators': [39207, 40295, 3420], 'label': '40320.a.5040.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.bb1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394200
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.s1.a1', '1680.u1.a1', '2520.a1.a1', '2520.j1.a1', '2520.q1.a1'], 'contains': ['10080.i1.a1', '10080.j1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4360, -1, 4402, -1, 4799, -1, 5289, -1], 'generators': [647, 687, 572], 'label': '40320.a.5040.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.bc1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394201
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.i1.a1', '1680.t1.a1', '2520.b1.a1', '2520.i1.a1', '2520.q1.a1'], 'contains': ['10080.i1.a1', '10080.k1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4288, -1, 4231, -1, 4325, -1, 5763, -1], 'generators': [29, 5675, 514], 'label': '40320.a.5040.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.bd1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394202
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.bd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.r1.a1', '2520.b1.a1', '2520.f1.a1', '2520.t1.a1'], 'contains': ['10080.i2.a1', '10080.k1.a1', '10080.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3629, -1, 6363, -1, 4050, -1, 5967, -1], 'generators': [39929, 3420, 4142], 'label': '40320.a.5040.bd2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '5040.bd2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.bd2.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394203
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '210.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.a1.a1'], 'contains': ['420.j2.a1', '630.c1.a1', '840.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7439, -1, 2559, -1, 1424, -1, 8520, -1], 'generators': [14493, 3823, 4527, 60, 36899, 54, 23616], 'label': '40320.a.210.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394204
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5040.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.v1.a1', '1680.w1.a1', '1680.x1.a1', '1680.x2.a1', '2520.b1.a1', '2520.j1.a1', '2520.w1.a1'], 'contains': ['10080.l1.a1', '10080.m1.a1', '10080.m2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4015, -1, 6742, -1, 4869, -1, 5077, -1], 'generators': [31192, 36233, 39183], 'label': '40320.a.5040.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '5040.be1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66394205
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '5760.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5760.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '1920.a1.a1', '2880.a1.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 960, 'diagramx': [9952, -1, 22, -1, 3340, -1, 6853, -1], 'generators': [9562], 'label': '40320.a.5760.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '960.a1.a1', 'old_label': '5760.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5760.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 66394206
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1120.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.b1.a1', '2240.a1.a1', '2240.b1.a1', '3360.c1.a1', '3360.e1.a1', '3360.g1.a1'], 'contains': ['13440.a1.a1', '20160.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [956, -1, 8671, -1, 8578, -1, 1376, -1], 'generators': [103, 264], 'label': '40320.a.6720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '6720.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394207
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.c1.a1', '2240.a1.a1', '3360.a1.a1', '3360.b1.a1', '3360.d1.a1'], 'contains': ['13440.b1.a1', '20160.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [6212, -1, 5037, -1, 6012, -1, 3996, -1], 'generators': [29704, 24], 'label': '40320.a.6720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '6720.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394208
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.a1.a1', '1680.j1.a1', '2240.b1.a1', '3360.f1.a1', '3360.g1.a1'], 'contains': ['13440.a1.a1', '20160.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [447, -1, 9224, -1, 8665, -1, 1133, -1], 'generators': [384, 264], 'label': '40320.a.6720.c1.a1', 'mobius_quo': None, 'mobius_sub': -120, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '6720.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394209
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.k1.a1', '1680.l1.a1', '1680.p1.a1', '2240.c1.a1', '3360.a1.a1', '3360.h1.a1', '3360.k1.a1'], 'contains': ['13440.b1.a1', '20160.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8797, -1, 1202, -1, 4169, -1, 5736, -1], 'generators': [34378, 32924], 'label': '40320.a.6720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '6720.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394210
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.o1.a1', '1680.q1.a1', '2240.c1.a1', '3360.b1.a1', '3360.i1.a1', '3360.k1.a1'], 'contains': ['13440.b1.a1', '20160.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [8474, -1, 1450, -1, 4325, -1, 5447, -1], 'generators': [36654, 33046], 'label': '40320.a.6720.e1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '6720.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394211
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.b1.a1', '1680.m1.a1', '2240.d1.a1', '3360.e1.a1', '3360.f1.a1', '3360.l1.a1', '3360.m1.a1', '3360.n1.a1', '3360.p1.a1', '3360.s1.a1'], 'contains': ['13440.a1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1280, -1, 8854, -1, 7666, -1, 2376, -1], 'generators': [5094, 15], 'label': '40320.a.6720.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '6720.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394212
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.d1.a1', '1680.w1.a1', '2240.d1.a1', '2240.e1.a1', '3360.c1.a1', '3360.g1.a1', '3360.s1.a1'], 'contains': ['13440.a1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [1930, -1, 8208, -1, 8492, -1, 1619, -1], 'generators': [3, 1561], 'label': '40320.a.6720.g1.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.g1.a1', 'old_label': '6720.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394213
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.e1.a1', '1680.n1.a1', '1680.x1.a1', '1680.x2.a1', '2240.e1.a1', '3360.d1.a1', '3360.k1.a1', '3360.o1.a1'], 'contains': ['13440.b1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [7239, -1, 2779, -1, 5327, -1, 4500, -1], 'generators': [34837, 4475], 'label': '40320.a.6720.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '6720.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394214
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '210.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.a1.a1'], 'contains': ['420.a1.a1', '420.b1.a1', '420.d1.a1', '420.e1.a1', '420.f1.a1', '420.g1.a1', '420.h1.a1', '630.b1.a1', '840.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2520, -1, 7701, -1, 6658, -1, 3549, -1], 'generators': [103, 4527, 21048, 3109, 31376, 54, 10814], 'label': '40320.a.210.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '210.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 66394215
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1.a1', '1680.g1.a1', '2240.f1.a1', '3360.a1.a1', '3360.i1.a1', '3360.o1.a1'], 'contains': ['13440.b1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [7963, -1, 1944, -1, 5887, -1, 4171, -1], 'generators': [617, 572], 'label': '40320.a.6720.i1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '6720.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394216
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.c1.a1', '1680.r1.a1', '2240.g1.a1', '3360.c1.a1', '3360.f1.a1', '3360.l1.a1'], 'contains': ['13440.a1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2575, -1, 7360, -1, 8250, -1, 1790, -1], 'generators': [143, 3032], 'label': '40320.a.6720.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '6720.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394217
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3360.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.s1.a1', '2240.f1.a1', '3360.b1.a1', '3360.h1.a1', '3360.o1.a1'], 'contains': ['13440.b1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [7806, -1, 2137, -1, 5681, -1, 4278, -1], 'generators': [348, 572], 'label': '40320.a.6720.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '6720.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394218
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '6720.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.t1.a1', '2240.g1.a1', '3360.d1.a1', '3360.h1.a1', '3360.i1.a1'], 'contains': ['13440.b1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [8023, -1, 1874, -1, 5752, -1, 4349, -1], 'generators': [5576, 9905], 'label': '40320.a.6720.k2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1680.a1.a1', 'old_label': '6720.k2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.k2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394219
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '8064.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2688.a1.a1', '4032.a1.a1', '4032.b1.a1', '4032.c1.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [160, -1, 8730, -1, 8908, -1, 1036, -1], 'generators': [4446], 'label': '40320.a.8064.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '8064.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8064.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 66394220
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.a1.a1', '3360.b1.a1', '5040.a1.a1', '5040.e1.a1'], 'contains': ['20160.a1.a1', '20160.b1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7047, -1, 3047, -1, 5171, -1, 4576, -1], 'generators': [40295, 24], 'label': '40320.a.10080.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '10080.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394221
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2016.a1.a1', '3360.c1.a1', '3360.d1.a1', '3360.f1.a1', '5040.a1.a1', '5040.b1.a1', '5040.c1.a1', '5040.d1.a1', '5040.d2.a1', '5040.e1.a1', '5040.i1.a1'], 'contains': ['20160.a1.a1', '20160.c1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3308, -1, 6156, -1, 5483, -1, 4424, -1], 'generators': [341, 264], 'label': '40320.a.10080.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '10080.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394222
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.e1.a1', '3360.g1.a1', '5040.e1.a1', '5040.f1.a1', '5040.g1.a1', '5040.h1.a1', '5040.i1.a1'], 'contains': ['20160.a1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2779, -1, 7240, -1, 5403, -1, 4793, -1], 'generators': [288, 264], 'label': '40320.a.10080.c1.a1', 'mobius_quo': None, 'mobius_sub': -96, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '10080.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394223
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5040.e1.a1', '5040.j1.a1', '5040.k1.a1', '5040.l1.a1', '5040.m1.a1', '5040.n1.a1', '5040.o1.a1', '5040.v1.a1', '5040.w1.a1', '5040.y1.a1'], 'contains': ['20160.b1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6443, -1, 3716, -1, 2985, -1, 7090, -1], 'generators': [269, 5356], 'label': '40320.a.10080.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '10080.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394224
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.h1.a1', '3360.i1.a1', '5040.a1.a1', '5040.j1.a1', '5040.p1.a1'], 'contains': ['20160.b1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [8721, -1, 1281, -1, 4509, -1, 5579, -1], 'generators': [3444, 40295], 'label': '40320.a.10080.e1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.b1.a1', 'old_label': '10080.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394225
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '210.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.a1.a1'], 'contains': ['420.j2.a1', '630.f1.a1', '840.k1.a1', '840.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [9142, -1, 523, -1, 1241, -1, 8703, -1], 'generators': [14493, 3823, 4527, 60, 32, 36899, 23616], 'label': '40320.a.210.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.c1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394226
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5040.l1.a1', '5040.p1.a1', '5040.q1.a1', '5040.r1.a1', '5040.v1.a1', '5040.x1.a1', '5040.z1.a1'], 'contains': ['20160.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9505, -1, 445, -1, 559, -1, 9441, -1], 'generators': [39541, 5356], 'label': '40320.a.10080.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.f1.a1', 'old_label': '10080.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394227
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.k1.a1', '5040.a1.a1', '5040.f1.a1', '5040.s1.a1', '5040.t1.a1', '5040.u1.a1', '5040.w1.a1', '5040.y1.a1'], 'contains': ['20160.b1.a1', '20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6812, -1, 3294, -1, 3588, -1, 6200, -1], 'generators': [32924, 33046], 'label': '40320.a.10080.g1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '10080.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394228
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.j1.a1', '5040.v1.a1', '5040.x1.a1', '5040.y1.a1', '5040.z1.a1', '5040.ba1.a1'], 'contains': ['20160.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [9238, -1, 837, -1, 1095, -1, 8905, -1], 'generators': [21769, 32924], 'label': '40320.a.10080.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.d1.a1', 'old_label': '10080.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394229
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.l1.a1', '3360.o1.a1', '5040.a1.a1', '5040.d1.a1', '5040.g1.a1', '5040.j1.a1', '5040.bb1.a1', '5040.bc1.a1', '5040.bd1.a1'], 'contains': ['20160.c1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [5335, -1, 4370, -1, 4980, -1, 5037, -1], 'generators': [647, 572], 'label': '40320.a.10080.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '10080.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394230
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5040.d2.a1', '5040.e1.a1', '5040.j1.a1', '5040.s1.a1', '5040.t1.a1', '5040.bb1.a1', '5040.bd2.a1'], 'contains': ['20160.c1.a1', '20160.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5268, -1, 4772, -1, 4072, -1, 5930, -1], 'generators': [3031, 10825], 'label': '40320.a.10080.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '10080.i2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.i2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394231
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2016.b1.a1', '3360.m1.a1', '5040.b1.a1', '5040.h1.a1', '5040.k1.a1', '5040.s1.a1', '5040.bc1.a1'], 'contains': ['20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2990, -1, 6678, -1, 5058, -1, 4868, -1], 'generators': [360, 288], 'label': '40320.a.10080.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '10080.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394232
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.j1.a1', '5040.c1.a1', '5040.f1.a1', '5040.k1.a1', '5040.m1.a1', '5040.t1.a1', '5040.bd1.a1', '5040.bd2.a1'], 'contains': ['20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3676, -1, 5878, -1, 3996, -1, 6005, -1], 'generators': [39183, 25769], 'label': '40320.a.10080.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.b1.a1', 'old_label': '10080.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394233
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1120.k1.a1', '2016.c1.a1', '3360.n1.a1', '5040.b1.a1', '5040.c1.a1', '5040.g1.a1', '5040.n1.a1', '5040.u1.a1', '5040.bb1.a1', '5040.be1.a1'], 'contains': ['20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3877, -1, 6557, -1, 4905, -1, 5112, -1], 'generators': [35508, 29821], 'label': '40320.a.10080.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1260.e1.a1', 'old_label': '10080.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394234
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.p1.a1', '3360.q1.a1', '3360.r2.a1', '5040.d1.a1', '5040.h1.a1', '5040.w1.a1', '5040.bd2.a1', '5040.be1.a1'], 'contains': ['20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2916, -1, 6773, -1, 5252, -1, 4712, -1], 'generators': [82, 55], 'label': '40320.a.10080.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '10080.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394235
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '10080.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3360.r1.a1', '3360.s1.a1', '5040.d2.a1', '5040.i1.a1', '5040.o1.a1', '5040.u1.a1', '5040.bc1.a1', '5040.bd1.a1', '5040.be1.a1'], 'contains': ['20160.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4260, -1, 4525, -1, 4694, -1, 5254, -1], 'generators': [5094, 5041], 'label': '40320.a.10080.m2.a1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '10080.m2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.m2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66394236
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '210.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '70.c1.a1'], 'contains': ['420.i1.a1', '420.j1.a1', '420.k1.a1', '630.g1.a1', '840.t1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8602, -1, 1474, -1, 2257, -1, 7879, -1], 'generators': [29714, 21769, 32924, 19342, 15852, 3758, 36273], 'label': '40320.a.210.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.d1.a1', 'old_label': '210.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.d1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394237
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '13440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2688.a1.a1', '3360.q1.a1', '4480.a1.a1', '6720.a1.a1', '6720.c1.a1', '6720.f1.a1', '6720.g1.a1', '6720.j1.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1079, -1, 8837, -1, 8250, -1, 1790, -1], 'generators': [104], 'label': '40320.a.13440.a1.a1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '13440.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394256
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '168.a1.a1'], 'contains': ['672.e1.a1', '1680.c1.a1', '2016.a1.a1', '3360.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [5385, -1, 4730, -1, 5690, -1, 4284, -1], 'generators': [4863, 24, 32223], 'label': '40320.a.336.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394238
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '13440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1920.a1.a1', '3360.j1.a1', '3360.r1.a1', '3360.r2.a1', '4480.a1.a1', '6720.b1.a1', '6720.d1.a1', '6720.e1.a1', '6720.h1.a1', '6720.i1.a1', '6720.k1.a1', '6720.k2.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [7882, -1, 2028, -1, 5327, -1, 4500, -1], 'generators': [39876], 'label': '40320.a.13440.b1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '560.a1.a1', 'old_label': '13440.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13440.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66394239
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '20160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4032.a1.a1', '6720.a1.a1', '6720.b1.a1', '6720.c1.a1', '10080.a1.a1', '10080.b1.a1', '10080.c1.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2492, -1, 6915, -1, 5798, -1, 4156, -1], 'generators': [264], 'label': '40320.a.20160.a1.a1', 'mobius_quo': None, 'mobius_sub': 720, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '20160.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394240
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '20160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6720.d1.a1', '6720.e1.a1', '10080.a1.a1', '10080.d1.a1', '10080.e1.a1', '10080.f1.a1', '10080.g1.a1', '10080.h1.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8474, -1, 1219, -1, 4169, -1, 5736, -1], 'generators': [21769], 'label': '40320.a.20160.b1.a1', 'mobius_quo': None, 'mobius_sub': 96, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '20160.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394241
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '20160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4032.b1.a1', '6720.f1.a1', '6720.g1.a1', '6720.h1.a1', '10080.b1.a1', '10080.c1.a1', '10080.d1.a1', '10080.g1.a1', '10080.i1.a1', '10080.i2.a1', '10080.j1.a1', '10080.k1.a1', '10080.l1.a1', '10080.m1.a1', '10080.m2.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3413, -1, 6310, -1, 5155, -1, 4830, -1], 'generators': [82], 'label': '40320.a.20160.c1.a1', 'mobius_quo': None, 'mobius_sub': 96, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '20160.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394242
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '20160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.a1.a1', '4032.c1.a1', '6720.i1.a1', '6720.j1.a1', '6720.k1.a1', '6720.k2.a1', '10080.a1.a1', '10080.b1.a1', '10080.e1.a1', '10080.i1.a1', '10080.i2.a1'], 'contains': ['40320.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7106, -1, 3492, -1, 5513, -1, 4386, -1], 'generators': [572], 'label': '40320.a.20160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '20160.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394243
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '40320.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': ['5760.a1.a1', '8064.a1.a1', '13440.a1.a1', '13440.b1.a1', '20160.a1.a1', '20160.b1.a1', '20160.c1.a1', '20160.d1.a1'], 'contains': [], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5237, 5000, 5114, 5000, 5405, 5000, 4462, 5000], 'generators': [], 'label': '40320.a.40320.a1.a1', 'mobius_quo': 1, 'mobius_sub': -20160, 'normal_closure': '40320.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '40320.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66394244
    {'ambient': '40320.a', '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': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16.a1.a1', '56.c1.a1', '168.b1.a1', '280.b1.a1', '960.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': '8T50', 'count': 8, 'diagramx': [4685, -1, 6982, -1, 6936, -1, 3258, -1], 'generators': [54, 1458], 'label': '40320.a.8.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '40320.a', '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': '5040.w'}
  • id: 66394245
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '210.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '105.a1.a1'], 'contains': ['420.j2.a1', '630.g1.a1', '840.q1.a1', '840.t1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8770, -1, 1205, -1, 1553, -1, 8390, -1], 'generators': [34378, 28662, 21769, 32924, 19342, 39024, 33046], 'label': '40320.a.210.d2.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '210.d2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.d2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394246
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '112.b1.a1', '112.c1.a1'], 'contains': ['672.d1.a1', '1120.h1.a1', '1344.b1.a1', '2240.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [808, -1, 8232, -1, 9100, -1, 682, -1], 'generators': [3750, 39853, 13016], 'label': '40320.a.224.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '224.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '240.189'}
  • id: 66394247
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1'], 'contains': ['720.a1.a1', '1680.p1.a1', '1920.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9731, -1, 242, -1, 1637, -1, 8460, -1], 'generators': [13926, 21769, 32924, 19342, 23728], 'label': '40320.a.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 66394248
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '120.a1.a1'], 'contains': ['1680.q1.a1', '1920.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9621, -1, 767, -1, 2787, -1, 7665, -1], 'generators': [29947, 9039], 'label': '40320.a.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '336.208'}
  • id: 66394249
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '30.a1.a1'], 'contains': ['1680.x1.a1', '1680.x2.a1', '1920.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [7245, -1, 3224, -1, 4117, -1, 5856, -1], 'generators': [23299, 31166], 'label': '40320.a.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.c1.a1', 'old_label': '240.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 66394250
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '280.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['560.a1.a1', '560.b1.a1', '560.d1.a1', '560.f1.a1', '560.g1.a1', '560.h1.a1', '560.i1.a1', '2520.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4438, -1, 5341, -1, 6234, -1, 3711, -1], 'generators': [34142, 13504, 5675, 33905, 24, 5], 'label': '40320.a.280.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '280.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394251
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '280.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '56.b1.a1', '70.a1.a1'], 'contains': ['560.c1.a1', '560.e1.a1', '560.j1.a1', '840.h1.a1', '840.j1.a1', '1120.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1349, -1, 9025, -1, 8443, -1, 1940, -1], 'generators': [627, 1640, 639, 80, 403, 21], 'label': '40320.a.280.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '280.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 66394252
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '280.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.a1.a1', '140.b1.a1', '140.c1.a1'], 'contains': ['840.r1.a1', '840.s1.a1', '1120.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3140, -1, 7140, -1, 6083, -1, 4181, -1], 'generators': [721, 15966, 1232, 21048, 4264, 48], 'label': '40320.a.280.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '280.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394253
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '315.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1.a1', '105.a1.a1'], 'contains': ['630.a1.a1', '630.b1.a1', '630.c1.a1', '630.d1.a1', '630.e1.a1', '630.f1.a1', '630.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6478, -1, 3025, -1, 1095, -1, 8850, -1], 'generators': [4527, 60, 3109, 31376, 54, 6479, 10814], 'label': '40320.a.315.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '315.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '315.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394254
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '112.a1.a1', '168.b1.a1'], 'contains': ['672.d1.a1', '1680.b1.a1', '2016.a1.a1', '3360.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [963, -1, 7401, -1, 9462, -1, 511, -1], 'generators': [510, 3872, 21], 'label': '40320.a.336.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.b1.a1', 'old_label': '336.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394255
    {'ambient': '40320.a', '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': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '8.a1.a1'], 'contains': ['112.d1.a1', '240.c1.a1', '336.g1.a1', '560.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': '16T1838', 'count': 8, 'diagramx': [4662, -1, 6929, -1, 7055, -1, 3207, -1], 'generators': [1614, 5080], 'label': '40320.a.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '40320.a', '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': '5040.w'}
  • id: 66394257
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1'], 'contains': ['672.a1.a1', '672.b1.a1', '672.c1.a1', '1008.a1.a1', '1680.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [2629, -1, 8772, -1, 8033, -1, 1770, -1], 'generators': [30326, 13712, 30, 24, 31743], 'label': '40320.a.336.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '336.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 66394258
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '112.b1.a1', '168.b1.a1'], 'contains': ['672.d1.a1', '1680.j1.a1', '2016.b1.a1', '3360.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [653, -1, 8453, -1, 8961, -1, 784, -1], 'generators': [149, 54], 'label': '40320.a.336.d1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '336.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394259
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '168.a1.a1'], 'contains': ['672.e1.a1', '1680.o1.a1', '2016.c1.a1', '3360.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [6920, -1, 2852, -1, 4237, -1, 5736, -1], 'generators': [38579, 9624], 'label': '40320.a.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '336.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394260
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '168.a1.a1'], 'contains': ['672.e1.a1', '1680.s1.a1', '2016.b1.a1', '3360.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [6659, -1, 3316, -1, 5476, -1, 4386, -1], 'generators': [289, 597], 'label': '40320.a.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '336.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394261
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.d1.a1', '112.c1.a1', '168.b1.a1'], 'contains': ['672.d1.a1', '1680.w1.a1', '2016.c1.a1', '3360.s1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [2718, -1, 8031, -1, 8815, -1, 1158, -1], 'generators': [5131, 5054], 'label': '40320.a.336.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.b1.a1', 'old_label': '336.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394262
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.b1.a1'], 'contains': ['840.d1.a1', '840.m1.a1', '840.o1.a1', '1260.b1.a1', '1680.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3651, -1, 7536, -1, 6541, -1, 3549, -1], 'generators': [31400, 103, 4527, 3109, 21410, 11102], 'label': '40320.a.420.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 66394263
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.a1.a1', '210.b1.a1'], 'contains': ['840.d1.a1', '840.n1.a1', '840.r1.a1', '1260.d1.a1', '1680.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2073, -1, 9257, -1, 6658, -1, 3361, -1], 'generators': [4527, 31106, 3109, 31376, 54, 10814], 'label': '40320.a.420.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 66394264
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '105.a1.a1'], 'contains': ['840.a1.a1', '840.c1.a1', '840.e1.a1', '840.f1.a1', '840.g1.a1', '840.k1.a1', '840.q1.a1', '1260.e1.a1', '1680.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7168, -1, 2713, -1, 4590, -1, 5346, -1], 'generators': [36875, 722, 14435, 36873, 24, 8461], 'label': '40320.a.420.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '420.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394265
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.b1.a1'], 'contains': ['840.i1.a1', '840.n1.a1', '840.o1.a1', '1260.a1.a1', '1680.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2877, -1, 8460, -1, 6424, -1, 3889, -1], 'generators': [103, 4527, 3109, 21410, 11102, 54], 'label': '40320.a.420.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394266
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['56.a1.a1', '56.c1.a1', '56.d1.a1', '168.a1.a1', '168.b1.a1', '280.a1.a1', '420.c1.a1', '420.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': '28T502', 'count': 28, 'diagramx': [4861, -1, 5449, -1, 5988, -1, 4241, -1], 'generators': [36875, 24, 39665], 'label': '40320.a.28.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 66394267
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.a1.a1', '210.b1.a1'], 'contains': ['840.i1.a1', '840.m1.a1', '840.r1.a1', '1260.d1.a1', '1680.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2336, -1, 7277, -1, 6946, -1, 3052, -1], 'generators': [103, 4527, 3109, 31376, 54, 10814], 'label': '40320.a.420.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '420.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 66394268
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '210.b1.a1'], 'contains': ['840.b1.a1', '840.d1.a1', '840.i1.a1', '840.j1.a1', '840.p1.a1', '1260.e1.a1', '1680.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1949, -1, 7839, -1, 7582, -1, 2371, -1], 'generators': [36875, 39573, 39183, 40295, 24, 3032], 'label': '40320.a.420.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394269
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.b1.a1'], 'contains': ['840.m1.a1', '840.n1.a1', '840.p1.a1', '1260.g1.a1', '1680.u1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2515, -1, 7645, -1, 7088, -1, 3212, -1], 'generators': [31400, 103, 4527, 21048, 3109, 21410], 'label': '40320.a.420.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.g1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 66394270
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.b1.a1', '210.b1.a1'], 'contains': ['840.o1.a1', '840.p1.a1', '840.r1.a1', '1260.o1.a1', '1680.v1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3005, -1, 8626, -1, 5992, -1, 4006, -1], 'generators': [721, 15966, 21048, 4264, 566, 48], 'label': '40320.a.420.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '420.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.h1.a1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 66394271
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.b1.a1', '210.d1.a1'], 'contains': ['840.s1.a1', '1260.o1.a1', '1680.n1.a1', '1680.x2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7610, -1, 3479, -1, 2567, -1, 7768, -1], 'generators': [39309, 18968, 19342, 15852, 3758, 36273], 'label': '40320.a.420.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.d1.a1', 'old_label': '420.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.i1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394272
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.c1.a1', '210.d1.a1'], 'contains': ['840.s1.a1', '1260.p1.a1', '1680.p1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8586, -1, 1573, -1, 2101, -1, 8035, -1], 'generators': [13075, 16703, 576, 35152, 25181, 11536], 'label': '40320.a.420.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.d1.a1', 'old_label': '420.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.j1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394273
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.a1.a1', '210.c1.a1', '210.d2.a1'], 'contains': ['1260.p2.a1', '1680.k1.a1', '1680.l1.a1', '1680.p1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [9192, -1, 523, -1, 1415, -1, 8529, -1], 'generators': [34378, 28662, 21769, 32924, 19342, 39024], 'label': '40320.a.420.j2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '420.j2.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.j2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394274
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '420.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.c1.a1', '210.d1.a1'], 'contains': ['840.s1.a1', '1260.p1.a1', '1680.q1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [8395, -1, 1382, -1, 2257, -1, 7879, -1], 'generators': [39309, 29714, 19342, 15852, 3758, 36273], 'label': '40320.a.420.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.c1.a1', 'old_label': '420.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.k1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}
  • id: 66394275
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.a1.a1'], 'contains': ['1120.a1.a1', '1120.b1.a1', '1120.f1.a1', '1120.g1.a1', '1120.i1.a1', '1680.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [8037, -1, 1920, -1, 6569, -1, 3271, -1], 'generators': [34142, 13504, 5675, 33905, 24], 'label': '40320.a.560.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394276
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '280.a1.a1'], 'contains': ['1120.b1.a1', '1120.j1.a1', '1120.k1.a1', '5040.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4094, -1, 5668, -1, 5853, -1, 4121, -1], 'generators': [39062, 25745, 34023, 39183, 24], 'label': '40320.a.560.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394277
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['210.d1.a1', '210.d2.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': '30T1153', 'count': 30, 'diagramx': [8754, -1, 1228, -1, 2515, -1, 7779, -1], 'generators': [9039, 19342, 21769, 19246, 32924], 'label': '40320.a.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1344.11686'}
  • id: 66394278
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '140.a1.a1', '280.b1.a1'], 'contains': ['1120.h1.a1', '1680.b1.a1', '1680.h1.a1', '2240.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1349, -1, 9159, -1, 8714, -1, 1259, -1], 'generators': [627, 1640, 639, 80, 403], 'label': '40320.a.560.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '560.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 66394279
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1.a1', '280.a1.a1'], 'contains': ['1120.e1.a1', '1120.g1.a1', '1120.j1.a1', '5040.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3906, -1, 5872, -1, 5008, -1, 4795, -1], 'generators': [5699, 34142, 13504, 33905, 5], 'label': '40320.a.560.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394280
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '140.a1.a1', '280.b1.a1'], 'contains': ['1120.h1.a1', '1680.e1.a1', '1680.j1.a1', '2240.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1145, -1, 9709, -1, 8582, -1, 1940, -1], 'generators': [627, 1640, 639, 403, 21], 'label': '40320.a.560.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '560.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394281
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '280.a1.a1'], 'contains': ['1120.e1.a1', '1120.i1.a1', '1120.k1.a1', '5040.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4312, -1, 6063, -1, 6720, -1, 3120, -1], 'generators': [316, 639, 233, 120, 237], 'label': '40320.a.560.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394282
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '280.a1.a1'], 'contains': ['1120.b1.a1', '1120.c1.a1', '1120.d1.a1', '1120.e1.a1', '1120.l1.a1', '1680.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1654, -1, 8350, -1, 9244, -1, 934, -1], 'generators': [34142, 13504, 33905, 24, 5], 'label': '40320.a.560.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394283
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '280.a1.a1'], 'contains': ['1120.g1.a1', '1120.k1.a1', '1120.l1.a1', '5040.u1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4734, -1, 5125, -1, 5157, -1, 4533, -1], 'generators': [21045, 34990, 3766, 141, 3032], 'label': '40320.a.560.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394284
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.a1.a1'], 'contains': ['1120.i1.a1', '1120.j1.a1', '1120.l1.a1', '5040.bd1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [4436, -1, 5249, -1, 6380, -1, 3423, -1], 'generators': [34142, 29, 13504, 5675, 33905], 'label': '40320.a.560.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.a1.a1', 'old_label': '560.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 66394285
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '560.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '112.c1.a1', '140.b1.a1', '280.b1.a1'], 'contains': ['1120.h1.a1', '1680.v1.a1', '1680.w1.a1', '1680.x2.a1', '2240.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [3207, -1, 7035, -1, 7885, -1, 2089, -1], 'generators': [8070, 27630, 15961, 15, 18246], 'label': '40320.a.560.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '280.b1.a1', 'old_label': '560.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 66394286
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['315.a1.a1'], 'contains': ['1260.f1.a1', '1260.l1.a1', '1260.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8195, -1, 1763, -1, 681, -1, 9263, -1], 'generators': [4527, 60, 7812, 54, 34430, 10814], 'label': '40320.a.630.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394287
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.b1.a1', '315.a1.a1'], 'contains': ['1260.a1.a1', '1260.b1.a1', '1260.c1.a1', '1260.d1.a1', '1260.e1.a1', '1260.f1.a1', '1260.g1.a1', '1260.j1.a1', '1260.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5805, -1, 4675, -1, 2353, -1, 7533, -1], 'generators': [4527, 21048, 3109, 31376, 54, 10814], 'label': '40320.a.630.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 66394288
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '35.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['70.a1.a1', '70.b1.a1', '70.c1.a1', '315.a1.a1', '560.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': '35T44', 'count': 35, 'diagramx': [4104, -1, 3277, -1, 5259, -1, 4711, -1], 'generators': [10814, 6479, 4527, 31376, 3109, 21048, 31106, 103, 54], 'label': '40320.a.35.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1.a1', 'old_label': '35.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '35.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157849'}
  • id: 66394289
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.a1.a1', '315.a1.a1'], 'contains': ['1260.f1.a1', '1260.k1.a1', '1260.p2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6710, -1, 2905, -1, 1103, -1, 8840, -1], 'generators': [4527, 60, 54, 6479, 34430, 10814], 'label': '40320.a.630.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1.a1', 'old_label': '630.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.c1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 66394290
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['315.a1.a1'], 'contains': ['1260.j1.a1', '1260.k1.a1', '1260.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6469, -1, 3162, -1, 812, -1, 9133, -1], 'generators': [31400, 4527, 60, 6479, 34430, 10814], 'label': '40320.a.630.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394291
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.b1.a1', '315.a1.a1'], 'contains': ['1260.k1.a1', '1260.l1.a1', '1260.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6361, -1, 3270, -1, 942, -1, 9002, -1], 'generators': [4527, 60, 3109, 31376, 6479, 10814], 'label': '40320.a.630.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394292
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.c1.a1', '315.a1.a1'], 'contains': ['1260.h1.a1', '1260.i1.a1', '1260.j1.a1', '1260.l1.a1', '1260.p2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [9015, -1, 1013, -1, 522, -1, 9423, -1], 'generators': [31400, 4527, 60, 7812, 34430, 10814], 'label': '40320.a.630.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394293
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '630.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.d1.a1', '210.d2.a1', '315.a1.a1'], 'contains': ['1260.m1.a1', '1260.n1.a1', '1260.o1.a1', '1260.p1.a1', '1260.p2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8652, -1, 1397, -1, 1274, -1, 8670, -1], 'generators': [28662, 21769, 32924, 19342, 39024, 33046], 'label': '40320.a.630.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1.a1', 'old_label': '630.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 66394294
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '336.c1.a1'], 'contains': ['1344.a1.a1', '1344.b1.a1', '1344.c1.a1', '2016.a1.a1', '3360.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [600, -1, 7695, -1, 9942, -1, 58, -1], 'generators': [30, 4985, 24, 34672], 'label': '40320.a.672.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '672.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 66394295
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13440.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '336.c1.a1'], 'contains': ['1344.b1.a1', '2016.b1.a1', '3360.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [1476, -1, 9608, -1, 8396, -1, 1606, -1], 'generators': [13712, 30, 30320, 31743], 'label': '40320.a.672.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '672.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 66394296
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '336.c1.a1'], 'contains': ['1344.b1.a1', '2016.c1.a1', '3360.n1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [3260, -1, 9034, -1, 7764, -1, 2104, -1], 'generators': [657, 3750, 18460, 263], 'label': '40320.a.672.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '336.c1.a1', 'old_label': '672.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 66394297
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6720.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '224.a1.a1', '336.a1.a1', '336.d1.a1', '336.g1.a1'], 'contains': ['3360.q1.a1', '4032.b1.a1', '6720.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [848, -1, 7887, -1, 9249, -1, 673, -1], 'generators': [4472, 1565], 'label': '40320.a.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '672.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394298
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '336.b1.a1', '336.e1.a1', '336.f1.a1'], 'contains': ['3360.r1.a1', '4032.b1.a1', '6720.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [6841, -1, 3739, -1, 5724, -1, 4277, -1], 'generators': [26149, 30448], 'label': '40320.a.672.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '672.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
  • id: 66394299
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.d1.a1', '336.a1.a1', '336.b1.a1', '560.b1.a1', '840.b1.a1', '840.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4552, -1, 5519, -1, 5988, -1, 4119, -1], 'generators': [12993, 3420, 24], 'label': '40320.a.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
  • id: 66394300
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1'], 'contains': ['5040.ba1.a1', '5760.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9761, -1, 110, -1, 1338, -1, 8662, -1], 'generators': [16703, 8751, 35152, 11536], 'label': '40320.a.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 66394301
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.a1.a1', '420.c1.a1'], 'contains': ['1680.c1.a1', '1680.o1.a1', '1680.s1.a1', '2520.a1.a1', '3360.b1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6733, -1, 2814, -1, 4734, -1, 5239, -1], 'generators': [40295, 3420, 24, 27304, 39183], 'label': '40320.a.840.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.a1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394302
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '420.f1.a1'], 'contains': ['1680.b1.a1', '1680.r1.a1', '1680.w1.a1', '2520.b1.a1', '3360.c1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3270, -1, 7244, -1, 8241, -1, 1600, -1], 'generators': [2910, 3420, 24, 4142, 36665], 'label': '40320.a.840.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.f1.a1', 'old_label': '840.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394303
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '420.c1.a1'], 'contains': ['1680.c1.a1', '1680.t1.a1', '1680.x1.a1', '2520.b1.a1', '3360.d1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6198, -1, 3806, -1, 4866, -1, 5106, -1], 'generators': [25741, 3420, 24, 4142, 39905], 'label': '40320.a.840.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.c1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394304
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.a1.a1', '420.b1.a1', '420.f1.a1'], 'contains': ['1680.b1.a1', '1680.m1.a1', '2520.g1.a1', '3360.e1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1165, -1, 9428, -1, 7726, -1, 2686, -1], 'generators': [36875, 39573, 40295, 24, 3032], 'label': '40320.a.840.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.d1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394305
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.c1.a1'], 'contains': ['1680.g1.a1', '1680.o1.a1', '1680.t1.a1', '2520.i1.a1', '3360.i1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7141, -1, 2577, -1, 4376, -1, 5597, -1], 'generators': [36875, 722, 36873, 14459, 8461], 'label': '40320.a.840.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.e1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394306
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '420.c1.a1'], 'contains': ['1680.g1.a1', '1680.s1.a1', '1680.x1.a1', '2520.j1.a1', '3360.o1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6999, -1, 2938, -1, 5336, -1, 4974, -1], 'generators': [289, 341, 443, 55, 265], 'label': '40320.a.840.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.f1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394307
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.a1.a1', '420.c1.a1'], 'contains': ['1680.c1.a1', '1680.g1.a1', '1680.k1.a1', '2520.k1.a1', '3360.a1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7369, -1, 2695, -1, 4590, -1, 5453, -1], 'generators': [36875, 722, 36873, 24, 8461], 'label': '40320.a.840.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.g1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394308
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.b1.a1', '280.b1.a1'], 'contains': ['1680.d1.a1', '1680.e1.a1', '1680.f1.a1', '1680.h1.a1', '1680.i1.a1', '1680.u1.a1', '1680.v1.a1', '2520.j1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2496, -1, 7986, -1, 7241, -1, 2542, -1], 'generators': [1640, 639, 80, 403, 21], 'label': '40320.a.840.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.h1.a1', 'old_label': '840.h1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 66394309
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.d1.a1', '420.e1.a1', '420.f1.a1'], 'contains': ['1680.j1.a1', '1680.m1.a1', '1680.r1.a1', '2520.f1.a1', '3360.f1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1976, -1, 7577, -1, 7582, -1, 2200, -1], 'generators': [39597, 39207, 40319, 36899, 3032], 'label': '40320.a.840.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.i1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394310
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.b1.a1', '280.b1.a1', '336.c1.a1', '560.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1417, -1, 8521, -1, 8754, -1, 1259, -1], 'generators': [30, 5094, 24, 15070], 'label': '40320.a.56.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.b1.a1', 'old_label': '56.b1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '720.767'}
  • id: 66394311
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '168.b1.a1', '280.b1.a1', '420.f1.a1'], 'contains': ['1680.b1.a1', '1680.j1.a1', '1680.w1.a1', '2520.j1.a1', '3360.g1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1377, -1, 9278, -1, 8449, -1, 1392, -1], 'generators': [289, 285, 687, 572, 693], 'label': '40320.a.840.j1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.f1.a1', 'old_label': '840.j1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394312
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.c1.a1', '420.c1.a1'], 'contains': ['1680.k1.a1', '1680.s1.a1', '1680.t1.a1', '2520.q1.a1', '3360.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7250, -1, 2467, -1, 4003, -1, 5970, -1], 'generators': [722, 14435, 36873, 36899, 8461], 'label': '40320.a.840.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.k1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394313
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.c1.a1'], 'contains': ['1680.l1.a1', '2520.s1.a1', '3360.h1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [9875, -1, 161, -1, 447, -1, 9611, -1], 'generators': [14493, 2388, 6465, 4499, 32856], 'label': '40320.a.840.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '840.l1.a1', 'old_label': '840.l1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394314
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.a1.a1', '420.e1.a1', '420.g1.a1'], 'contains': ['1680.m1.a1', '1680.r1.a1', '2520.t1.a1', '3360.l1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3690, -1, 6856, -1, 7107, -1, 2829, -1], 'generators': [31400, 103, 4527, 3109, 10814], 'label': '40320.a.840.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.m1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.m1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394315
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.b1.a1', '420.d1.a1', '420.g1.a1'], 'contains': ['1680.m1.a1', '2520.u1.a1', '3360.m1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2245, -1, 9137, -1, 6862, -1, 3564, -1], 'generators': [4527, 3011, 31106, 31376, 10814], 'label': '40320.a.840.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.n1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.n1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394316
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.a1.a1', '420.d1.a1', '420.h1.a1'], 'contains': ['1680.m1.a1', '2520.v1.a1', '3360.n1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3562, -1, 8620, -1, 6070, -1, 3979, -1], 'generators': [1406, 15966, 21048, 4985, 48], 'label': '40320.a.840.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.o1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.o1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394317
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '420.f1.a1', '420.g1.a1', '420.h1.a1'], 'contains': ['1680.m1.a1', '1680.w1.a1', '2520.w1.a1', '3360.s1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2355, -1, 8466, -1, 7450, -1, 2371, -1], 'generators': [35433, 38457, 122, 5160, 5061], 'label': '40320.a.840.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.b1.a1', 'old_label': '840.p1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.p1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 66394318
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '210.d2.a1', '420.c1.a1'], 'contains': ['1680.k1.a1', '1680.o1.a1', '1680.x1.a1', '2520.w1.a1', '3360.k1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7581, -1, 2211, -1, 3789, -1, 6163, -1], 'generators': [1581, 34378, 32924, 32672, 33046], 'label': '40320.a.840.q1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.c1.a1', 'old_label': '840.q1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 66394319
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10080.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.c1.a1', '420.b1.a1', '420.e1.a1', '420.h1.a1'], 'contains': ['1680.m1.a1', '2520.bd1.a1', '3360.p1.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2095, -1, 9018, -1, 6192, -1, 3708, -1], 'generators': [721, 15966, 21048, 4264, 48], 'label': '40320.a.840.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.a1.a1', 'old_label': '840.r1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.r1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 66394320
    {'ambient': '40320.a', 'aut_centralizer_order': None, 'aut_label': '840.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.c1.a1', '420.i1.a1', '420.j1.a1', '420.k1.a1'], 'contains': ['2520.bd1.a1', '3360.j1.a1', '3360.r2.a1'], 'core': '40320.a1.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [7868, -1, 3163, -1, 2684, -1, 7768, -1], 'generators': [39309, 19342, 15852, 3758, 36273], 'label': '40320.a.840.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.c1.a1', 'old_label': '840.s1.a1', 'projective_image': '40320.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.s1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8654'}