Abstract group data - 2688.ci

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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': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 84, 'aut_gen_orders': [4, 4], 'aut_gens': [[8436478210975, 16771720457809], [5612940350783, 1341116577223], [19561376621209, 18065980834702]], 'aut_group': '1344.11686', 'aut_hash': 11686, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1344, 'aut_permdeg': 84, 'aut_perms': [380488078175992058887799732677930994690791404293436444774242996064266775069886005359054358007604687224256214592759973915036665, 280027694351628961747087595978118812871349836604428591556410403442536824284644433318497819812861088122512925028981400111077290], 'aut_phi_ratio': 1.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 14, 1, 1], [2, 84, 1, 1], [3, 224, 1, 1], [4, 84, 1, 1], [4, 168, 1, 1], [4, 336, 1, 1], [6, 224, 1, 3], [7, 192, 1, 2], [8, 336, 1, 1], [14, 192, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3:\\GL(3,2)', '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': 84, 'autcentquo_group': '1344.11686', 'autcentquo_hash': 11686, 'autcentquo_nilpotent': False, 'autcentquo_order': 1344, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^3:\\GL(3,2)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 14, 1], [2, 84, 1], [3, 224, 1], [4, 84, 1], [4, 168, 1], [4, 336, 1], [6, 224, 3], [7, 192, 2], [8, 336, 1], [14, 192, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1344.11686', 'commutator_count': 1, 'commutator_label': '2688.ci', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '168.42'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 61, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 14, 1, 1], [2, 84, 1, 1], [3, 224, 1, 1], [4, 84, 1, 1], [4, 168, 1, 1], [4, 336, 1, 1], [6, 224, 1, 1], [6, 224, 2, 1], [7, 192, 2, 1], [8, 336, 1, 1], [14, 192, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 2736, 'exponent': 168, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 2], [8, 1, 1], [24, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1344.11686', 'hash': 4126924433131064584, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [4, 7], 'inner_gens': [[8436478210975, 18066021114377], [14021941691398, 16771720457809]], 'inner_hash': 11686, 'inner_nilpotent': False, 'inner_order': 1344, 'inner_split': True, 'inner_tex': 'C_2^3:\\GL(3,2)', 'inner_used': [1, 2], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 1], [3, 2], [6, 1], [7, 3], [8, 4], [14, 1], [21, 2], [24, 2]], 'label': '2688.ci', 'linC_count': 3, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 1, 'linQ_dim': 8, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2^4:PSL(2,7)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 16, 'number_divisions': 13, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 129, 'number_subgroup_classes': 129, 'number_subgroups': 5770, 'old_label': None, 'order': 2688, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 99], [3, 224], [4, 588], [6, 672], [7, 384], [8, 336], [14, 384]], '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': True, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [6, 2], [7, 3], [8, 2], [14, 1], [16, 1], [21, 2], [48, 1]], 'representations': {'Perm': {'d': 16, 'gens': [8436478210975, 16771720457809]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4:\\PSL(2,7)', 'transitive_degree': 16, '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: 157248367
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 61, 'group_order': 2688, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 157248375
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 61, 'group_order': 2688, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 1313941673647, 'size': 1}
  • id: 157248376
    {'aut_label': '2B', 'centralizer': '14.c1.a1', 'counter': 3, 'group_counter': 61, 'group_order': 2688, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 1307674731006, 'size': 14}
  • id: 157248377
    {'aut_label': '2C', 'centralizer': '84.d1.a1', 'counter': 4, 'group_counter': 61, 'group_order': 2688, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 15343252226063, 'size': 84}
  • id: 157248378
    {'aut_label': '3A', 'centralizer': '224.a1.a1', 'counter': 5, 'group_counter': 61, 'group_order': 2688, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 8396155773360, 'size': 224}
  • id: 157248379
    {'aut_label': '4A', 'centralizer': '84.a1.a1', 'counter': 6, 'group_counter': 61, 'group_order': 2688, 'label': '4A', 'order': 4, 'powers': [2, 6, 6], 'representative': 12507121227576, 'size': 84}
  • id: 157248380
    {'aut_label': '4B', 'centralizer': '168.h1.a1', 'counter': 7, 'group_counter': 61, 'group_order': 2688, 'label': '4B', 'order': 4, 'powers': [3, 7, 7], 'representative': 16771412488015, 'size': 168}
  • id: 157248381
    {'aut_label': '4C', 'centralizer': '336.g1.a1', 'counter': 8, 'group_counter': 61, 'group_order': 2688, 'label': '4C', 'order': 4, 'powers': [4, 8, 8], 'representative': 4151377416952, 'size': 336}
  • id: 157248382
    {'aut_label': '6A', 'centralizer': '224.a1.a1', 'counter': 9, 'group_counter': 61, 'group_order': 2688, 'label': '6A', 'order': 6, 'powers': [5, 2, 9], 'representative': 1367680176702, 'size': 224}
  • id: 157248368
    {'aut_label': '6B1', 'centralizer': '224.a1.a1', 'counter': 10, 'group_counter': 61, 'group_order': 2688, 'label': '6B1', 'order': 6, 'powers': [5, 3, 10], 'representative': 14002301779201, 'size': 224}
  • id: 157248369
    {'aut_label': '6B-1', 'centralizer': '224.a1.a1', 'counter': 11, 'group_counter': 61, 'group_order': 2688, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 11], 'representative': 8402342872321, 'size': 224}
  • id: 157248370
    {'aut_label': '7A1', 'centralizer': '192.a1.a1', 'counter': 12, 'group_counter': 61, 'group_order': 2688, 'label': '7A1', 'order': 7, 'powers': [12, 13, 1], 'representative': 19528372690417, 'size': 192}
  • id: 157248371
    {'aut_label': '7A-1', 'centralizer': '192.a1.a1', 'counter': 13, 'group_counter': 61, 'group_order': 2688, 'label': '7A-1', 'order': 7, 'powers': [13, 12, 1], 'representative': 2816745966592, 'size': 192}
  • id: 157248372
    {'aut_label': '8A', 'centralizer': '336.j1.a1', 'counter': 14, 'group_counter': 61, 'group_order': 2688, 'label': '8A', 'order': 8, 'powers': [6, 14, 14], 'representative': 14021902132558, 'size': 336}
  • id: 157248373
    {'aut_label': '14A1', 'centralizer': '192.a1.a1', 'counter': 15, 'group_counter': 61, 'group_order': 2688, 'label': '14A1', 'order': 14, 'powers': [12, 16, 2], 'representative': 18078998918831, 'size': 192}
  • id: 157248374
    {'aut_label': '14A-1', 'centralizer': '192.a1.a1', 'counter': 16, 'group_counter': 61, 'group_order': 2688, 'label': '14A-1', 'order': 14, 'powers': [13, 15, 2], 'representative': 6927451747615, 'size': 192}
• 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: 15355081
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.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], 'schur_index': 1}
  • id: 15355086
    {'cdim': 3, 'counter': 2, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.3a', 'multiplicity': 2, 'nt': [42, 37], 'qdim': 6, 'qvalues': [6, 6, 6, -2, 0, -2, -2, 2, 0, 0, 0, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 15355087
    {'cdim': 6, 'counter': 3, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.6a', 'multiplicity': 1, 'nt': [7, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 2, 0, 2, 2, 0, 0, 0, 0, -1, -1, 0, -1, -1], 'schur_index': 1}
  • id: 15355088
    {'cdim': 7, 'counter': 4, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.7a', 'multiplicity': 1, 'nt': [8, 37], 'qdim': 7, 'qvalues': [7, 7, 7, -1, 1, -1, -1, -1, 1, 1, 1, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 15355089
    {'cdim': 7, 'counter': 5, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.7b', 'multiplicity': 1, 'nt': [8, 48], 'qdim': 7, 'qvalues': [7, 7, -1, -1, 1, 3, -1, -1, 1, -1, -1, 0, 0, 1, 0, 0], 'schur_index': 1}
  • id: 15355090
    {'cdim': 7, 'counter': 6, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.7c', 'multiplicity': 1, 'nt': [8, 48], 'qdim': 7, 'qvalues': [7, 7, -1, 3, 1, -1, -1, 1, 1, -1, -1, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 15355091
    {'cdim': 8, 'counter': 7, 'faithful': True, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.8a', 'multiplicity': 1, 'nt': [16, 1506], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, 1, 0, -1, -1], 'schur_index': 1}
  • id: 15355092
    {'cdim': 8, 'counter': 8, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.8b', 'multiplicity': 1, 'nt': [21, 14], 'qdim': 8, 'qvalues': [8, 8, 8, 0, -1, 0, 0, 0, -1, -1, -1, 1, 1, 0, 1, 1], 'schur_index': 1}
  • id: 15355082
    {'cdim': 14, 'counter': 10, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.14a', 'multiplicity': 1, 'nt': [28, 159], 'qdim': 14, 'qvalues': [14, 14, -2, 2, -1, 2, -2, 0, -1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 15355093
    {'cdim': 8, 'counter': 9, 'faithful': True, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.8c', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 2, 0, -2, -2], 'schur_index': 1}
  • id: 15355083
    {'cdim': 21, 'counter': 11, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.21a', 'multiplicity': 1, 'nt': [42, 210], 'qdim': 21, 'qvalues': [21, 21, -3, -3, 0, 1, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 15355084
    {'cdim': 21, 'counter': 12, 'faithful': False, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.21b', 'multiplicity': 1, 'nt': [42, 210], 'qdim': 21, 'qvalues': [21, 21, -3, 1, 0, -3, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0], 'schur_index': 1}
  • id: 15355085
    {'cdim': 24, 'counter': 13, 'faithful': True, 'group': '2688.ci', 'group_order': 2688, 'image': None, 'label': '2688.ci.24a', 'multiplicity': 2, 'nt': [112, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 1], '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: 35188409
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2688, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 2688, 'label': '2688.ci.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]]]}
  • id: 35188417
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 16, 'counter': 2, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '168.42', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1.a1', 'kernel_order': 16, 'label': '2688.ci.3a1', 'nt': [42, 37], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
  • id: 35188418
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 16, 'counter': 3, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '168.42', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1.a1', 'kernel_order': 16, 'label': '2688.ci.3a2', 'nt': [42, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35188419
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 16, 'counter': 4, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '168.42', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 16, 'label': '2688.ci.6a', 'nt': [7, 5], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35188420
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 16, 'counter': 5, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '168.42', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 16, 'label': '2688.ci.7a', 'nt': [8, 37], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188421
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 6, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11686', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1.a1', 'kernel_order': 2, 'label': '2688.ci.7b', 'nt': [8, 48], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188422
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 7, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11686', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1.a1', 'kernel_order': 2, 'label': '2688.ci.7c', 'nt': [8, 48], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188423
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 8, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '2688.ci', 'image_order': 2688, 'indicator': 1, 'kernel': '2688.a1.a1', 'kernel_order': 1, 'label': '2688.ci.8a', 'nt': [16, 1506], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35188424
    {'center': '168.a1.a1', 'center_index': 168, 'center_order': 16, 'counter': 9, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '168.42', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 16, 'label': '2688.ci.8b', 'nt': [21, 14], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 35188410
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 10, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '2688.ci', 'image_order': 2688, 'indicator': 0, 'kernel': '2688.a1.a1', 'kernel_order': 1, 'label': '2688.ci.8c1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35188411
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 11, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '2688.ci', 'image_order': 2688, 'indicator': 0, 'kernel': '2688.a1.a1', 'kernel_order': 1, 'label': '2688.ci.8c2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 35188412
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 12, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11686', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1.a1', 'kernel_order': 2, 'label': '2688.ci.14a', 'nt': [28, 159], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188413
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 13, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11686', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1.a1', 'kernel_order': 2, 'label': '2688.ci.21a', 'nt': [42, 210], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188414
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '1344.11686', 'image_order': 1344, 'indicator': 1, 'kernel': '1344.a1.a1', 'kernel_order': 2, 'label': '2688.ci.21b', 'nt': [42, 210], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 35188415
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 7, 'dim': 24, 'faithful': True, 'field': [2, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '2688.ci', 'image_order': 2688, 'indicator': 0, 'kernel': '2688.a1.a1', 'kernel_order': 1, 'label': '2688.ci.24a1', 'nt': [112, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
  • id: 35188416
    {'center': '1344.a1.a1', 'center_index': 1344, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 7, 'dim': 24, 'faithful': True, 'field': [2, -1, 1], 'group': '2688.ci', 'group_counter': 61, 'group_order': 2688, 'image': None, 'image_isoclass': '2688.ci', 'image_order': 2688, 'indicator': 0, 'kernel': '2688.a1.a1', 'kernel_order': 1, 'label': '2688.ci.24a2', 'nt': [112, 2], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
• 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: 182266843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2688, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '2688.ci.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': True, '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': ['D', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2688.ci', 'subgroup_hash': 4126924433131064584, 'subgroup_order': 2688, 'subgroup_tex': 'C_2^4:\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 182266884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '2688.ci.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.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': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18133', 'subgroup_hash': 18133, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '2688.ci.7.a2.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.5603', 'subgroup_hash': 5603, 'subgroup_order': 384, 'subgroup_tex': 'C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 182266917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.8.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 182266928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.8.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '336.114', 'subgroup_hash': 114, 'subgroup_order': 336, 'subgroup_tex': '\\SL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 182266939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1492', 'subgroup_hash': 1492, 'subgroup_order': 192, 'subgroup_tex': 'Q_8.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': 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: 182266961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1024', 'subgroup_hash': 1024, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.14.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': 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: 182266855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.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': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 182266866
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '168.42', 'subgroup_hash': 42, 'subgroup_order': 168, 'subgroup_tex': '\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
  • id: 182266877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '2688.ci.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.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': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 182266878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 182266879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.28.a1.a1', 'maximal': False, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.190', 'subgroup_hash': 190, 'subgroup_order': 96, 'subgroup_tex': '\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 182266880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': 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: 182266881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': 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: 182266882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': 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: 182266883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': 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: 182266886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': 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: 182266888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': 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: 182266889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.42.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.f2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': 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: 182266891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': 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: 182266892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': 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: 182266893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.b1.a1', 'maximal': False, '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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 182266894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.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': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 182266896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.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': 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: 182266897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 182266903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.28', 'subgroup_hash': 28, 'subgroup_order': 48, 'subgroup_tex': 'C_2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.56.j2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.28', 'subgroup_hash': 28, 'subgroup_order': 48, 'subgroup_tex': 'C_2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 182266905
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 182266907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 182266909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 182266913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 182266916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, '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: 182266920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': 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: 182266921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': 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: 182266922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': 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: 182266923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.c2.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 182266924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.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': False, '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': 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: 182266925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 182266933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.112.i3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.i3.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 182266934
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 21, 'label': '2688.ci.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.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': 128, 'quotient_simple': 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: 182266935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2688.ci.168.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,7)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 182266936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266953
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 182266955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.168.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 182266956
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 182266957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 182266959
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 182266960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 182266962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 182266963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.224.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.e2.a1', 'outer_equivalence': False, 'perfect': False, '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': 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: 182266964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266965
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182266846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182266847
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182266851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 182266852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 182266854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.336.p2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '2688.ci.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, '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: 182266858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, 'quotient_simple': 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: 182266859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.448.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, 'quotient_simple': 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: 182266860
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.448.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '448.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': 448, 'quotient_simple': 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: 182266861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266867
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.672.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 182266869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.h2.a1', 'outer_equivalence': False, 'perfect': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2688.ci.672.h3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.h3.a1', 'outer_equivalence': False, 'perfect': False, '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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 182266872
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '2688.ci.896.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '896.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': 896, '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': 3}
  • id: 182266873
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': True, 'core_order': 2, 'counter': 126, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2688.ci.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1344.11686', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11686, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:\\GL(3,2)', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'S', 'U0', 'C2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 182266874
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.1344.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2688.ci.1344.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 182266876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2688.ci', 'ambient_counter': 61, 'ambient_order': 2688, 'ambient_tex': 'C_2^4:\\PSL(2,7)', 'central': True, 'central_factor': False, 'centralizer_order': 2688, 'characteristic': True, 'core_order': 1, 'counter': 129, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2688.ci.2688.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2688.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '2688.ci', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4126924433131064584, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2688, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:\\PSL(2,7)', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C3'], '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: 182266843
    {'ambient': '2688.ci', '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': '1344.a1.a1', 'complements': ['2688.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['7.a1.a1', '7.a2.a1', '8.a1.a1', '8.b1.a1', '8.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4705, 5000, 5491, 5000, 7699, 5000, 6322, 5000], 'generators': [5633188645697, 40279687, 6227383801, 5167, 2796410977798, 1313941673647], 'label': '2688.ci.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1344.11686', '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': '1344.11686'}
  • id: 182266844
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '14.c2', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a2.a1'], 'contains': ['28.c1.a1', '42.f2.a1', '56.f1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4495, -1, 4578, -1, 5000, -1, 4998, -1], 'generators': [14035577500222, 11226233456334, 40279687, 6227383801, 5167, 11178550679160, 1313941673647], 'label': '2688.ci.14.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '14.c2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266845
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '168.f1.a1', '168.r1.a1'], 'contains': ['672.b1.a1', '672.h1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2300, -1, 6343, -1, 6568, -1, 7591, -1], 'generators': [12540174399054, 15337065127102, 1313941673647], 'label': '2688.ci.336.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.i1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266846
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.i2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.1', 'aut_weyl_index': 224, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c2.a1', '168.g1.a1', '168.q1.a1', '168.r1.a1'], 'contains': ['672.b1.a1', '672.h2.a1', '672.h3.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3624, -1, 7044, -1, 4751, -1, 7395, -1], 'generators': [15337065127102, 8416014572032, 1313941673647], 'label': '2688.ci.336.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '336.i2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 182266847
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '336.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.i1.a1', '168.p1.a1', '168.s1.a1'], 'contains': ['672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6374, -1, 3695, -1, 6117, -1, 3471, -1], 'generators': [14029390391183, 19534340084521, 1313941673647], 'label': '2688.ci.336.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.b1.a1', 'old_label': '336.j1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182266848
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '336.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '168.c1.a1', '168.s1.a1'], 'contains': ['672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6080, -1, 3956, -1, 7397, -1, 4012, -1], 'generators': [14029390391183, 11226233456334, 1313941673647], 'label': '2688.ci.336.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1.a1', 'old_label': '336.k1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266849
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '336.k2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d2.a1', '168.j1.a1', '168.p1.a1', '168.s1.a1'], 'contains': ['672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6714, -1, 4297, -1, 6938, -1, 4184, -1], 'generators': [9723728851798, 14035577500222, 1313941673647], 'label': '2688.ci.336.k2.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': '336.k2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266850
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 448, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.e1.a1', '168.g1.a1'], 'contains': ['672.d1.a1', '672.h2.a1', '672.h3.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3359, -1, 6852, -1, 3594, -1, 6873, -1], 'generators': [14029390396096, 8416014572032, 1307674731006], 'label': '2688.ci.336.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '336.l1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182266851
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 112, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.f1.a1', '168.k1.a1'], 'contains': ['672.e1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [9477, -1, 2277, -1, 353, -1, 2163, -1], 'generators': [8409787909078, 1307674731006, 15343291784903], 'label': '2688.ci.336.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '336.m1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182266852
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.a1', '168.m1.a1'], 'contains': ['672.d1.a1', '672.e1.a1', '672.f1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [7464, -1, 2104, -1, 2591, -1, 3102, -1], 'generators': [8416014572032, 40279687, 1307714284921], 'label': '2688.ci.336.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.m1.a1', 'old_label': '336.n1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182266853
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.h1.a1', '168.a1.a1'], 'contains': ['672.f1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7171, -1, 319, -1, 4212, -1, 3827, -1], 'generators': [40279687, 6227383801, 1313941668480], 'label': '2688.ci.336.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '336.o1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182266854
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.i1.a1', '112.i2.a1', '168.r1.a1'], 'contains': ['672.g1.a1', '672.h1.a1', '672.h2.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1247, -1, 7933, -1, 7112, -1, 8393, -1], 'generators': [14029390396096, 12533907461328, 8416014572032], 'label': '2688.ci.336.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.r1.a1', 'old_label': '336.p1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182266855
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.a1.a1', '112.h1.a1', '128.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': '16T1506', 'count': 8, 'diagramx': [3841, -1, 4096, -1, 7866, -1, 7495, -1], 'generators': [16744502096766, 40279687, 6227383801, 1313941668480, 13994992552729], 'label': '2688.ci.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '2688.ci', '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': '168.43'}
  • id: 182266856
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '336.p2', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.i3.a1', '168.r1.a1'], 'contains': ['672.g1.a1', '672.h1.a1', '672.h3.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1536, -1, 7312, -1, 6291, -1, 8221, -1], 'generators': [12540174399054, 15337065127102, 8416014572032], 'label': '2688.ci.336.p2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.r1.a1', 'old_label': '336.p2.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p2.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 182266857
    {'ambient': '2688.ci', 'aut_centralizer_order': 7, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 448, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '128.a1.a1', '192.a1.a1'], 'contains': ['2688.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [183, -1, 5361, -1, 9447, -1, 9275, -1], 'generators': [16738235159040], 'label': '2688.ci.384.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182266858
    {'ambient': '2688.ci', 'aut_centralizer_order': 6, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '112.b1.a1', '112.c1.a1', '112.c2.a1', '112.d1.a1', '112.d2.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1'], 'contains': ['896.a1.a1', '1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [2675, -1, 8239, -1, 7571, -1, 6622, -1], 'generators': [11172324026286, 1313941673647], 'label': '2688.ci.448.a1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '448.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182266859
    {'ambient': '2688.ci', 'aut_centralizer_order': 6, 'aut_label': '448.b1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1344, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.e1.a1', '112.f1.a1', '112.h1.a1', '224.a1.a1'], 'contains': ['896.a1.a1', '1344.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [4132, -1, 5944, -1, 3842, -1, 5439, -1], 'generators': [11178550679160, 1313901393960], 'label': '2688.ci.448.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '224.a1.a1', 'old_label': '448.b1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182266860
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '448.c1', 'aut_quo_index': None, 'aut_stab_index': 224, 'aut_weyl_group': '6.1', 'aut_weyl_index': 224, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.a1', '112.i1.a1', '112.i2.a1', '112.i3.a1', '224.b1.a1'], 'contains': ['896.a1.a1', '1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 224, 'diagramx': [729, -1, 9925, -1, 7264, -1, 8525, -1], 'generators': [8416014572032, 6967859633585], 'label': '2688.ci.448.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '224.b1.a1', 'old_label': '448.c1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 182266861
    {'ambient': '2688.ci', 'aut_centralizer_order': 96, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '14.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.e1.a1'], 'contains': ['1344.a1.a1', '1344.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6877, -1, 3092, -1, 3342, -1, 3365, -1], 'generators': [40279687, 1313941673647], 'label': '2688.ci.672.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '1344.11686', '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': '2.1'}
  • id: 182266862
    {'ambient': '2688.ci', 'aut_centralizer_order': 16, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.a1', '336.a1.a1', '336.b1.a1', '336.f1.a1', '336.g1.a1', '336.h1.a1', '336.i1.a1', '336.i2.a1'], 'contains': ['1344.a1.a1', '1344.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3748, -1, 5766, -1, 5665, -1, 5791, -1], 'generators': [8416014572032, 1313941673647], 'label': '2688.ci.672.b1.a1', 'mobius_quo': None, 'mobius_sub': 16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '672.b1.a1', 'projective_image': '1344.11686', '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': '2.1'}
  • id: 182266863
    {'ambient': '2688.ci', 'aut_centralizer_order': 16, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.c1.a1', '336.a1.a1', '336.c1.a1', '336.f1.a1', '336.h1.a1', '336.j1.a1', '336.k1.a1', '336.k2.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5703, -1, 4327, -1, 6117, -1, 4184, -1], 'generators': [9723728851798, 1313941673647], 'label': '2688.ci.672.c1.a1', 'mobius_quo': None, 'mobius_sub': 16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '672.c1.a1', 'projective_image': '1344.11686', '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': '2.1'}
  • id: 182266864
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.b1.a1', '336.l1.a1', '336.n1.a1'], 'contains': ['1344.b1.a1', '1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6374, -1, 3418, -1, 3144, -1, 3839, -1], 'generators': [8416014572032, 1307674731006], 'label': '2688.ci.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.i1.a1', 'old_label': '672.d1.a1', 'projective_image': '2688.ci', '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': '2.1'}
  • id: 182266865
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '168.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.d1.a1', '336.m1.a1', '336.n1.a1'], 'contains': ['1344.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [8449, -1, 2149, -1, 2095, -1, 2604, -1], 'generators': [8409787909078, 1307674731006], 'label': '2688.ci.672.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.e2.a1', 'old_label': '672.e1.a1', 'projective_image': '2688.ci', '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': '2.1'}
  • id: 182266866
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.42', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['112.i1.a1', '112.i2.a1', '128.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': '16T1507', 'count': 8, 'diagramx': [508, -1, 9484, -1, 8946, -1, 9629, -1], 'generators': [5639415298583, 4104045423952], 'label': '2688.ci.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 182266867
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.1', 'aut_weyl_index': 224, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.d1.a1', '336.e1.a1', '336.n1.a1', '336.o1.a1'], 'contains': ['1344.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6696, -1, 1838, -1, 3540, -1, 3643, -1], 'generators': [40279687, 1307714289846], 'label': '2688.ci.672.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '672.f1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 182266868
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '672.g1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.g1.a1', '336.p1.a1', '336.p2.a1'], 'contains': ['1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [2160, -1, 7352, -1, 5943, -1, 7773, -1], 'generators': [15337065127102, 20842054369200], 'label': '2688.ci.672.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.r1.a1', 'old_label': '672.g1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182266869
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '672.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '6.1', 'aut_weyl_index': 224, 'centralizer': '336.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e1.a1', '336.i1.a1', '336.p1.a1', '336.p2.a1'], 'contains': ['1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1452, -1, 7172, -1, 6568, -1, 8221, -1], 'generators': [12540174399054, 15337065127102], 'label': '2688.ci.672.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '672.h1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 182266870
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '672.h2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.1', 'aut_weyl_index': 224, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e2.a1', '336.i2.a1', '336.l1.a1', '336.p1.a1'], 'contains': ['1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2395, -1, 7618, -1, 5466, -1, 7958, -1], 'generators': [14029390396096, 8416014572032], 'label': '2688.ci.672.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '672.h2.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.h2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 182266871
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '672.h3', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.i2.a1', '336.l1.a1', '336.p2.a1'], 'contains': ['1344.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2651, -1, 6798, -1, 5010, -1, 7460, -1], 'generators': [15337065127102, 8416014572032], 'label': '2688.ci.672.h3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.d1.a1', 'old_label': '672.h3.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.h3.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182266872
    {'ambient': '2688.ci', 'aut_centralizer_order': 6, 'aut_label': '896.a1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '224.d1.a1', '224.e1.a1', '224.e2.a1', '448.a1.a1', '448.b1.a1', '448.c1.a1'], 'contains': ['2688.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [1181, -1, 8797, -1, 6779, -1, 8130, -1], 'generators': [11172324026286], 'label': '2688.ci.896.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '896.a1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '896.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 182266873
    {'ambient': '2688.ci', 'aut_centralizer_order': 1344, 'aut_label': '1344.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1344, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1'], 'contains': ['2688.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3571, 5000, 5306, 5000, 6117, 5000, 5422, 5000], 'generators': [1313941673647], 'label': '2688.ci.1344.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['168.a1.a1'], 'normal_contains': ['2688.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1344.11686', 'quotient_action_kernel_order': 1344, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 182266874
    {'ambient': '2688.ci', 'aut_centralizer_order': 96, 'aut_label': '1344.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1344, 'centralizer': '14.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.b1.a1', '672.a1.a1', '672.d1.a1', '672.e1.a1', '672.f1.a1'], 'contains': ['2688.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6506, -1, 3253, -1, 3441, -1, 3741, -1], 'generators': [1313901393960], 'label': '2688.ci.1344.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '1344.b1.a1', 'projective_image': '2688.ci', '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': '1.1'}
  • id: 182266875
    {'ambient': '2688.ci', 'aut_centralizer_order': 16, 'aut_label': '1344.c1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1344, 'centralizer': '84.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.c1.a1', '672.b1.a1', '672.d1.a1', '672.g1.a1', '672.h1.a1', '672.h2.a1', '672.h3.a1'], 'contains': ['2688.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2395, -1, 7052, -1, 5805, -1, 7773, -1], 'generators': [8416014572032], 'label': '2688.ci.1344.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.d1.a1', 'old_label': '1344.c1.a1', 'projective_image': '2688.ci', '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': '1.1'}
  • id: 182266876
    {'ambient': '2688.ci', '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': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['384.a1.a1', '896.a1.a1', '1344.a1.a1', '1344.b1.a1', '1344.c1.a1'], 'contains': [], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2395, 5000, 5500, 5000, 6117, 5000, 7773, 5000], 'generators': [], 'label': '2688.ci.2688.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '2688.a1.a1', 'normal_contained_in': ['1344.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '2688.a1.a1', 'projective_image': '2688.ci', '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': '1.1'}
  • id: 182266877
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '7.a2.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.f2.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6657, -1, 2037, -1, 3144, -1, 2791, -1], 'generators': [8416014572032, 6227383801, 40279687, 1313941673647, 5167, 14035577500222, 11226233456334], 'label': '2688.ci.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266878
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.a1.a1', '168.a1.a1', '192.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4302, -1, 2774, -1, 7593, -1, 6806, -1], 'generators': [40279687, 6227383801, 5167, 18045909894961, 1313941673647], 'label': '2688.ci.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182266879
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['56.b1.a1', '56.h1.a1', '56.j2.a1', '84.b1.a1', '112.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5696, -1, 6670, -1, 6665, -1, 4804, -1], 'generators': [6227388726, 15323740179846, 19574789506871, 18072820281295, 20849066796112, 1313941673647], 'label': '2688.ci.28.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': '28.a1.a1', 'projective_image': '1344.11686', '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': '48.48'}
  • id: 182266880
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['56.a1.a1', '56.g1.a1', '56.i2.a1', '84.d1.a1', '112.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3478, -1, 7199, -1, 5563, -1, 7519, -1], 'generators': [19541392791118, 6227388726, 20876236859231, 14022252552966, 18072820281295, 1313941673647], 'label': '2688.ci.28.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '28.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266881
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '14.b1.a1', '14.c2.a1'], 'contains': ['84.j1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2770, -1, 5283, -1, 6945, -1, 5355, -1], 'generators': [14035577500222, 11226233456334, 5167, 11172324026286, 1313941673647, 6266937726], 'label': '2688.ci.28.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '28.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266882
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '7.a2.a1'], 'contains': ['56.d1.a1', '56.e1.a1', '56.f1.a1', '84.k1.a1', '112.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4926, -1, 5033, -1, 5309, -1, 4538, -1], 'generators': [8416014572032, 5666412286390, 40279687, 6227383801, 5167, 1313941673647], 'label': '2688.ci.28.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '28.d1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266883
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1.a1'], 'contains': ['84.e1.a1', '84.f1.a1', '84.h1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7947, -1, 2149, -1, 2363, -1, 2017, -1], 'generators': [9723728851798, 11226273010249, 14035577500222, 5167, 1313941673647, 6266937726], 'label': '2688.ci.42.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266884
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.c1.a1', '21.a1.a1', '28.a1.a1', '28.b1.a1', '28.d1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5495, -1, 5491, -1, 5314, -1, 4622, -1], 'generators': [6227383801, 14016065454007, 40279687, 1313941673647, 5167, 20876236859231, 16765145545374, 19541392791118], 'label': '2688.ci.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.1493'}
  • id: 182266885
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1.a1'], 'contains': ['84.e1.a1', '84.g1.a1', '84.i1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7619, -1, 1800, -1, 1508, -1, 1660, -1], 'generators': [11226273010249, 8416014572032, 14035577500222, 5167, 1313941673647, 6266937726], 'label': '2688.ci.42.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266886
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.b1.a1', '84.g1.a1', '84.h1.a1', '84.j1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6855, -1, 3185, -1, 3864, -1, 3085, -1], 'generators': [9723728851798, 14035577500222, 11226233456334, 5167, 1313941673647, 6266937726], 'label': '2688.ci.42.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266887
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1', '84.f1.a1', '84.i1.a1', '84.j1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6184, -1, 3921, -1, 3540, -1, 3497, -1], 'generators': [8416014572032, 14035577500222, 11226233456334, 5167, 1313941673647, 6266937726], 'label': '2688.ci.42.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266888
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1.a1'], 'contains': ['84.f1.a1', '84.g1.a1', '84.k1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7190, -1, 2898, -1, 3144, -1, 2791, -1], 'generators': [14035577500222, 40279687, 20842054369200, 6227383801, 5167, 1313941673647], 'label': '2688.ci.42.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266889
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.227', 'aut_weyl_index': 14, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1', '21.a1.a1'], 'contains': ['84.e2.a1', '84.h1.a1', '84.i1.a1', '84.k1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8941, -1, 1383, -1, 1941, -1, 1232, -1], 'generators': [8416014572032, 14035577500222, 40279687, 6227383801, 5167, 1313941673647], 'label': '2688.ci.42.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.f1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 182266890
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '42.f2', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c2.a1', '21.a1.a1'], 'contains': ['84.e1.a1', '84.j1.a1', '84.k1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8382, -1, 824, -1, 2748, -1, 2398, -1], 'generators': [14035577500222, 11226233456334, 40279687, 6227383801, 5167, 1313941673647], 'label': '2688.ci.42.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '42.f2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266891
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1'], 'contains': ['336.o1.a1', '384.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4063, -1, 2254, -1, 7547, -1, 6863, -1], 'generators': [16744502096766, 40279687, 6227383801, 1313941668480], 'label': '2688.ci.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 182266892
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1', '28.b1.a1'], 'contains': ['112.c2.a1', '112.e1.a1', '168.g1.a1', '224.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3616, -1, 7702, -1, 4159, -1, 7792, -1], 'generators': [19541392791118, 6227388726, 20876236859231, 14022252552966, 1313941673647], 'label': '2688.ci.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '56.a1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266893
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1', '28.a1.a1'], 'contains': ['112.d2.a1', '168.j1.a1', '224.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5367, -1, 5984, -1, 6665, -1, 4371, -1], 'generators': [19541392791118, 6227388726, 15323740179846, 19574789506871, 1313941673647], 'label': '2688.ci.56.b1.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.b1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266894
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 112, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1'], 'contains': ['112.f1.a1', '168.k1.a1', '224.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [8554, -1, 3253, -1, 459, -1, 2750, -1], 'generators': [19541392791118, 19568522569385, 6227388726, 15329927288887, 1313941673647], 'label': '2688.ci.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '56.c1.a1', 'projective_image': '1344.11686', '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': '12.3'}
  • id: 182266895
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '7.a2', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c2.a1', '21.a1.a1', '28.d1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4705, -1, 4888, -1, 5698, -1, 5135, -1], 'generators': [8416014572032, 6227383801, 40279687, 1313941673647, 11178550679160, 5167, 14035577500222, 11226233456334], 'label': '2688.ci.7.a2.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '7.a2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a2.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266896
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1', '28.d1.a1'], 'contains': ['112.b1.a1', '112.g1.a1', '168.m1.a1', '224.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2549, -1, 5401, -1, 5309, -1, 6052, -1], 'generators': [5660184902831, 8416014572032, 5167, 1313941673647, 6266937726], 'label': '2688.ci.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '56.d1.a1', 'projective_image': '1344.11686', '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': '48.48'}
  • id: 182266897
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '28.d1.a1'], 'contains': ['112.b1.a1', '168.n1.a1', '224.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4580, -1, 4870, -1, 5582, -1, 5470, -1], 'generators': [9723728851798, 5660184902831, 5167, 1313941673647, 6266937726], 'label': '2688.ci.56.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '56.e1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266898
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '14.c1.a1', '14.c2.a1', '28.d1.a1'], 'contains': ['112.b1.a1', '112.h1.a1', '168.a1.a1', '224.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4222, -1, 4580, -1, 4957, -1, 4991, -1], 'generators': [40279687, 6227383801, 5167, 11178550679160, 1313941673647], 'label': '2688.ci.56.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '56.f1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266899
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1'], 'contains': ['112.c2.a1', '168.q1.a1', '224.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3158, -1, 7413, -1, 6208, -1, 8089, -1], 'generators': [19547619454072, 16765185829974, 20876236859231, 14016025900080, 1313941673647], 'label': '2688.ci.56.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '56.g1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266900
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.d2.a1', '168.p1.a1', '224.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5696, -1, 7025, -1, 8084, -1, 6538, -1], 'generators': [15323740179846, 19574789506871, 18072820281295, 20849066796112, 1313941673647], 'label': '2688.ci.56.h1.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.h1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266901
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '14.b1.a1'], 'contains': ['112.c1.a1', '112.i1.a1', '112.i3.a1', '168.r1.a1', '224.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1245, -1, 8650, -1, 8574, -1, 9174, -1], 'generators': [12540174399054, 15337065127102, 8416014572032, 11172324026286, 1313941673647], 'label': '2688.ci.56.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '56.i1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266902
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.i2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.b1.a1'], 'contains': ['112.c2.a1', '112.i2.a1', '168.r1.a1', '224.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1916, -1, 9110, -1, 7267, -1, 8851, -1], 'generators': [19547619454072, 20876236859231, 14016025900080, 18072820281295, 1313941673647], 'label': '2688.ci.56.i2.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '56.i2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i2.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266903
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '14.a1.a1'], 'contains': ['112.d1.a1', '168.s1.a1', '224.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4950, -1, 6334, -1, 9174, -1, 5688, -1], 'generators': [9723728851798, 14035577500222, 11232500393808, 11172324026286, 1313941673647], 'label': '2688.ci.56.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.j1.a1', 'old_label': '56.j1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266904
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '56.j2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.48', 'aut_weyl_index': 28, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1'], 'contains': ['112.d2.a1', '168.s1.a1', '224.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5894, -1, 6726, -1, 8301, -1, 6322, -1], 'generators': [16765185829974, 15323740179846, 19574789506871, 20849066796112, 1313941673647], 'label': '2688.ci.56.j2.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.j2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j2.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 182266905
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '21.1', 'aut_weyl_index': 64, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['128.a1.a1', '192.a1.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [775, -1, 8208, -1, 9657, -1, 8489, -1], 'generators': [15296439899934, 18045909894961, 1313941673647], 'label': '2688.ci.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182266906
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '56.f1.a1', '64.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4050, -1, 4337, -1, 7699, -1, 6806, -1], 'generators': [40279687, 6227383801, 5167, 18045909894961, 13994992552729, 1313941673647], 'label': '2688.ci.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': '1344.11686', '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': '168.43'}
  • id: 182266907
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.c1.a1'], 'contains': ['168.c1.a1', '168.h1.a1', '168.i1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [7268, -1, 2765, -1, 3511, -1, 2317, -1], 'generators': [14035577500222, 9723728856953, 11226233456334, 6266942641, 1313941673647], 'label': '2688.ci.84.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '84.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266908
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '42.c1.a1'], 'contains': ['168.c1.a1', '168.i1.a1', '168.j1.a1', '168.p1.a1', '168.s1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6787, -1, 3713, -1, 5848, -1, 3696, -1], 'generators': [14035577500222, 11226233456334, 9717461919239, 6266942641, 1313941673647], 'label': '2688.ci.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '84.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266909
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.d1.a1'], 'contains': ['168.d1.a1', '168.e1.a1', '168.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5849, -1, 3995, -1, 3190, -1, 3985, -1], 'generators': [15337065127102, 11226233456334, 8409827468158, 6266942641, 1313941673647], 'label': '2688.ci.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266910
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1', '42.d1.a1'], 'contains': ['168.e1.a1', '168.f1.a1', '168.g1.a1', '168.q1.a1', '168.r1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3590, -1, 6723, -1, 4558, -1, 7177, -1], 'generators': [15337065127102, 8416014572032, 11226233456334, 6266942641, 1313941673647], 'label': '2688.ci.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '84.d1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266911
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.a1.a1', '42.b1.a1', '42.f2.a1'], 'contains': ['168.l1.a1', '168.o1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8364, -1, 873, -1, 1305, -1, 672, -1], 'generators': [11226273010249, 14035577500222, 5167, 1313941673647, 6266937726], 'label': '2688.ci.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266912
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.e2', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.14', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.f1.a1'], 'contains': ['168.b1.a1', '168.d1.a1', '168.h1.a1', '168.k1.a1', '168.m1.a1', '168.n1.a1', '168.o1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9603, -1, 1292, -1, 1056, -1, 425, -1], 'generators': [40284840, 14035577500222, 6227383801, 8409827468158, 1313941673647], 'label': '2688.ci.84.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '84.e2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e2.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 182266913
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.e1.a1', '168.l1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6433, -1, 3076, -1, 2644, -1, 3135, -1], 'generators': [14035577500222, 20842054369200, 5167, 1313941673647, 6266937726], 'label': '2688.ci.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.f1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266914
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.138', 'aut_weyl_index': 21, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.b1.a1', '42.c1.a1', '42.e1.a1'], 'contains': ['168.i1.a1', '168.l1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7562, -1, 2363, -1, 2917, -1, 1998, -1], 'generators': [14035577500222, 5167, 19534340084521, 1313941673647, 6266937726], 'label': '2688.ci.84.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.g1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 182266915
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.a1.a1', '42.c1.a1', '42.f1.a1'], 'contains': ['168.b1.a1', '168.h1.a1', '168.j1.a1', '168.l1.a1', '168.n1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8682, -1, 1716, -1, 2395, -1, 918, -1], 'generators': [40284840, 8416014572032, 14035577500222, 6227383801, 1313941673647], 'label': '2688.ci.84.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.h1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266916
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.b1.a1', '168.d1.a1', '168.g1.a1', '168.l1.a1', '168.m1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7878, -1, 2027, -1, 1653, -1, 1653, -1], 'generators': [15337065127102, 40284840, 8416014572032, 6227383801, 1313941673647], 'label': '2688.ci.84.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.i1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266917
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.42', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16.b1.a1', '56.i1.a1', '56.i2.a1', '64.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [896, -1, 8536, -1, 8574, -1, 8851, -1], 'generators': [5639415298583, 4104045423952, 1313941673647], 'label': '2688.ci.8.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 182266918
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '42.c1.a1', '42.d1.a1', '42.f2.a1'], 'contains': ['168.c1.a1', '168.f1.a1', '168.l1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6184, -1, 3431, -1, 3833, -1, 3406, -1], 'generators': [14035577500222, 11226233456334, 5167, 1313941673647, 6266937726], 'label': '2688.ci.84.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '84.j1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266919
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.d1.a1', '42.e1.a1', '42.f1.a1', '42.f2.a1'], 'contains': ['168.a1.a1', '168.l1.a1', '168.m1.a1', '168.n1.a1', '168.o1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9079, -1, 518, -1, 2074, -1, 1237, -1], 'generators': [8416014572032, 40279687, 6227383801, 5167, 1313941673647], 'label': '2688.ci.84.k1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.k1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266920
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.4', 'aut_weyl_index': 112, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '28.b1.a1', '28.d1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '224.c1.a1', '336.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [4796, -1, 6313, -1, 7083, -1, 4871, -1], 'generators': [8416014572032, 6227383801, 6967859633585, 1313941673647], 'label': '2688.ci.112.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '1344.11686', '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': '12.4'}
  • id: 182266921
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '56.d1.a1', '56.e1.a1', '56.f1.a1'], 'contains': ['224.d1.a1', '336.e1.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3132, -1, 5056, -1, 5582, -1, 5676, -1], 'generators': [5167, 11172324026286, 1313941673647, 6266937726], 'label': '2688.ci.112.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '112.b1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266922
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '56.i1.a1'], 'contains': ['224.e1.a1', '336.i1.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1366, -1, 8645, -1, 9423, -1, 9030, -1], 'generators': [12540174399054, 15337065127102, 11172324026286, 1313941673647], 'label': '2688.ci.112.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '112.c1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266923
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.c2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '56.g1.a1', '56.i2.a1'], 'contains': ['224.e2.a1', '336.i2.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2288, -1, 9052, -1, 6240, -1, 8614, -1], 'generators': [20882464237865, 14022252552966, 20849066796112, 1313941673647], 'label': '2688.ci.112.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '112.c2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266924
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '56.j1.a1'], 'contains': ['336.k1.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4515, -1, 5927, -1, 9062, -1, 5410, -1], 'generators': [14029390391183, 11226233456334, 11172324026286, 1313941673647], 'label': '2688.ci.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.j1.a1', 'old_label': '112.d1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266925
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.d2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '56.h1.a1', '56.j2.a1'], 'contains': ['336.k2.a1', '448.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5252, -1, 7092, -1, 8323, -1, 6478, -1], 'generators': [15323740179846, 19574789506871, 20849066796112, 1313941673647], 'label': '2688.ci.112.d2.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': '112.d2.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266926
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 112, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1'], 'contains': ['224.e2.a1', '336.l1.a1', '448.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2748, -1, 7795, -1, 3647, -1, 7474, -1], 'generators': [19541392791118, 20876236859231, 14022252552966, 1307714284921], 'label': '2688.ci.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '112.e1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182266927
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 112, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1'], 'contains': ['336.m1.a1', '448.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [8334, -1, 3059, -1, 82, -1, 2587, -1], 'generators': [19541392791118, 15323699900161, 1307714284921, 19574749958111], 'label': '2688.ci.112.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '112.f1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182266928
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.42', 'aut_weyl_index': 8, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['56.j1.a1', '56.j2.a1', '64.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4966, -1, 7165, -1, 9137, -1, 6322, -1], 'generators': [5633188645697, 2796410977798, 1313941673647], 'label': '2688.ci.8.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 182266929
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1'], 'contains': ['224.d1.a1', '336.n1.a1', '448.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2518, -1, 5565, -1, 4502, -1, 6016, -1], 'generators': [8416014572032, 1313941668480, 6967859633585, 6266942641], 'label': '2688.ci.112.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.d1.a1', 'old_label': '112.g1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266930
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '12.3', 'aut_weyl_index': 112, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.f1.a1'], 'contains': ['224.d1.a1', '336.o1.a1', '448.b1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4187, -1, 4561, -1, 4251, -1, 5144, -1], 'generators': [40279687, 5167, 1307714289846, 12480038310967], 'label': '2688.ci.112.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.f1.a1', 'old_label': '112.h1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 182266931
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.i1.a1'], 'contains': ['224.e1.a1', '336.p1.a1', '448.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [676, -1, 9748, -1, 8871, -1, 9715, -1], 'generators': [12479998031280, 14029390396096, 12533907461328, 8416014572032], 'label': '2688.ci.112.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '112.i1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266932
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.i2', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.i2.a1'], 'contains': ['224.e2.a1', '336.p1.a1', '448.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1006, -1, 9925, -1, 7281, -1, 9543, -1], 'generators': [19541392796033, 15323740185001, 18072820281295, 19574749952944], 'label': '2688.ci.112.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i2.a1', 'old_label': '112.i2.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266933
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '112.i3', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.i1.a1'], 'contains': ['224.e1.a1', '336.p2.a1', '448.c1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [836, -1, 9566, -1, 8697, -1, 9370, -1], 'generators': [15337065127102, 8416014572032, 11226233451169, 11172324026286], 'label': '2688.ci.112.i3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '112.i3.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i3.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266934
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '21.1', 'aut_weyl_index': 64, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '64.a1.a1'], 'contains': ['384.a1.a1', '896.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [81, -1, 8150, -1, 9911, -1, 9911, -1], 'generators': [18045909890046, 15296439899934], 'label': '2688.ci.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 182266935
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '168.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.42', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': ['16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.f1.a1', '84.k1.a1'], 'contains': ['336.e1.a1', '336.o1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8177, 5000, 75, 5000, 3142, 5000, 3119, 5000], 'generators': [40279687, 6227383801, 5167, 1313941673647], 'label': '2688.ci.168.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': '168.42', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
  • id: 182266936
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.14', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.e2.a1', '84.h1.a1', '84.i1.a1'], 'contains': ['336.b1.a1', '336.c1.a1', '336.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8393, -1, 1813, -1, 1295, -1, 1182, -1], 'generators': [8416014572032, 14035577500222, 6266942641, 1313941673647], 'label': '2688.ci.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '168.b1.a1', 'projective_image': '1344.11686', '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': '16.14'}
  • id: 182266937
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '84.b1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.c1.a1', '336.f1.a1', '336.h1.a1', '336.k1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5967, -1, 3550, -1, 5307, -1, 3327, -1], 'generators': [14035577500222, 11226233456334, 1313941673647, 6266937726], 'label': '2688.ci.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '168.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266938
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.c1.a1', '84.e2.a1', '84.i1.a1'], 'contains': ['336.b1.a1', '336.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7961, -1, 2398, -1, 1022, -1, 1780, -1], 'generators': [9723728856953, 15343291779976, 6266942641, 1313941673647], 'label': '2688.ci.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.d1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266939
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a2.a1'], 'contains': ['28.c1.a1', '42.c1.a1', '56.e1.a1', '56.j1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4906, -1, 5277, -1, 6056, -1, 5353, -1], 'generators': [9723728851798, 14035577500222, 11226233456334, 5167, 11172324026286, 1313941673647, 6266937726], 'label': '2688.ci.14.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '14.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266940
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.c1.a1', '84.d1.a1', '84.f1.a1'], 'contains': ['336.b1.a1', '336.g1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5032, -1, 4778, -1, 2905, -1, 4115, -1], 'generators': [15337065127102, 20842054369200, 6266942641, 1313941673647], 'label': '2688.ci.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.e1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266941
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.c1.a1', '84.d1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.f1.a1', '336.h1.a1', '336.i1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5394, -1, 4077, -1, 5029, -1, 4414, -1], 'generators': [12540174399054, 14035577500222, 1313941673647, 6266937726], 'label': '2688.ci.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '168.f1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266942
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '84.d1.a1', '84.i1.a1'], 'contains': ['336.b1.a1', '336.i2.a1', '336.l1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3906, -1, 7048, -1, 2668, -1, 6679, -1], 'generators': [15337065127102, 8416014572032, 6266942641, 1313941673647], 'label': '2688.ci.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.g1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266943
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 168, 'centralizer': '168.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '84.e2.a1', '84.h1.a1'], 'contains': ['336.c1.a1', '336.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8912, -1, 1584, -1, 2136, -1, 676, -1], 'generators': [14035577500222, 9723728856953, 6266942641, 1313941673647], 'label': '2688.ci.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.h1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 182266944
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '672.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '84.b1.a1', '84.g1.a1'], 'contains': ['336.c1.a1', '336.j1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [7034, -1, 2737, -1, 3361, -1, 2364, -1], 'generators': [20842014815287, 14035577500222, 6266942641, 1313941673647], 'label': '2688.ci.168.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '168.i1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266945
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.227', 'aut_weyl_index': 14, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '84.b1.a1', '84.h1.a1'], 'contains': ['336.c1.a1', '336.k2.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7685, -1, 3015, -1, 5911, -1, 2855, -1], 'generators': [14035577500222, 9717461919239, 6266942641, 1313941673647], 'label': '2688.ci.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.j1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 182266946
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '48.50', 'aut_weyl_index': 28, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '84.e2.a1'], 'contains': ['336.d1.a1', '336.m1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [9919, -1, 1301, -1, 353, -1, 413, -1], 'generators': [8409827468158, 15343291779976, 6266942641, 1313941673647], 'label': '2688.ci.168.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '168.k1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': '48.50'}
  • id: 182266947
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.e1.a1', '84.f1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1', '84.j1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1', '336.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7297, -1, 2107, -1, 2402, -1, 2079, -1], 'generators': [40284840, 8416014572032, 6227383801, 1313941673647], 'label': '2688.ci.168.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.l1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266948
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.14', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '84.e2.a1', '84.i1.a1', '84.k1.a1'], 'contains': ['336.b1.a1', '336.d1.a1', '336.e1.a1', '336.n1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8669, -1, 668, -1, 1597, -1, 1481, -1], 'generators': [8416014572032, 40279687, 6227388726, 1313941673647], 'label': '2688.ci.168.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '168.m1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 182266949
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '16.14', 'aut_weyl_index': 84, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.e1.a1', '84.e2.a1', '84.h1.a1', '84.k1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9219, -1, 959, -1, 1900, -1, 911, -1], 'generators': [40279687, 6227388726, 8409827468158, 1313941673647], 'label': '2688.ci.168.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '168.n1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 182266950
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.955', 'aut_weyl_index': 7, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a2.a1'], 'contains': ['28.c1.a1', '42.d1.a1', '56.d1.a1', '56.i1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2770, -1, 5896, -1, 5747, -1, 5659, -1], 'generators': [8416014572032, 14035577500222, 11226233456334, 5167, 11172324026286, 1313941673647, 6266937726], 'label': '2688.ci.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '14.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 182266951
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.27', 'aut_weyl_index': 42, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.e1.a1', '84.e2.a1', '84.k1.a1'], 'contains': ['336.d1.a1', '336.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9468, -1, 376, -1, 749, -1, 114, -1], 'generators': [40284840, 6227383801, 8409827468158, 1313941673647], 'label': '2688.ci.168.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.o1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 182266952
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.h1.a1', '84.b1.a1'], 'contains': ['336.h1.a1', '336.j1.a1', '336.k2.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6479, -1, 4442, -1, 6854, -1, 3770, -1], 'generators': [9723728851798, 12540174399054, 14035577500222, 1313941673647], 'label': '2688.ci.168.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.b1.a1', 'old_label': '168.p1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266953
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.q1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 168, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.g1.a1', '84.d1.a1'], 'contains': ['336.f1.a1', '336.g1.a1', '336.i2.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3606, -1, 6819, -1, 4727, -1, 7177, -1], 'generators': [8416014572032, 11226233456334, 15343252226063, 1313941673647], 'label': '2688.ci.168.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.d1.a1', 'old_label': '168.q1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 182266954
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '168.r1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 168, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.i1.a1', '56.i2.a1', '84.d1.a1'], 'contains': ['336.g1.a1', '336.i1.a1', '336.i2.a1', '336.p1.a1', '336.p2.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2290, -1, 7721, -1, 6568, -1, 8013, -1], 'generators': [12540174399054, 15337065127102, 8416014572032, 1313941673647], 'label': '2688.ci.168.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.d1.a1', 'old_label': '168.r1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 182266955
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '168.s1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.11', 'aut_weyl_index': 84, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.j1.a1', '56.j2.a1', '84.b1.a1'], 'contains': ['336.j1.a1', '336.k1.a1', '336.k2.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6240, -1, 3814, -1, 7743, -1, 3545, -1], 'generators': [9723728851798, 14029390391183, 11226233456334, 1313941673647], 'label': '2688.ci.168.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.b1.a1', 'old_label': '168.s1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 182266956
    {'ambient': '2688.ci', 'aut_centralizer_order': 7, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 448, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '64.a1.a1'], 'contains': ['384.a1.a1', '1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [1706, -1, 5252, -1, 9693, -1, 7742, -1], 'generators': [18045909894961, 1313941673647], 'label': '2688.ci.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 182266957
    {'ambient': '2688.ci', 'aut_centralizer_order': 6, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '2.1', 'aut_weyl_index': 672, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '56.f1.a1', '112.a1.a1'], 'contains': ['448.a1.a1', '448.b1.a1', '672.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [4330, -1, 6121, -1, 3949, -1, 4931, -1], 'generators': [40279687, 11178550679160, 1313941673647], 'label': '2688.ci.224.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '1344.11686', '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': '2.1'}
  • id: 182266958
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.4', 'aut_weyl_index': 112, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '56.h1.a1', '56.i1.a1', '56.i2.a1', '112.a1.a1'], 'contains': ['448.a1.a1', '448.c1.a1', '672.b1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [2035, -1, 8482, -1, 7571, -1, 7867, -1], 'generators': [8416014572032, 6967859633585, 1313941673647], 'label': '2688.ci.224.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '224.b1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 182266959
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.4', 'aut_weyl_index': 112, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.e1.a1', '56.g1.a1', '56.j1.a1', '56.j2.a1', '112.a1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [4612, -1, 6387, -1, 7898, -1, 6193, -1], 'generators': [9723728851798, 6967859633585, 1313941673647], 'label': '2688.ci.224.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '224.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 182266960
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '112.g1.a1', '112.h1.a1'], 'contains': ['672.f1.a1', '896.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2986, -1, 5579, -1, 4502, -1, 5676, -1], 'generators': [12479998031280, 1307674735921, 5167], 'label': '2688.ci.224.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.d1.a1', 'old_label': '224.d1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266961
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.227', 'aut_weyl_index': 14, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['42.f1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.f1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5612, -1, 4979, -1, 4381, -1, 4373, -1], 'generators': [19541392791118, 40279687, 20876236859231, 6227383801, 5167, 14016065454007, 1313941673647], 'label': '2688.ci.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
  • id: 182266962
    {'ambient': '2688.ci', 'aut_centralizer_order': 1, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '1344.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '112.i1.a1', '112.i3.a1'], 'contains': ['672.h1.a1', '896.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [476, -1, 9096, -1, 8697, -1, 8829, -1], 'generators': [15337065127102, 11226233451169, 11172324026286], 'label': '2688.ci.224.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.i1.a1', 'old_label': '224.e1.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266963
    {'ambient': '2688.ci', 'aut_centralizer_order': 2, 'aut_label': '224.e2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c2.a1', '112.e1.a1', '112.i2.a1'], 'contains': ['672.h2.a1', '896.a1.a1'], 'core': '2688.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1194, -1, 9530, -1, 5769, -1, 8657, -1], 'generators': [20882464237865, 14022252552966, 20849066796112], 'label': '2688.ci.224.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.b1.a1', 'old_label': '224.e2.a1', 'projective_image': '2688.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 182266964
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '168.c1.a1', '168.f1.a1', '168.l1.a1'], 'contains': ['672.a1.a1', '672.b1.a1', '672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5778, -1, 3330, -1, 5595, -1, 3643, -1], 'generators': [40284840, 8416014572032, 1313941673647], 'label': '2688.ci.336.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.j1.a1', 'old_label': '336.a1.a1', 'projective_image': '1344.11686', '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': '4.2'}
  • id: 182266965
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 168, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.b1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1', '168.l1.a1', '168.m1.a1'], 'contains': ['672.a1.a1', '672.b1.a1', '672.d1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6544, -1, 3064, -1, 2869, -1, 3286, -1], 'generators': [8416014572032, 6266942641, 1313941673647], 'label': '2688.ci.336.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '1344.11686', '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': '8.3'}
  • id: 182266966
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.3', 'aut_weyl_index': 168, 'centralizer': '168.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.b1.a1', '168.c1.a1', '168.h1.a1', '168.i1.a1', '168.j1.a1', '168.l1.a1', '168.n1.a1'], 'contains': ['672.a1.a1', '672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7716, -1, 2520, -1, 3330, -1, 2609, -1], 'generators': [9717461919239, 6266942641, 1313941673647], 'label': '2688.ci.336.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '1344.11686', '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': '8.3'}
  • id: 182266967
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '168.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.b1.a1', '168.d1.a1', '168.h1.a1', '168.k1.a1', '168.m1.a1', '168.n1.a1', '168.o1.a1'], 'contains': ['672.a1.a1', '672.e1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8973, -1, 1467, -1, 1597, -1, 1182, -1], 'generators': [8409827468158, 6266942641, 1313941673647], 'label': '2688.ci.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.f1.a1', 'old_label': '336.d1.a1', 'projective_image': '1344.11686', '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': '4.2'}
  • id: 182266968
    {'ambient': '2688.ci', 'aut_centralizer_order': 8, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.12', 'aut_weyl_index': 56, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '168.a1.a1', '168.l1.a1', '168.m1.a1', '168.n1.a1', '168.o1.a1'], 'contains': ['672.a1.a1', '672.f1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8344, -1, 934, -1, 3067, -1, 2348, -1], 'generators': [40279687, 6227383801, 1313941673647], 'label': '2688.ci.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '168.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a2.a1', 'old_label': '336.e1.a1', 'projective_image': '1344.11686', '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': '24.12'}
  • id: 182266969
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 168, 'centralizer': '336.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.c1.a1', '168.f1.a1', '168.q1.a1'], 'contains': ['672.b1.a1', '672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5284, -1, 4629, -1, 5343, -1, 4605, -1], 'generators': [14035577500222, 11226233456334, 1313941673647], 'label': '2688.ci.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.d1.a1', 'old_label': '336.f1.a1', 'projective_image': '1344.11686', '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': '8.3'}
  • id: 182266970
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 336, 'centralizer': '336.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.e1.a1', '168.q1.a1', '168.r1.a1'], 'contains': ['672.b1.a1', '672.g1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3118, -1, 6597, -1, 5014, -1, 7134, -1], 'generators': [15337065127102, 20842054369200, 1313941673647], 'label': '2688.ci.336.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.d1.a1', 'old_label': '336.g1.a1', 'projective_image': '1344.11686', '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': '4.2'}
  • id: 182266971
    {'ambient': '2688.ci', 'aut_centralizer_order': 4, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '8.3', 'aut_weyl_index': 168, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.c1.a1', '168.f1.a1', '168.p1.a1'], 'contains': ['672.b1.a1', '672.c1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5619, -1, 4129, -1, 5943, -1, 4357, -1], 'generators': [12540174399054, 14035577500222, 1313941673647], 'label': '2688.ci.336.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '336.h1.a1', 'projective_image': '1344.11686', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}