Abstract group data - 64.237

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8, 32], [5, 18, 24, 48], [5, 2, 8, 48], [21, 22, 12, 52], [17, 10, 24, 48], [1, 2, 24, 32], [17, 22, 8, 32], [21, 18, 12, 52], [1, 22, 24, 48], [36, 26, 24, 5], [17, 2, 8, 36]], 'aut_group': '1024.dis', 'aut_hash': 6444867003695716502, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 16, 'aut_perms': [442644671419, 5686235269819, 4377642824803, 1328391578083, 442644652800, 5686235251726, 5773413933283, 5330808824646, 9446996961070, 5686235279082], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 2, 1], [4, 2, 2, 2], [4, 2, 4, 2], [4, 4, 1, 1], [4, 4, 2, 1], [4, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2^2\\wr C_2)^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '4.2', 'autcentquo_hash': 2, 'autcentquo_nilpotent': True, 'autcentquo_order': 4, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 2], [4, 2, 12], [4, 4, 7]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '16.14', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 237, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 2], [4, 2, 1, 4], [4, 2, 2, 4], [4, 4, 1, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 5040, 'exponent': 4, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '16.14', 'hash': 237, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[1, 18, 8, 52], [17, 2, 24, 48], [1, 18, 8, 32], [21, 18, 8, 32]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': True, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 8], [4, 1]], 'label': '64.237', 'linC_count': 16, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.C2^2', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 12, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 25, 'number_divisions': 21, 'number_normal_subgroups': 75, 'number_subgroup_autclasses': 53, 'number_subgroup_classes': 106, 'number_subgroups': 141, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 11], [4, 52]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[17, 22, 12, 32], [1, 26, 24, 32], [32, 2, 8, 1], [1, 2, 12, 32], [1, 22, 8, 32], [1, 2, 24, 32]], 'outer_group': '64.226', 'outer_hash': 226, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 8, 'outer_perms': [11543, 5, 120, 7, 16, 5160], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [4, 5]], 'representations': {'PC': {'code': 2289741697395242, 'gens': [1, 2, 4, 6], 'pres': [6, 2, 2, 2, 2, 2, 2, 217, 31, 297, 69, 1877, 875]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 149886396087, 61179005627, 30594431879, 40905199377, 115200433752]}, 'Perm': {'d': 16, 'gens': [355459467406, 1596153451261, 3069968803996, 4359920118978, 5599050065280, 18498]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.C_2^2', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 105737865
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 237, 'group_order': 64, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 105737876
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 237, 'group_order': 64, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 105737883
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 237, 'group_order': 64, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 20, 'size': 1}
  • id: 105737884
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 237, 'group_order': 64, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 4, 'size': 1}
  • id: 105737885
    {'aut_label': '2D', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 237, 'group_order': 64, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 32, 'size': 4}
  • id: 105737886
    {'aut_label': '2D', 'centralizer': '4.a1.b1', 'counter': 6, 'group_counter': 237, 'group_order': 64, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 105737887
    {'aut_label': '4A', 'centralizer': '2.d1.a1', 'counter': 7, 'group_counter': 237, 'group_order': 64, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 8, 'size': 2}
  • id: 105737888
    {'aut_label': '4A', 'centralizer': '2.d1.a1', 'counter': 8, 'group_counter': 237, 'group_order': 64, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 12, 'size': 2}
  • id: 105737889
    {'aut_label': '4C', 'centralizer': '2.f1.a1', 'counter': 9, 'group_counter': 237, 'group_order': 64, 'label': '4C', 'order': 4, 'powers': [3], 'representative': 33, 'size': 2}
  • id: 105737866
    {'aut_label': '4C', 'centralizer': '2.f1.a1', 'counter': 10, 'group_counter': 237, 'group_order': 64, 'label': '4D', 'order': 4, 'powers': [3], 'representative': 49, 'size': 2}
  • id: 105737867
    {'aut_label': '4E1', 'centralizer': '2.h1.a1', 'counter': 11, 'group_counter': 237, 'group_order': 64, 'label': '4E1', 'order': 4, 'powers': [4], 'representative': 2, 'size': 2}
  • id: 105737868
    {'aut_label': '4E1', 'centralizer': '2.h1.a1', 'counter': 12, 'group_counter': 237, 'group_order': 64, 'label': '4E-1', 'order': 4, 'powers': [4], 'representative': 6, 'size': 2}
  • id: 105737869
    {'aut_label': '4F1', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 237, 'group_order': 64, 'label': '4F1', 'order': 4, 'powers': [2], 'representative': 40, 'size': 2}
  • id: 105737870
    {'aut_label': '4F1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 237, 'group_order': 64, 'label': '4F-1', 'order': 4, 'powers': [2], 'representative': 56, 'size': 2}
  • id: 105737871
    {'aut_label': '4E1', 'centralizer': '2.h1.b1', 'counter': 15, 'group_counter': 237, 'group_order': 64, 'label': '4G1', 'order': 4, 'powers': [4], 'representative': 10, 'size': 2}
  • id: 105737872
    {'aut_label': '4E1', 'centralizer': '2.h1.b1', 'counter': 16, 'group_counter': 237, 'group_order': 64, 'label': '4G-1', 'order': 4, 'powers': [4], 'representative': 14, 'size': 2}
  • id: 105737873
    {'aut_label': '4F1', 'centralizer': '2.a1.b1', 'counter': 17, 'group_counter': 237, 'group_order': 64, 'label': '4H1', 'order': 4, 'powers': [2], 'representative': 9, 'size': 2}
  • id: 105737874
    {'aut_label': '4F1', 'centralizer': '2.a1.b1', 'counter': 18, 'group_counter': 237, 'group_order': 64, 'label': '4H-1', 'order': 4, 'powers': [2], 'representative': 25, 'size': 2}
  • id: 105737875
    {'aut_label': '4I', 'centralizer': '4.m1.c1', 'counter': 19, 'group_counter': 237, 'group_order': 64, 'label': '4I', 'order': 4, 'powers': [3], 'representative': 34, 'size': 4}
  • id: 105737877
    {'aut_label': '4I', 'centralizer': '4.m1.d1', 'counter': 20, 'group_counter': 237, 'group_order': 64, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 3, 'size': 4}
  • id: 105737878
    {'aut_label': '4I', 'centralizer': '4.m1.a1', 'counter': 21, 'group_counter': 237, 'group_order': 64, 'label': '4K', 'order': 4, 'powers': [3], 'representative': 42, 'size': 4}
  • id: 105737879
    {'aut_label': '4L', 'centralizer': '4.f1.a1', 'counter': 22, 'group_counter': 237, 'group_order': 64, 'label': '4L', 'order': 4, 'powers': [4], 'representative': 41, 'size': 4}
  • id: 105737880
    {'aut_label': '4M', 'centralizer': '4.j1.a1', 'counter': 23, 'group_counter': 237, 'group_order': 64, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 35, 'size': 4}
  • id: 105737881
    {'aut_label': '4I', 'centralizer': '4.m1.b1', 'counter': 24, 'group_counter': 237, 'group_order': 64, 'label': '4N', 'order': 4, 'powers': [3], 'representative': 11, 'size': 4}
  • id: 105737882
    {'aut_label': '4M', 'centralizer': '4.j1.b1', 'counter': 25, 'group_counter': 237, 'group_order': 64, 'label': '4O', 'order': 4, 'powers': [2], 'representative': 43, 'size': 4}
• 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: 3572564
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3572575
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 3572578
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 3572579
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 3572580
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 3572581
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3572582
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 3572583
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3572584
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 3572565
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 3572566
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 3572567
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 3572568
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 3572569
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3572570
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 3572571
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3572572
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.2a', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572573
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.2b', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572574
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.2c', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572576
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.2d', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572577
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '64.237', 'group_order': 64, 'image': None, 'label': '64.237.4a', 'multiplicity': 1, 'nt': [16, 20], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• gps_char •

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

  
  
  • id: 5142615
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 64, 'label': '64.237.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5142626
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.b1', 'kernel_order': 32, 'label': '64.237.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5142633
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 32, 'label': '64.237.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5142634
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 32, 'label': '64.237.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5142635
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 32, 'label': '64.237.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5142636
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.d1', 'kernel_order': 32, 'label': '64.237.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5142637
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.c1', 'kernel_order': 32, 'label': '64.237.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5142638
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 32, 'label': '64.237.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5142639
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 32, 'label': '64.237.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5142616
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 32, 'label': '64.237.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5142617
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 32, 'label': '64.237.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5142618
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 32, 'label': '64.237.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5142619
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 32, 'label': '64.237.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5142620
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.b1', 'kernel_order': 32, 'label': '64.237.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5142621
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 32, 'label': '64.237.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5142622
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 64, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 32, 'label': '64.237.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 5142623
    {'center': '4.k1.a1', 'center_index': 4, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 4, 'label': '64.237.2a1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142624
    {'center': '4.k1.a1', 'center_index': 4, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 4, 'label': '64.237.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142625
    {'center': '4.k1.a1', 'center_index': 4, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.b1', 'kernel_order': 4, 'label': '64.237.2b1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142627
    {'center': '4.k1.a1', 'center_index': 4, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.b1', 'kernel_order': 4, 'label': '64.237.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142628
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 16, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 4, 'label': '64.237.2c1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142629
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 16, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 4, 'label': '64.237.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142630
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 16, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 4, 'label': '64.237.2d1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142631
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 16, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 4, 'label': '64.237.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142632
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '64.237', 'group_counter': 237, 'group_order': 64, 'image': None, 'image_isoclass': '32.50', 'image_order': 32, 'indicator': -1, 'kernel': '32.c1.a1', 'kernel_order': 2, 'label': '64.237.4a', 'nt': [16, 20], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 59432311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '64.237.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.237', 'subgroup_hash': 237, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 59432329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432373
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.c1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.c1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 59432321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.e1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 59432322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.2.h1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432327
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432341
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432365
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59432366
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59432367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432368
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432369
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.8.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59432394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.237.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432398
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432399
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 59432401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 59432403
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59432404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 59432405
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': 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: 59432408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432409
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432410
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59432411
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432412
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59432414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.237.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59432415
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432416
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59432313
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59432314
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 101, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['C5'], '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: 59432315
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 102, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432316
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 103, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.237.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59432317
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, '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: 59432318
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.237.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 59432319
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.237', 'ambient_counter': 237, 'ambient_order': 64, 'ambient_tex': 'C_4^2.C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '64.237.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '64.237', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 237, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C6'], '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: 59432311
    {'ambient': '64.237', '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': '16.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.c1.c1', '2.c1.d1', '2.d1.a1', '2.e1.a1', '2.e1.b1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.h1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4797, 5235, 5508, 4933, 4790, 5300, 5509, 4947], 'generators': [1, 2, 8, 32], 'label': '64.237.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.c1', '2.c1.d1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '2.e1.b1', '2.h1.a1', '2.h1.b1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '16.14', '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': '16.14'}
  • id: 59432312
    {'ambient': '64.237', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.c1.a1', '4.c1.b1', '4.e1.a1', '4.f1.a1', '4.k1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2438, 7540, 8126, 2732, 2438, 7641, 8161, 2740], 'generators': [1, 8, 32], 'label': '64.237.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.a1', '4.c1.b1', '4.c1.a1', '4.e1.a1', '4.k1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432313
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3869, -1, 5490, -1, 3661, -1, 5489, -1], 'generators': [41], 'label': '64.237.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.k1.a1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432314
    {'ambient': '64.237', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.d1.a1', '16.d1.b1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.f1.b1'], 'contains': ['64.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5949, 4705, 8153, 5241, 5736, 4768, 8114, 5040], 'generators': [16], 'label': '64.237.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.48', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432315
    {'ambient': '64.237', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.c1.b1', '16.g1.a1', '16.g1.b1', '16.h1.a1', '16.h1.b1', '16.h1.c1', '16.h1.d1'], 'contains': ['64.a1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3443, 5545, 2435, 4623, 3236, 5619, 2435, 4636], 'generators': [20], 'label': '64.237.32.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.b1', '16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '32.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.48', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432316
    {'ambient': '64.237', 'aut_centralizer_order': 1024, 'aut_label': '32.c1', 'aut_quo_index': 30, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.i1.a1', '16.i1.b1', '16.j1.a1', '16.j1.b1', '16.k1.a1'], 'contains': ['64.a1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4750, 5125, 5050, 4824, 4542, 5193, 5057, 4838], 'generators': [4], 'label': '64.237.32.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '32.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.50', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432317
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.g1.a1', '16.i1.a1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': '32T216', 'count': 4, 'diagramx': [4324, -1, 4839, -1, 4116, -1, 4847, -1], 'generators': [32], 'label': '64.237.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.237', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432318
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.g1.b1', '16.i1.b1'], 'contains': ['64.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': '32T216', 'count': 4, 'diagramx': [4324, -1, 4629, -1, 4116, -1, 4636, -1], 'generators': [1], 'label': '64.237.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.b1', 'old_label': '32.d1.b1', 'projective_image': '64.237', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432319
    {'ambient': '64.237', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.b1'], 'contains': [], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4536, 5125, 4839, 4824, 4329, 5193, 4847, 4838], 'generators': [], 'label': '64.237.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.a1.a1', '32.c1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.237', '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': '1.1'}
  • id: 59432320
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.c1', '4.d1.a1', '4.d1.c1', '4.e1.a1', '4.j1.a1', '4.l1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3200, 6070, 3233, 3044, 3200, 6151, 3234, 3054], 'generators': [1, 2, 32], 'label': '64.237.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.c1', '4.b1.a1', '4.d1.c1', '4.d1.a1', '4.e1.a1', '4.j1.a1', '4.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432321
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.b1.d1', '4.d1.b1', '4.d1.d1', '4.e1.a1', '4.j1.b1', '4.l1.b1'], 'core': '2.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3200, 6070, 2955, 4933, 3200, 6151, 2955, 4947], 'generators': [1, 10, 32], 'label': '64.237.2.e1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.d1', '4.b1.b1', '4.d1.d1', '4.d1.b1', '4.e1.a1', '4.j1.b1', '4.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432322
    {'ambient': '64.237', 'aut_centralizer_order': 8, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.c1.a1', 'complements': ['32.d1.a1', '32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.f1.a1', '4.g1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1', '4.n1.a1', '4.n1.b1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6947, 4203, 7740, 5247, 6947, 4260, 7775, 5262], 'generators': [33, 2, 8], 'label': '64.237.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.g1.a1', '4.f1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1', '4.n1.a1', '4.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432323
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55805', 'aut_weyl_index': 4, 'centralizer': '16.a1.a1', 'complements': ['32.d1.a1', '32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.f1.a1', '4.h1.a1', '4.h1.b1', '4.l1.a1', '4.l1.b1', '4.p1.a1', '4.p1.b1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3745, 5534, 1915, 3647, 3744, 5608, 1915, 3658], 'generators': [33, 34, 8], 'label': '64.237.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.f1.a1', '4.h1.a1', '4.h1.b1', '4.l1.b1', '4.l1.a1', '4.p1.b1', '4.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432324
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.d1.a1', 'complements': ['32.d1.a1', '32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.a1', '4.k1.a1', '4.l1.b1', '4.m1.a1', '4.m1.b1', '4.o1.b1', '4.o1.d1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4424, 6742, 7341, 2359, 4424, 6831, 7376, 2365], 'generators': [33, 2, 40], 'label': '64.237.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.a1', '4.m1.b1', '4.o1.b1', '4.o1.d1', '4.k1.a1', '4.j1.a1', '4.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432325
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.d1.b1', 'complements': ['32.d1.a1', '32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.b1', '4.k1.a1', '4.l1.a1', '4.m1.c1', '4.m1.d1', '4.o1.a1', '4.o1.c1'], 'core': '2.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4424, 6742, 5851, 4620, 4424, 6831, 5850, 4633], 'generators': [33, 34, 40], 'label': '64.237.2.h1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.m1.c1', '4.m1.d1', '4.o1.a1', '4.o1.c1', '4.k1.a1', '4.j1.b1', '4.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432326
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.e1.a1', '8.i1.a1', '8.i1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7686, 2943, 9436, 9279, 7686, 2983, 9435, 9306], 'generators': [8, 32, 4], 'label': '64.237.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.a1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432327
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.d1.a1'], 'contains': ['8.a1.b1', '8.b1.a1', '8.e1.b1', '8.i1.c1', '8.i1.d1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7686, 2943, 9006, 6712, 7686, 2983, 9006, 6732], 'generators': [1, 8, 4], 'label': '64.237.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.b1', '8.e1.b1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432328
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.f1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4152, 4810, 4404, 7696, 4152, 4874, 4404, 7718], 'generators': [2, 32], 'label': '64.237.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432329
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.e1.a1', 'complements': ['32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.g1.a1', '4.h1.a1', '4.m1.a1', '4.m1.c1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6020, 3217, 6589, 6598, 6020, 3260, 6589, 6617], 'generators': [2, 8, 32], 'label': '64.237.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.m1.a1', '4.m1.c1', '4.g1.a1', '4.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432330
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.d1.b1', '8.f1.c1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4152, 4810, 2632, 8229, 4152, 4874, 2632, 8254], 'generators': [10, 32], 'label': '64.237.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '8.d1.b1', '8.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432331
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.c1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.d1.a1', '8.f1.b1'], 'core': '4.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4152, 4810, 2069, 1513, 4152, 4874, 2069, 1518], 'generators': [1, 2], 'label': '64.237.4.b1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.c1', 'normal_contained_in': ['2.a1.b1', '2.c1.c1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.d1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432413
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.c1.a1', '32.d1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4324, -1, 4839, -1, 4116, -1, 4847, -1], 'generators': [32, 4], 'label': '64.237.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.i1.a1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432332
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.d1', '2.e1.b1'], 'contains': ['8.a1.b1', '8.d1.b1', '8.f1.d1'], 'core': '4.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4152, 4810, 1759, 7080, 4152, 4874, 1760, 7101], 'generators': [1, 10], 'label': '64.237.4.b1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.d1', 'normal_contained_in': ['2.a1.b1', '2.c1.d1', '2.e1.b1'], 'normal_contains': ['8.a1.b1', '8.d1.b1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432333
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.b1', '8.g1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2934, 6968, 5892, 6119, 2934, 7062, 5891, 6136], 'generators': [9, 32], 'label': '64.237.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.c1.a1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432334
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.c1', '2.c1.d1', '2.d1.a1'], 'contains': ['8.a1.b1', '8.e1.a1', '8.g1.a1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2934, 6968, 6200, 130, 2934, 7062, 6200, 130], 'generators': [1, 40], 'label': '64.237.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.c1.c1', '2.c1.d1', '2.d1.a1'], 'normal_contains': ['8.a1.b1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432335
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.f1.b1', '8.h1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 2155, 2941, 7388, 5310, 2184, 2941, 7410], 'generators': [3, 32], 'label': '64.237.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.h1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432336
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.f1.d1', '8.h1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 2155, 3559, 8911, 5310, 2184, 3559, 8937], 'generators': [11, 32], 'label': '64.237.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '8.h1.b1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432337
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.d1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.f1.a1', '8.h1.a1'], 'core': '4.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 2155, 3868, 3044, 5310, 2184, 3868, 3054], 'generators': [1, 34], 'label': '64.237.4.d1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.c1', 'normal_contained_in': ['2.b1.b1', '2.c1.d1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.h1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432338
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.c1', '2.e1.b1'], 'contains': ['8.a1.b1', '8.f1.c1', '8.h1.b1'], 'core': '4.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 2155, 3250, 3606, 5310, 2184, 3250, 3617], 'generators': [1, 42], 'label': '64.237.4.d1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.d1', 'normal_contained_in': ['2.b1.b1', '2.c1.c1', '2.e1.b1'], 'normal_contains': ['8.a1.b1', '8.h1.b1', '8.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432339
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.e1.a1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.c1.a1', '8.k1.a1', '8.k1.b1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [351, 8981, 912, 947, 352, 9101, 912, 950], 'generators': [1, 32, 16], 'label': '64.237.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.d1.a1', '2.e1.a1', '2.e1.b1'], 'normal_contains': ['8.a1.b1', '8.a1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432340
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '8.e1.b1', 'complements': ['32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.c1', '4.b1.d1', '4.g1.a1', '4.h1.b1', '4.m1.b1', '4.m1.d1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6020, 3217, 4495, 7080, 6020, 3260, 4494, 7101], 'generators': [1, 2, 8], 'label': '64.237.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.c1', '4.b1.d1', '4.m1.b1', '4.m1.d1', '4.g1.a1', '4.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432341
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.g1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2356, 7540, 8175, 1781, 2355, 7641, 8175, 1786], 'generators': [33, 8], 'label': '64.237.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.d1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432342
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '4.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8968, 1555, 8413, 9620, 8969, 1576, 8413, 9648], 'generators': [2, 8], 'label': '64.237.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432343
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.f1.c1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8426, 1018, 4685, 5587, 8425, 1032, 4686, 5603], 'generators': [34, 8], 'label': '64.237.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.c1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432344
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.b1', '8.f1.d1'], 'core': '4.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8426, 1018, 1478, 9870, 8425, 1032, 1478, 9899], 'generators': [3, 8], 'label': '64.237.4.h1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.b1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432345
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.f1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.h1.b1', '8.j1.a1', '8.j1.b1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9649, 348, 9837, 8571, 9649, 352, 9837, 8596], 'generators': [35, 8, 4], 'label': '64.237.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.b1', '2.b1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '8.h1.b1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432346
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.f1.a1', '2.h1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.h1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4731, 6397, 7951, 1246, 4731, 6482, 7950, 1250], 'generators': [33, 2], 'label': '64.237.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.f1.a1'], 'normal_contains': ['8.d1.a1', '8.c1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432414
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1'], 'contains': ['32.c1.a1', '32.d1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4324, -1, 4614, -1, 4116, -1, 4623, -1], 'generators': [1, 4], 'label': '64.237.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '16.i1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432347
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.j1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.b1', '2.f1.a1', '2.h1.b1'], 'contains': ['8.c1.a1', '8.d1.b1', '8.h1.b1'], 'core': '4.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4731, 6397, 4924, 5099, 4731, 6482, 4923, 5114], 'generators': [33, 10], 'label': '64.237.4.j1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.b1', 'normal_contained_in': ['2.e1.b1', '2.h1.b1', '2.f1.a1'], 'normal_contains': ['8.d1.b1', '8.c1.a1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432348
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.k1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.h1.b1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.e1.b1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1841, 9652, 8664, 410, 1841, 9781, 8664, 411], 'generators': [33, 40], 'label': '64.237.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.h1.b1'], 'normal_contains': ['8.e1.a1', '8.e1.b1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432349
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.g1.a1', '2.h1.b1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.f1.b1', '8.l1.a1', '8.l1.c1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1162, 8182, 537, 2704, 1161, 8291, 537, 2712], 'generators': [33, 34, 16], 'label': '64.237.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.b1', '2.g1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432350
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.b1', '2.g1.a1', '2.h1.a1'], 'contains': ['8.c1.a1', '8.f1.c1', '8.f1.d1', '8.l1.b1', '8.l1.d1'], 'core': '4.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1162, 8182, 163, 2331, 1161, 8291, 163, 2338], 'generators': [33, 42, 16], 'label': '64.237.4.l1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.b1', 'normal_contained_in': ['2.e1.b1', '2.h1.a1', '2.g1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.c1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432351
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': ['32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.h1.b1', '4.i1.a1', '4.o1.a1', '4.o1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7686, 2231, 6192, 8023, 7686, 2261, 6192, 8046], 'generators': [3, 8, 32], 'label': '64.237.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.b1', '4.d1.a1', '4.o1.a1', '4.o1.b1', '4.i1.a1', '4.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432352
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.c1', '2.h1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.f1.c1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5890, 5382, 7475, 647, 5889, 5454, 7475, 649], 'generators': [2, 40], 'label': '64.237.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.c1', '2.h1.a1'], 'normal_contains': ['8.e1.a1', '8.d1.a1', '8.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432353
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.m1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.h1.a1'], 'contains': ['8.d1.a1', '8.e1.b1', '8.f1.d1'], 'core': '4.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5890, 5382, 5399, 6385, 5889, 5454, 5399, 6404], 'generators': [9, 2], 'label': '64.237.4.m1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.h1.a1'], 'normal_contains': ['8.e1.b1', '8.d1.a1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432354
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.m1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.d1', '2.h1.b1'], 'contains': ['8.d1.b1', '8.e1.a1', '8.f1.a1'], 'core': '4.m1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5890, 5382, 5624, 4876, 5889, 5454, 5623, 4890], 'generators': [34, 40], 'label': '64.237.4.m1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.c1', 'normal_contained_in': ['2.a1.a1', '2.c1.d1', '2.h1.b1'], 'normal_contains': ['8.e1.a1', '8.d1.b1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432355
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '4.m1.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.h1.b1'], 'contains': ['8.d1.b1', '8.e1.b1', '8.f1.b1'], 'core': '4.m1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5890, 5382, 4136, 7963, 5889, 5454, 4136, 7986], 'generators': [9, 10], 'label': '64.237.4.m1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.d1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.h1.b1'], 'normal_contains': ['8.e1.b1', '8.d1.b1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.d1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432356
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.n1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.c1.c1', '2.f1.a1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.h1.b1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6947, 4209, 6482, 3886, 6947, 4266, 6482, 3898], 'generators': [41, 2], 'label': '64.237.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.c1.c1', '2.c1.a1', '2.f1.a1'], 'normal_contains': ['8.d1.a1', '8.h1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432357
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '4.n1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.c1.d1', '2.f1.a1'], 'contains': ['8.d1.b1', '8.g1.a1', '8.h1.a1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6947, 4209, 5161, 5336, 6947, 4266, 5161, 5352], 'generators': [41, 10], 'label': '64.237.4.n1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.c1.d1', '2.c1.b1', '2.f1.a1'], 'normal_contains': ['8.d1.b1', '8.h1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432358
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.c1', '2.h1.b1'], 'contains': ['8.e1.a1', '8.f1.b1', '8.h1.b1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6405, 3672, 6734, 3325, 6404, 3722, 6734, 3335], 'generators': [3, 40], 'label': '64.237.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.c1', '2.h1.b1'], 'normal_contains': ['8.e1.a1', '8.h1.b1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432359
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.d1', '2.h1.a1'], 'contains': ['8.e1.a1', '8.f1.d1', '8.h1.a1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6405, 3672, 7237, 4137, 6404, 3722, 7237, 4149], 'generators': [35, 40], 'label': '64.237.4.o1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.b1.a1', '2.c1.d1', '2.h1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432360
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.a1', '2.h1.b1'], 'contains': ['8.e1.b1', '8.f1.a1', '8.h1.b1'], 'core': '4.o1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6405, 3672, 6985, 5838, 6404, 3722, 6985, 5855], 'generators': [9, 34], 'label': '64.237.4.o1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.c1', 'normal_contained_in': ['2.b1.b1', '2.c1.a1', '2.h1.b1'], 'normal_contains': ['8.e1.b1', '8.h1.b1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.c1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432361
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 64, 'centralizer': '8.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.b1', '2.h1.a1'], 'contains': ['8.e1.b1', '8.f1.c1', '8.h1.a1'], 'core': '4.o1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6405, 3672, 7712, 4388, 6404, 3722, 7713, 4401], 'generators': [9, 42], 'label': '64.237.4.o1.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.d1', 'normal_contained_in': ['2.b1.b1', '2.c1.b1', '2.h1.a1'], 'normal_contains': ['8.e1.b1', '8.h1.a1', '8.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59432415
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5263, -1, 5968, -1, 5056, -1, 5968, -1], 'generators': [2], 'label': '64.237.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.j1.a1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432362
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': ['32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.d1.c1', '4.d1.d1', '4.h1.a1', '4.i1.a1', '4.o1.c1', '4.o1.d1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7686, 2231, 6985, 5587, 7686, 2261, 6985, 5603], 'generators': [1, 34, 8], 'label': '64.237.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.d1.d1', '4.d1.c1', '4.o1.c1', '4.o1.d1', '4.i1.a1', '4.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432363
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.p1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.c1.d1', '2.g1.a1'], 'contains': ['8.f1.a1', '8.f1.d1', '8.g1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3543, 5890, 2350, 4639, 3543, 5968, 2350, 4652], 'generators': [41, 34], 'label': '64.237.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.c1.d1', '2.c1.a1', '2.g1.a1'], 'normal_contains': ['8.f1.a1', '8.f1.d1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432364
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '4.p1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.c1.c1', '2.g1.a1'], 'contains': ['8.f1.b1', '8.f1.c1', '8.g1.a1'], 'core': '4.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3543, 5890, 1226, 2017, 3543, 5968, 1226, 2024], 'generators': [41, 42], 'label': '64.237.4.p1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.b1', 'normal_contained_in': ['2.c1.c1', '2.c1.b1', '2.g1.a1'], 'normal_contains': ['8.f1.c1', '8.f1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432365
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.g1.a1', '16.i1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3762, 5446, 4828, 7298, 3762, 5519, 4828, 7317], 'generators': [32, 4, 16], 'label': '64.237.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.b1.a1', '4.b1.b1', '4.d1.b1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432366
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.b1.c1', '4.b1.d1', '4.c1.b1', '4.d1.c1', '4.d1.d1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.d1.b1', '16.g1.b1', '16.i1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3762, 5446, 3859, 3044, 3762, 5519, 3860, 3054], 'generators': [1, 4, 16], 'label': '64.237.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.b1', '4.b1.c1', '4.b1.d1', '4.d1.d1', '4.d1.c1', '4.e1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432367
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.h1.b1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8426, 2430, 8101, 7595, 8425, 2462, 8101, 7614], 'generators': [8, 4], 'label': '64.237.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.b1', '4.a1.a1', '4.g1.a1', '4.f1.a1', '4.i1.a1', '4.h1.a1', '4.h1.b1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432368
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.f1.a1', '4.j1.a1', '4.j1.b1', '4.k1.a1', '4.l1.a1', '4.l1.b1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.c1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2314, 7669, 4530, 2356, 2314, 7771, 4530, 2360], 'generators': [33, 16], 'label': '64.237.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.e1.a1', '4.k1.a1', '4.f1.a1', '4.j1.a1', '4.j1.b1', '4.l1.b1', '4.l1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.b1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432369
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.b1.c1', '4.g1.a1', '4.j1.a1', '4.m1.a1', '4.m1.b1', '4.n1.a1'], 'contains': ['16.a1.a1', '16.j1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6014, 4810, 6242, 4083, 6014, 4874, 6241, 4095], 'generators': [2, 16], 'label': '64.237.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.c1', '4.b1.a1', '4.m1.a1', '4.m1.b1', '4.g1.a1', '4.j1.a1', '4.n1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432370
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.h1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.b1.d1', '4.g1.a1', '4.j1.b1', '4.m1.c1', '4.m1.d1', '4.n1.b1'], 'contains': ['16.a1.a1', '16.j1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6014, 4810, 5126, 6908, 6014, 4874, 5126, 6926], 'generators': [10, 16], 'label': '64.237.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.d1', '4.b1.b1', '4.m1.c1', '4.m1.d1', '4.g1.a1', '4.j1.b1', '4.n1.b1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432371
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.b1', '4.k1.a1', '4.m1.a1', '4.m1.c1', '4.o1.a1', '4.o1.b1'], 'contains': ['16.a1.a1', '16.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5210, 6082, 7358, 2748, 5210, 6163, 7357, 2756], 'generators': [40, 4], 'label': '64.237.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.b1', '4.m1.a1', '4.m1.c1', '4.o1.a1', '4.o1.b1', '4.k1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432372
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.a1', '4.k1.a1', '4.m1.b1', '4.m1.d1', '4.o1.c1', '4.o1.d1'], 'contains': ['16.a1.a1', '16.e1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5210, 6082, 6985, 5974, 5210, 6163, 6985, 5991], 'generators': [9, 4], 'label': '64.237.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.a1', '4.m1.b1', '4.m1.d1', '4.o1.c1', '4.o1.d1', '4.k1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432373
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.b1', '4.m1.b1', '4.n1.a1', '4.o1.c1', '4.p1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 4933, 5508, 6203, 5163, 4999, 5509, 6221], 'generators': [9, 2, 32], 'label': '64.237.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.b1.a1', '4.d1.b1', '4.m1.b1', '4.o1.c1', '4.n1.a1', '4.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432374
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.m1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.c1', '4.h1.a1', '4.l1.a1', '4.m1.c1', '4.o1.c1', '4.p1.a1'], 'contains': ['16.a1.a1', '16.h1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 4017, 4157, 5194, 4406, 4070, 4158, 5210], 'generators': [34, 16], 'label': '64.237.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.c1', '4.m1.c1', '4.o1.c1', '4.h1.a1', '4.l1.a1', '4.p1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432375
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.m1.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.c1', '4.d1.a1', '4.h1.b1', '4.l1.a1', '4.m1.d1', '4.o1.a1', '4.p1.b1'], 'contains': ['16.a1.a1', '16.h1.b1'], 'core': '8.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 4017, 2818, 4453, 4406, 4070, 2818, 4466], 'generators': [3, 16], 'label': '64.237.8.f1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.b1', 'normal_contained_in': ['4.b1.c1', '4.d1.a1', '4.m1.d1', '4.o1.a1', '4.h1.b1', '4.l1.a1', '4.p1.b1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432376
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.d1.d1', '4.h1.a1', '4.l1.b1', '4.m1.a1', '4.o1.d1', '4.p1.b1'], 'contains': ['16.a1.a1', '16.h1.c1'], 'core': '8.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 4017, 3561, 3713, 4406, 4070, 3562, 3723], 'generators': [42, 16], 'label': '64.237.8.f1.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.c1', 'normal_contained_in': ['4.b1.b1', '4.d1.d1', '4.m1.a1', '4.o1.d1', '4.h1.a1', '4.l1.b1', '4.p1.b1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432377
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.m1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.d1', '4.d1.b1', '4.h1.b1', '4.l1.b1', '4.m1.b1', '4.o1.b1', '4.p1.a1'], 'contains': ['16.a1.a1', '16.h1.d1'], 'core': '8.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 4017, 3190, 6363, 4406, 4070, 3190, 6382], 'generators': [11, 16], 'label': '64.237.8.f1.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.d1', 'normal_contained_in': ['4.b1.d1', '4.d1.b1', '4.m1.b1', '4.o1.b1', '4.h1.b1', '4.l1.b1', '4.p1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.d1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432378
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '8.g1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.c1.b1', '4.f1.a1', '4.n1.a1', '4.n1.b1', '4.p1.a1', '4.p1.b1'], 'contains': ['16.a1.a1', '16.k1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3118, 6876, 5498, 3342, 3118, 6967, 5498, 3352], 'generators': [41, 16], 'label': '64.237.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.b1', '4.c1.a1', '4.f1.a1', '4.n1.a1', '4.n1.b1', '4.p1.b1', '4.p1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432379
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.d1.c1', '4.i1.a1', '4.j1.a1', '4.n1.b1', '4.o1.b1', '4.o1.d1'], 'contains': ['16.a1.a1', '16.f1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6818, 3223, 6613, 4824, 6817, 3266, 6613, 4838], 'generators': [35, 4], 'label': '64.237.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.d1.c1', '4.d1.a1', '4.o1.b1', '4.o1.d1', '4.i1.a1', '4.j1.a1', '4.n1.b1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432380
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.j1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.d1.d1', '4.i1.a1', '4.j1.b1', '4.n1.a1', '4.o1.a1', '4.o1.c1'], 'contains': ['16.a1.a1', '16.f1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6818, 3223, 5869, 5565, 6817, 3266, 5869, 5581], 'generators': [43, 4], 'label': '64.237.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.d1.d1', '4.d1.b1', '4.o1.a1', '4.o1.c1', '4.i1.a1', '4.j1.b1', '4.n1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432381
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7622, -1, 9216, -1, 7621, -1, 9216, -1], 'generators': [8, 32], 'label': '64.237.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432382
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.b1', '16.d1.a1', '16.e1.a1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7622, -1, 8845, -1, 7621, -1, 8845, -1], 'generators': [12, 32], 'label': '64.237.8.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.i1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432383
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1'], 'contains': ['16.b1.a1', '16.d1.b1', '16.e1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7622, -1, 8473, -1, 7621, -1, 8473, -1], 'generators': [1, 8], 'label': '64.237.8.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.i1.c1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432384
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.d1.a1', '4.m1.d1', '4.n1.b1', '4.o1.d1', '4.p1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 4933, 4098, 5895, 5163, 4999, 4097, 5912], 'generators': [9, 10, 32], 'label': '64.237.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.b1.b1', '4.d1.a1', '4.m1.d1', '4.o1.d1', '4.n1.b1', '4.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432385
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1'], 'contains': ['16.b1.b1', '16.d1.b1', '16.e1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7622, -1, 7729, -1, 7621, -1, 7729, -1], 'generators': [1, 12], 'label': '64.237.8.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.i1.d1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432386
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.f1.b1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9040, -1, 9698, -1, 9040, -1, 9698, -1], 'generators': [35, 8], 'label': '64.237.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.j1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432387
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.b1.b1', '16.f1.a1', '16.f1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9040, -1, 9501, -1, 9040, -1, 9501, -1], 'generators': [35, 12], 'label': '64.237.8.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.j1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432388
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.c1.a1', '16.g1.a1', '16.g1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1274, -1, 2337, -1, 1274, -1, 2337, -1], 'generators': [1, 32], 'label': '64.237.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.k1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432389
    {'ambient': '64.237', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.c1.b1', '16.g1.a1', '16.g1.b1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1274, -1, 2534, -1, 1274, -1, 2533, -1], 'generators': [17, 32], 'label': '64.237.8.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.k1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432390
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.h1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1699, -1, 1943, -1, 1699, -1, 1943, -1], 'generators': [33, 34], 'label': '64.237.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '8.l1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432391
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1'], 'contains': ['16.c1.a1', '16.h1.c1', '16.h1.d1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1699, -1, 1549, -1, 1699, -1, 1549, -1], 'generators': [33, 42], 'label': '64.237.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.l1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432392
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.c1.b1', '16.h1.a1', '16.h1.b1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1699, -1, 2140, -1, 1699, -1, 2140, -1], 'generators': [49, 34], 'label': '64.237.8.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '8.l1.c1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432393
    {'ambient': '64.237', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1'], 'contains': ['16.c1.b1', '16.h1.c1', '16.h1.d1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1699, -1, 1746, -1, 1699, -1, 1746, -1], 'generators': [49, 42], 'label': '64.237.8.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.l1.d1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59432416
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1'], 'contains': ['32.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5263, -1, 5050, -1, 5056, -1, 5057, -1], 'generators': [10], 'label': '64.237.16.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '16.j1.b1', 'projective_image': '32.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432394
    {'ambient': '64.237', 'aut_centralizer_order': 1024, 'aut_label': '16.a1', 'aut_quo_index': 5040, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.f1.b1', '8.f1.c1', '8.f1.d1', '8.g1.a1', '8.h1.a1', '8.h1.b1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4808, 5125, 5260, 4824, 4601, 5193, 5268, 4838], 'generators': [4, 16], 'label': '64.237.16.a1.a1', 'mobius_quo': 2, 'mobius_sub': 64, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.b1', '8.a1.a1', '8.e1.a1', '8.e1.b1', '8.b1.a1', '8.d1.a1', '8.d1.b1', '8.c1.a1', '8.h1.b1', '8.h1.a1', '8.f1.c1', '8.f1.a1', '8.f1.b1', '8.f1.d1', '8.g1.a1'], 'normal_contains': ['32.b1.a1', '32.a1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '16.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432395
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.c1', '4.c1.b1', '4.d1.d1', '4.m1.a1', '4.n1.a1', '4.o1.a1', '4.p1.b1'], 'core': '2.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 4933, 5200, 2017, 5163, 4999, 5200, 2024], 'generators': [1, 2, 40], 'label': '64.237.2.c1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.b1.c1', '4.d1.d1', '4.m1.a1', '4.o1.a1', '4.n1.a1', '4.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.c1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432396
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.i1.a1', '8.i1.c1', '8.j1.a1'], 'contains': ['32.a1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8023, 3713, 8651, 6979, 8023, 3763, 8615, 6778], 'generators': [8], 'label': '64.237.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '32.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432397
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.i1.b1', '8.i1.d1', '8.j1.b1'], 'contains': ['32.a1.a1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8023, 3713, 8454, 6475, 8023, 3763, 8418, 6071], 'generators': [12], 'label': '64.237.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '32.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432398
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.k1.a1', '8.l1.a1', '8.l1.b1'], 'contains': ['32.b1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2006, 6467, 1943, 2889, 2113, 6867, 1943, 2879], 'generators': [33], 'label': '64.237.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432399
    {'ambient': '64.237', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.k1.b1', '8.l1.c1', '8.l1.d1'], 'contains': ['32.b1.a1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2006, 6467, 2534, 4104, 2113, 6867, 2533, 4111], 'generators': [49], 'label': '64.237.16.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.b1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.b1', 'projective_image': '32.48', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.4', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432400
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.i1.a1', '8.i1.b1'], 'contains': ['32.a1.a1', '32.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5718, -1, 8047, -1, 5511, -1, 8011, -1], 'generators': [32, 16], 'label': '64.237.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432401
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.i1.c1', '8.i1.d1'], 'contains': ['32.a1.a1', '32.d1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5718, -1, 7625, -1, 5511, -1, 7590, -1], 'generators': [1, 16], 'label': '64.237.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '16.d1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432402
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.i1.a1', '8.i1.b1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6174, -1, 8257, -1, 5966, -1, 8221, -1], 'generators': [40], 'label': '64.237.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432403
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.i1.c1', '8.i1.d1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6174, -1, 7836, -1, 5966, -1, 7800, -1], 'generators': [9], 'label': '64.237.16.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '16.e1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59432404
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6818, -1, 9327, -1, 6817, -1, 9430, -1], 'generators': [35], 'label': '64.237.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432405
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '8.j1.a1', '8.j1.b1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6818, -1, 9042, -1, 6817, -1, 9094, -1], 'generators': [43], 'label': '64.237.16.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.f1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432406
    {'ambient': '64.237', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.267', 'aut_weyl_index': 16, 'centralizer': '16.a1.a1', 'complements': ['32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.d1', '4.c1.b1', '4.d1.c1', '4.m1.c1', '4.n1.b1', '4.o1.b1', '4.p1.a1'], 'core': '2.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 4933, 4891, 4279, 5163, 4999, 4891, 4292], 'generators': [1, 34, 40], 'label': '64.237.2.c1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.b1.d1', '4.d1.c1', '4.m1.c1', '4.o1.b1', '4.n1.b1', '4.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.d1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 59432407
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.k1.a1', '8.k1.b1'], 'contains': ['32.b1.a1', '32.d1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2988, -1, 2968, -1, 2781, -1, 2968, -1], 'generators': [32, 20], 'label': '64.237.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432408
    {'ambient': '64.237', 'aut_centralizer_order': 128, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.k1.a1', '8.k1.b1'], 'contains': ['32.b1.a1', '32.d1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2988, -1, 2744, -1, 2781, -1, 2744, -1], 'generators': [1, 20], 'label': '64.237.16.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.g1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432409
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.l1.a1', '8.l1.c1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3443, -1, 2337, -1, 3236, -1, 2337, -1], 'generators': [34], 'label': '64.237.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '16.h1.a1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432410
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '8.l1.a1', '8.l1.c1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3443, -1, 2140, -1, 3236, -1, 2140, -1], 'generators': [3], 'label': '64.237.16.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.b1', 'old_label': '16.h1.b1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432411
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.c1', '8.l1.b1', '8.l1.d1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3443, -1, 1746, -1, 3236, -1, 1746, -1], 'generators': [42], 'label': '64.237.16.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.h1.c1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59432412
    {'ambient': '64.237', 'aut_centralizer_order': 64, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.d1', '8.l1.b1', '8.l1.d1'], 'contains': ['32.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3443, -1, 1549, -1, 3236, -1, 1549, -1], 'generators': [11], 'label': '64.237.16.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.h1.d1', 'projective_image': '32.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}