Abstract group data - 64.255

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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], 'aut_gens': [[1, 2, 4, 8], [1, 34, 5, 9], [33, 34, 7, 58], [1, 2, 23, 42], [1, 2, 5, 9], [1, 2, 5, 8], [1, 2, 4, 40], [1, 34, 37, 56], [1, 3, 37, 41], [1, 2, 20, 25]], 'aut_group': '1024.djy', 'aut_hash': 7016268009201775304, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 16, 'aut_perms': [13412044800, 8388882064078, 5413204737070, 998282880, 1321086787996, 1321086781009, 1321086810670, 997925329, 1307674743221], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 4, 2, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 2, 1], [4, 4, 4, 1], [8, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7:C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '8.5', 'autcentquo_hash': 5, 'autcentquo_nilpotent': True, 'autcentquo_order': 8, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 2], [4, 2, 4], [4, 4, 6], [8, 4, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '16.11', 'commutator_count': 1, 'commutator_label': '4.1', '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': 255, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['32.44', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 2], [4, 2, 1, 4], [4, 4, 1, 6], [8, 4, 1, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 5040, 'exponent': 8, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '16.14', 'hash': 255, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [1, 2, 2, 4], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 40], [1, 2, 4, 24], [1, 34, 52, 8]], 'inner_hash': 11, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2\\times D_4', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 2]], 'label': '64.255', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'Q16:C2^2', 'ngens': 4, 'nilpotency_class': 3, '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': 11, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 22, 'number_divisions': 22, 'number_normal_subgroups': 81, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 129, 'number_subgroups': 185, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 15], [4, 32], [8, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[33, 2, 6, 10], [33, 34, 4, 8], [1, 34, 4, 9], [1, 34, 5, 9], [33, 35, 4, 41]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [1174447, 1174440, 120, 367936, 811565], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [4, 2]], 'representations': {'PC': {'code': 1161363587123228, 'gens': [1, 2, 3, 4], 'pres': [6, -2, 2, 2, 2, -2, -2, 158, 489, 159, 69, 376, 88]}, 'Perm': {'d': 18, 'gens': [363934935953335, 798262263879265, 106019364585769, 1180877878802329, 1559466605471046, 1180877878802328]}}, 'schur_multiplier': [2, 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': 'Q_{16}: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: 105738146
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 255, 'group_order': 64, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 105738157
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 255, 'group_order': 64, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 1, 'size': 1}
  • id: 105738161
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 255, 'group_order': 64, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 33, 'size': 1}
  • id: 105738162
    {'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 255, 'group_order': 64, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
  • id: 105738163
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 5, 'group_counter': 255, 'group_order': 64, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 2, 'size': 2}
  • id: 105738164
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 6, 'group_counter': 255, 'group_order': 64, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 3, 'size': 2}
  • id: 105738165
    {'aut_label': '2F', 'centralizer': '4.m1', 'counter': 7, 'group_counter': 255, 'group_order': 64, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 12, 'size': 4}
  • id: 105738166
    {'aut_label': '2F', 'centralizer': '4.m1', 'counter': 8, 'group_counter': 255, 'group_order': 64, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 13, 'size': 4}
  • id: 105738167
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 255, 'group_order': 64, 'label': '4A', 'order': 4, 'powers': [4], 'representative': 18, 'size': 2}
  • id: 105738147
    {'aut_label': '4B', 'centralizer': '2.c1', 'counter': 10, 'group_counter': 255, 'group_order': 64, 'label': '4B', 'order': 4, 'powers': [4], 'representative': 17, 'size': 2}
  • id: 105738148
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 255, 'group_order': 64, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 19, 'size': 2}
  • id: 105738149
    {'aut_label': '4D', 'centralizer': '2.c1', 'counter': 12, 'group_counter': 255, 'group_order': 64, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 16, 'size': 2}
  • id: 105738150
    {'aut_label': '4E', 'centralizer': '4.l1', 'counter': 13, 'group_counter': 255, 'group_order': 64, 'label': '4E', 'order': 4, 'powers': [4], 'representative': 4, 'size': 4}
  • id: 105738151
    {'aut_label': '4E', 'centralizer': '4.l1', 'counter': 14, 'group_counter': 255, 'group_order': 64, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 6, 'size': 4}
  • id: 105738152
    {'aut_label': '4E', 'centralizer': '4.l1', 'counter': 15, 'group_counter': 255, 'group_order': 64, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 5, 'size': 4}
  • id: 105738153
    {'aut_label': '4H', 'centralizer': '4.m1', 'counter': 16, 'group_counter': 255, 'group_order': 64, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 14, 'size': 4}
  • id: 105738154
    {'aut_label': '4E', 'centralizer': '4.l1', 'counter': 17, 'group_counter': 255, 'group_order': 64, 'label': '4I', 'order': 4, 'powers': [4], 'representative': 7, 'size': 4}
  • id: 105738155
    {'aut_label': '4H', 'centralizer': '4.m1', 'counter': 18, 'group_counter': 255, 'group_order': 64, 'label': '4J', 'order': 4, 'powers': [4], 'representative': 15, 'size': 4}
  • id: 105738156
    {'aut_label': '8A', 'centralizer': '4.e1', 'counter': 19, 'group_counter': 255, 'group_order': 64, 'label': '8A', 'order': 8, 'powers': [12], 'representative': 8, 'size': 4}
  • id: 105738158
    {'aut_label': '8A', 'centralizer': '4.e1', 'counter': 20, 'group_counter': 255, 'group_order': 64, 'label': '8B', 'order': 8, 'powers': [12], 'representative': 10, 'size': 4}
  • id: 105738159
    {'aut_label': '8A', 'centralizer': '4.e1', 'counter': 21, 'group_counter': 255, 'group_order': 64, 'label': '8C', 'order': 8, 'powers': [12], 'representative': 9, 'size': 4}
  • id: 105738160
    {'aut_label': '8A', 'centralizer': '4.e1', 'counter': 22, 'group_counter': 255, 'group_order': 64, 'label': '8D', 'order': 8, 'powers': [12], 'representative': 11, '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: 3572797
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3572808
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 3572812
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1c', '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], 'schur_index': 1}
  • id: 3572813
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1d', '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], 'schur_index': 1}
  • id: 3572814
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1e', '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], 'schur_index': 1}
  • id: 3572815
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1f', '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], 'schur_index': 1}
  • id: 3572816
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1g', '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], 'schur_index': 1}
  • id: 3572817
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1h', '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], 'schur_index': 1}
  • id: 3572818
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1i', '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], 'schur_index': 1}
  • id: 3572798
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1j', '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], 'schur_index': 1}
  • id: 3572799
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1k', '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], 'schur_index': 1}
  • id: 3572800
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1l', '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], 'schur_index': 1}
  • id: 3572801
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1m', '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], 'schur_index': 1}
  • id: 3572802
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1n', '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], 'schur_index': 1}
  • id: 3572803
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1o', '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], 'schur_index': 1}
  • id: 3572804
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.1p', '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], 'schur_index': 1}
  • id: 3572805
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572806
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572807
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572809
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3572810
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.4a', 'multiplicity': 1, 'nt': [16, 32], '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], 'schur_index': 2}
  • id: 3572811
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '64.255', 'group_order': 64, 'image': None, 'label': '64.255.4b', 'multiplicity': 1, 'nt': [16, 32], '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], '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: 5142896
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 64, 'label': '64.255.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5142907
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 5142911
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1c', '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]]]}
  • id: 5142912
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1d', '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]]]}
  • id: 5142913
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1e', '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]]]}
  • id: 5142914
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1f', '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]]]}
  • id: 5142915
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1g', '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]]]}
  • id: 5142916
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1h', '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]]]}
  • id: 5142917
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.255.1i', '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]]]}
  • id: 5142897
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.255.1j', '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]]]}
  • id: 5142898
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.255.1k', '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]]]}
  • id: 5142899
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 32, 'label': '64.255.1l', '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]]]}
  • id: 5142900
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 32, 'label': '64.255.1m', '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]]]}
  • id: 5142901
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 32, 'label': '64.255.1n', '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]]]}
  • id: 5142902
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 32, 'label': '64.255.1o', '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]]]}
  • id: 5142903
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 32, 'label': '64.255.1p', '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]]]}
  • id: 5142904
    {'center': '4.a1', 'center_index': 4, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1', 'kernel_order': 8, 'label': '64.255.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142905
    {'center': '4.a1', 'center_index': 4, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.d1', 'kernel_order': 8, 'label': '64.255.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142906
    {'center': '4.a1', 'center_index': 4, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1', 'kernel_order': 8, 'label': '64.255.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142908
    {'center': '4.a1', 'center_index': 4, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 8, 'label': '64.255.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5142909
    {'center': '16.a1', 'center_index': 16, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 2, 'label': '64.255.4a', 'nt': [16, 32], '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]]]}
  • id: 5142910
    {'center': '16.a1', 'center_index': 16, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '64.255', 'group_counter': 255, 'group_order': 64, 'image': None, 'image_isoclass': '32.44', 'image_order': 32, 'indicator': -1, 'kernel': '32.a1', 'kernel_order': 2, 'label': '64.255.4b', 'nt': [16, 32], '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]]]}
• 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: 59433249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}: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': '64.255.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 59433260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59433271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, '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': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}: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': '64.255.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}: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': '64.255.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, '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': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '64.255.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, '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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59433304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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': ['U1'], '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: 59433305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, '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: 59433250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, '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: 59433251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, '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: 59433252
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59433254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 59433258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59433264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433265
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59433266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, '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: 59433268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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: 59433270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433274
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.255.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 59433275
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 59433276
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, '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: 59433277
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, '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: 59433278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, '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: 59433279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, '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: 59433280
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, '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: 59433281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, '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: 59433283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, '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: 59433284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, '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: 59433285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.8.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1', 'outer_equivalence': True, 'perfect': False, '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: 59433286
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59433287
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.255.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 59433288
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.255.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433289
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.255.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433290
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.255.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 59433291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59433292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59433294
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.255.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59433295
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.255.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59433296
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.255.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': 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: 59433297
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '64.255.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.44', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 59433298
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.255.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', '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: 59433299
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.255.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, '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: 59433300
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.255.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, '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: 59433301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.255', 'ambient_counter': 255, 'ambient_order': 64, 'ambient_tex': 'Q_{16}:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '64.255.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '64.255', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 255, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', '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: 59433249
    {'ambient': '64.255', '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', 'complements': ['64.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4880, 4508, 4899, 4600], 'generators': [1, 2, 4, 8], 'label': '64.255.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433250
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.49', 'aut_weyl_index': 32, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.d1', '2.e1'], 'contains': ['8.c1', '8.g1', '8.k1', '8.r1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6863, 7403, 6897, 7553], 'generators': [1, 6, 16], 'label': '64.255.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.d1', '2.e1'], 'normal_contains': ['8.c1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433251
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.49', 'aut_weyl_index': 32, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.e1'], 'contains': ['8.c1', '8.h1', '8.l1', '8.s1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2872, 4451, 2886, 4542], 'generators': [1, 30, 16], 'label': '64.255.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.e1'], 'normal_contains': ['8.c1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433252
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.e1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.c1', '8.i1'], 'core': '4.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4481, 5565, 4503, 5678], 'generators': [1, 10], 'label': '64.255.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.c1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '16.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433253
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.f1'], 'contains': ['8.e1', '8.f1', '8.h1', '8.m1', '8.o1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [3437, 3516, 3455, 3588], 'generators': [29, 2, 16], 'label': '64.255.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.f1'], 'normal_contains': ['8.e1', '8.f1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433254
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 32, 'centralizer': '8.a1', 'complements': ['16.g1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.f1'], 'contains': ['8.e1', '8.g1', '8.n1', '8.q1'], 'core': '4.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [8984, 2581, 9028, 2634], 'generators': [5, 2, 16], 'label': '64.255.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.f1'], 'normal_contains': ['8.e1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433255
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.c1', 'complements': ['16.g1'], 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.e1', '8.i1'], 'core': '4.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [5505, 1614, 5532, 1647], 'generators': [9, 2], 'label': '64.255.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.e1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59433256
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.a1', 'complements': ['16.f1'], 'conjugacy_class_count': 8, 'contained_in': ['2.d1', '2.f1'], 'contains': ['8.f1', '8.g1', '8.i1'], 'core': '4.i1', 'coset_action_label': None, 'count': 8, 'diagramx': [3905, 9475, 3924, 9669], 'generators': [29, 10], 'label': '64.255.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.d1', '2.f1'], 'normal_contains': ['8.f1', '8.g1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433257
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '16.a1', 'complements': ['16.g1', '16.f1'], 'conjugacy_class_count': 8, 'contained_in': ['2.e1', '2.f1'], 'contains': ['8.g1', '8.h1', '8.i1'], 'core': '4.j1', 'coset_action_label': None, 'count': 8, 'diagramx': [5037, 6483, 5062, 6615], 'generators': [5, 10], 'label': '64.255.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.e1', '2.f1'], 'normal_contains': ['8.g1', '8.h1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433258
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.j1', '8.l1', '8.m1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1065, -1, 1071, -1], 'generators': [1, 2, 28], 'label': '64.255.4.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.k1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433259
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.k1', '8.n1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8261, -1, 8301, -1], 'generators': [1, 2, 4], 'label': '64.255.4.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.l1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433260
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '4.f1', '4.k1', '4.m1', '4.o1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2444, 3906, 2490, 3986], 'generators': [1, 2, 28, 16], 'label': '64.255.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.d1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433261
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 32, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.j1', '8.l1', '8.o1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [342, -1, 344, -1], 'generators': [1, 18, 28], 'label': '64.255.4.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.m1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433262
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 16, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.b1', '8.k1', '8.q1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7537, -1, 7574, -1], 'generators': [1, 18, 4], 'label': '64.255.4.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.n1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433263
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.d1', '8.m1', '8.o1', '8.p1', '8.s1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [2306, -1, 2317, -1], 'generators': [17, 2, 28], 'label': '64.255.4.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.o1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433264
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.49', 'aut_weyl_index': 32, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.d1', '8.n1', '8.q1', '8.r1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9658, -1, 9706, -1], 'generators': [17, 2, 4], 'label': '64.255.4.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.p1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433265
    {'ambient': '64.255', 'aut_centralizer_order': 128, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.k1', '4.l1'], 'contains': ['16.a1', '16.b1', '16.f1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5652, 1411, 5680, 1439], 'generators': [1, 2, 32], 'label': '64.255.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '16.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433266
    {'ambient': '64.255', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.m1', '4.n1'], 'contains': ['16.a1', '16.c1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5116, 2297, 5141, 2343], 'generators': [1, 18], 'label': '64.255.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433267
    {'ambient': '64.255', '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.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.d1', '16.e1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4093, 5094, 4112, 5197], 'generators': [1, 16], 'label': '64.255.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.d1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433268
    {'ambient': '64.255', 'aut_centralizer_order': 128, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.o1', '4.p1'], 'contains': ['16.b1', '16.c1', '16.d1'], 'core': '8.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [6188, 525, 6219, 535], 'generators': [17, 2], 'label': '64.255.8.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.b1', '16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '32.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433269
    {'ambient': '64.255', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.f1', '4.g1', '4.h1'], 'contains': ['16.b1', '16.c1', '16.e1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [6858, 3402, 6892, 3472], 'generators': [3, 16], 'label': '64.255.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.f1', '4.g1', '4.h1'], 'normal_contains': ['16.b1', '16.c1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '32.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433270
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': 21, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.f1', '4.i1'], 'contains': ['16.e1', '16.h1'], 'core': '8.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [3226, 7817, 3242, 7968], 'generators': [29, 16], 'label': '64.255.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.b1', '4.f1', '4.i1'], 'normal_contains': ['16.e1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433271
    {'ambient': '64.255', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.53387', 'aut_weyl_index': 4, 'centralizer': '8.a1', 'complements': ['32.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.g1', '4.l1', '4.n1', '4.p1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7537, 2581, 7574, 2634], 'generators': [1, 2, 4, 16], 'label': '64.255.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.g1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433272
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 42, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.g1', '4.i1', '4.j1'], 'contains': ['16.e1', '16.i1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [7370, 6524, 7406, 6657], 'generators': [5, 16], 'label': '64.255.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.c1', '4.g1', '4.i1', '4.j1'], 'normal_contains': ['16.e1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433273
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.h1', 'aut_quo_index': 21, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.f1', '4.j1'], 'contains': ['16.e1', '16.j1'], 'core': '8.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [3580, 4247, 3598, 4334], 'generators': [31, 16], 'label': '64.255.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.d1', '4.f1', '4.j1'], 'normal_contains': ['16.e1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 59433274
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 42, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.e1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.h1', '4.i1', '4.j1'], 'contains': ['16.e1'], 'core': '8.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [4604, 5939, 4627, 6060], 'generators': [9], 'label': '64.255.8.i1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1', 'normal_contained_in': ['4.e1', '4.h1', '4.i1', '4.j1'], 'normal_contains': ['16.e1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '32.46', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433275
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.k1', '4.m1'], 'contains': ['16.a1', '16.g1', '16.h1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [446, -1, 448, -1], 'generators': [1, 28, 32], 'label': '64.255.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.j1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433276
    {'ambient': '64.255', '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': '4.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.l1', '4.n1'], 'contains': ['16.a1', '16.i1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7882, -1, 7920, -1], 'generators': [1, 6], 'label': '64.255.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.k1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433277
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '4.k1', '4.m1'], 'contains': ['16.a1', '16.j1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [982, -1, 987, -1], 'generators': [1, 30], 'label': '64.255.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.l1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433278
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.k1', '4.o1'], 'contains': ['16.b1', '16.h1', '16.j1'], 'core': '16.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2517, -1, 2530, -1], 'generators': [29, 2], 'label': '64.255.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.m1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433279
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '4.l1', '4.p1'], 'contains': ['16.b1', '16.i1'], 'core': '16.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [9260, -1, 9305, -1], 'generators': [5, 2], 'label': '64.255.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.n1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433280
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 256, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.m1', '4.o1'], 'contains': ['16.c1', '16.h1', '16.j1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [2005, -1, 2015, -1], 'generators': [29, 18], 'label': '64.255.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.o1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433281
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.o1'], 'contains': ['16.d1', '16.h1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [1493, -1, 1501, -1], 'generators': [17, 28], 'label': '64.255.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.p1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433282
    {'ambient': '64.255', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 8, 'centralizer': '8.c1', 'complements': ['32.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.e1', '4.h1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6105, 1036, 6135, 1058], 'generators': [1, 2, 8], 'label': '64.255.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.e1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 59433283
    {'ambient': '64.255', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '4.n1', '4.p1'], 'contains': ['16.c1', '16.i1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [8748, -1, 8791, -1], 'generators': [5, 18], 'label': '64.255.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.q1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433284
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.p1'], 'contains': ['16.d1', '16.i1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [8393, -1, 8435, -1], 'generators': [17, 6], 'label': '64.255.8.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.r1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433285
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 128, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '4.o1'], 'contains': ['16.d1', '16.j1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [2872, -1, 2886, -1], 'generators': [17, 30], 'label': '64.255.8.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.s1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433286
    {'ambient': '64.255', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.j1', '8.k1', '8.l1'], 'contains': ['32.a1', '32.b1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3871, 3378, 3890, 3447], 'generators': [1, 32], 'label': '64.255.16.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '16.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433287
    {'ambient': '64.255', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.d1', '8.e1', '8.m1', '8.n1'], 'contains': ['32.b1', '32.c1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5740, 1475, 5769, 1506], 'generators': [3, 32], 'label': '64.255.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.d1', '8.e1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433288
    {'ambient': '64.255', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.d1', '8.e1', '8.o1', '8.q1'], 'contains': ['32.b1'], 'core': '16.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5362, 2167, 5388, 2211], 'generators': [19], 'label': '64.255.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.d1', '8.e1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433289
    {'ambient': '64.255', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.d1', '8.p1', '8.r1', '8.s1'], 'contains': ['32.b1'], 'core': '16.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4249, 2752, 4271, 2808], 'generators': [17], 'label': '64.255.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.c1', '8.d1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433290
    {'ambient': '64.255', 'aut_centralizer_order': 512, 'aut_label': '16.e1', 'aut_quo_index': 1260, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.e1', '8.f1', '8.g1', '8.h1', '8.i1'], 'contains': ['32.b1'], 'core': '16.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [4604, 5094, 4627, 5197], 'generators': [16], 'label': '64.255.16.e1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.e1', 'normal_contained_in': ['8.c1', '8.e1', '8.f1', '8.g1', '8.h1', '8.i1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '32.46', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433291
    {'ambient': '64.255', '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': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1'], 'contains': ['32.a1', '32.c1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4983, -1, 5007, -1], 'generators': [1, 2], 'label': '64.255.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.f1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433292
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1'], 'contains': ['32.a1', '32.d1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2089, -1, 2099, -1], 'generators': [1, 28], 'label': '64.255.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '16.g1', 'projective_image': '32.44', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433293
    {'ambient': '64.255', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '16.a1', 'complements': ['32.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '4.i1'], 'core': '2.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3566, 7874, 3583, 8034], 'generators': [1, 6, 28], 'label': '64.255.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433294
    {'ambient': '64.255', 'aut_centralizer_order': 128, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.j1', '8.m1', '8.o1', '8.p1'], 'contains': ['32.b1', '32.d1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2493, -1, 2505, -1], 'generators': [29, 32], 'label': '64.255.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.h1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433295
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 512, 'centralizer': '4.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.k1', '8.n1', '8.q1', '8.r1'], 'contains': ['32.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8138, -1, 8178, -1], 'generators': [5], 'label': '64.255.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.i1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433296
    {'ambient': '64.255', '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': '4.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.h1', '8.l1', '8.m1', '8.o1', '8.s1'], 'contains': ['32.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2872, -1, 2886, -1], 'generators': [31], 'label': '64.255.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.j1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 59433297
    {'ambient': '64.255', 'aut_centralizer_order': 512, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': ['2.f1'], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.f1', '16.g1'], 'contains': ['64.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3880, 3362, 3900, 3430], 'generators': [1], 'label': '64.255.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '32.44', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.44', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433298
    {'ambient': '64.255', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.h1', '16.i1', '16.j1'], 'contains': ['64.a1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4249, 2768, 4271, 2825], 'generators': [32], 'label': '64.255.32.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.46', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.46', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433299
    {'ambient': '64.255', 'aut_centralizer_order': 256, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.f1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': '32T369', 'count': 4, 'diagramx': [4983, -1, 5007, -1], 'generators': [3], 'label': '64.255.32.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.c1', 'projective_image': '64.255', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433300
    {'ambient': '64.255', '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.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '16.h1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': '32T278', 'count': 8, 'diagramx': [2493, -1, 2505, -1], 'generators': [29], 'label': '64.255.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1', 'old_label': '32.d1', 'projective_image': '64.255', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433301
    {'ambient': '64.255', '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', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1'], 'contains': [], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4063, 3069, 4088, 3123], 'generators': [], 'label': '64.255.64.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.255', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 59433302
    {'ambient': '64.255', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 8, 'centralizer': '16.a1', 'complements': ['32.c1', '32.d1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.e1', '4.j1'], 'core': '2.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4515, 6305, 4538, 6433], 'generators': [1, 6, 8], 'label': '64.255.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.e1', '4.j1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '16.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433303
    {'ambient': '64.255', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '64.226', 'aut_weyl_index': 16, 'centralizer': '16.a1', 'complements': ['32.a1', '32.c1', '32.d1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.h1', '4.i1', '4.j1'], 'core': '2.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [5239, 5110, 5265, 5214], 'generators': [5, 2, 8], 'label': '64.255.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.h1', '4.i1', '4.j1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '32.46', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 59433304
    {'ambient': '64.255', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 64, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6140, 565, 6170, 577], 'generators': [1, 2, 16], 'label': '64.255.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '16.11', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 59433305
    {'ambient': '64.255', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.49', 'aut_weyl_index': 32, 'centralizer': '8.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.c1', '8.f1', '8.j1', '8.p1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1739, 8516, 1748, 8690], 'generators': [1, 28, 16], 'label': '64.255.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.c1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}