Abstract group data - 64.216

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4], 'aut_gens': [[39049, 39087, 13797, 23693], [4225, 63593, 21283, 13451], [39049, 63721, 5031, 23693], [4225, 13413, 37671, 23693], [39049, 28769, 46573, 54405], [39049, 63593, 13797, 23693], [4225, 39087, 46573, 23693], [63631, 39087, 13797, 13451], [39049, 4263, 46573, 23693], [39049, 39087, 46573, 23693], [39049, 4263, 54059, 23693], [39049, 48365, 37807, 23693]], 'aut_group': '2048.cqx', 'aut_hash': 3003538303849465736, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 16, 'aut_perms': [5505165389326, 8395109434180, 6720512203704, 19200362299, 18498, 4215700707409, 5523854077413, 1327353713280, 1327353718609, 5523854090178, 8395109417809], 'aut_phi_ratio': 64.0, '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], [2, 4, 4, 1], [4, 2, 2, 2], [4, 4, 2, 1], [4, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5.D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '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, 6], [4, 2, 4], [4, 4, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '16.14', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 216, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 6], [4, 2, 1, 4], [4, 4, 1, 6]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 2520, 'exponent': 4, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '16.14', 'hash': 216, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[39049, 39087, 46573, 23693], [39049, 39087, 21283, 54405], [4225, 63593, 13797, 23693], [39049, 4263, 13797, 23693]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 2]], 'label': '64.216', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, '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': 'C4^2:C2^2', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 22, 'number_divisions': 22, 'number_normal_subgroups': 81, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 167, 'number_subgroups': 305, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 31], [4, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [23693, 4097, 23693, 23693, 54277, 4097, 4097], 'outer_gens': [[63631, 48237, 13797, 23693], [63631, 39087, 13797, 13451], [39049, 28897, 46437, 23693], [39049, 54443, 13797, 23693], [39049, 54443, 30185, 23693], [39049, 63593, 13797, 23693], [39049, 39087, 21283, 23693]], 'outer_group': '128.2216', 'outer_hash': 2216, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [258829927, 212340360, 83463965, 11291160, 11370960, 90842400, 90842416], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4^2:C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, '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': 18970941854804, 'gens': [1, 2, 3, 5], 'pres': [6, 2, 2, 2, 2, 2, 2, 650, 404, 50, 730, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [24992892284608672, 58301495115895688, 125055985569224674, 24992906222178876]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [32646211, 32681027, 5226561, 20290625, 18125889, 18191425]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4225, 63503, 39049, 37671, 54277, 4879]}, 'Perm': {'d': 12, 'gens': [40723325, 80641440, 135732247, 139361760, 167450520, 16]}}, 'schur_multiplier': [2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:C_2^2', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 176324756
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 216, 'group_order': 64, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 4097, 'size': 1}
  • id: 176324767
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 216, 'group_order': 64, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 38921, 'size': 1}
  • id: 176324771
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 216, 'group_order': 64, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 63503, 'size': 1}
  • id: 176324772
    {'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 216, 'group_order': 64, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 28679, 'size': 1}
  • id: 176324773
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 5, 'group_counter': 216, 'group_order': 64, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 39049, 'size': 2}
  • id: 176324774
    {'aut_label': '2D', 'centralizer': '2.b1', 'counter': 6, 'group_counter': 216, 'group_order': 64, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 28807, 'size': 2}
  • id: 176324775
    {'aut_label': '2F', 'centralizer': '4.a1', 'counter': 7, 'group_counter': 216, 'group_order': 64, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 39087, 'size': 4}
  • id: 176324776
    {'aut_label': '2F', 'centralizer': '4.a1', 'counter': 8, 'group_counter': 216, 'group_order': 64, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 54443, 'size': 4}
  • id: 176324777
    {'aut_label': '2F', 'centralizer': '4.a1', 'counter': 9, 'group_counter': 216, 'group_order': 64, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 4135, 'size': 4}
  • id: 176324757
    {'aut_label': '2F', 'centralizer': '4.a1', 'counter': 10, 'group_counter': 216, 'group_order': 64, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 23587, 'size': 4}
  • id: 176324758
    {'aut_label': '2J', 'centralizer': '4.i1', 'counter': 11, 'group_counter': 216, 'group_order': 64, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 13709, 'size': 4}
  • id: 176324759
    {'aut_label': '2J', 'centralizer': '4.i1', 'counter': 12, 'group_counter': 216, 'group_order': 64, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 29961, 'size': 4}
  • id: 176324760
    {'aut_label': '4A', 'centralizer': '2.d1', 'counter': 13, 'group_counter': 216, 'group_order': 64, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 23693, 'size': 2}
  • id: 176324761
    {'aut_label': '4A', 'centralizer': '2.d1', 'counter': 14, 'group_counter': 216, 'group_order': 64, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 48259, 'size': 2}
  • id: 176324762
    {'aut_label': '4C', 'centralizer': '2.c1', 'counter': 15, 'group_counter': 216, 'group_order': 64, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 54277, 'size': 2}
  • id: 176324763
    {'aut_label': '4C', 'centralizer': '2.c1', 'counter': 16, 'group_counter': 216, 'group_order': 64, 'label': '4D', 'order': 4, 'powers': [2], 'representative': 13323, 'size': 2}
  • id: 176324764
    {'aut_label': '4E', 'centralizer': '4.k1', 'counter': 17, 'group_counter': 216, 'group_order': 64, 'label': '4E', 'order': 4, 'powers': [3], 'representative': 13797, 'size': 4}
  • id: 176324765
    {'aut_label': '4E', 'centralizer': '4.k1', 'counter': 18, 'group_counter': 216, 'group_order': 64, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 30185, 'size': 4}
  • id: 176324766
    {'aut_label': '4G', 'centralizer': '4.i1', 'counter': 19, 'group_counter': 216, 'group_order': 64, 'label': '4G', 'order': 4, 'powers': [2], 'representative': 46349, 'size': 4}
  • id: 176324768
    {'aut_label': '4E', 'centralizer': '4.k1', 'counter': 20, 'group_counter': 216, 'group_order': 64, 'label': '4H', 'order': 4, 'powers': [4], 'representative': 46437, 'size': 4}
  • id: 176324769
    {'aut_label': '4G', 'centralizer': '4.i1', 'counter': 21, 'group_counter': 216, 'group_order': 64, 'label': '4I', 'order': 4, 'powers': [2], 'representative': 62857, 'size': 4}
  • id: 176324770
    {'aut_label': '4E', 'centralizer': '4.k1', 'counter': 22, 'group_counter': 216, 'group_order': 64, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 62825, '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: 18444092
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1a', '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: 18444103
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1b', '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: 18444107
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1c', '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: 18444108
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1d', '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: 18444109
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1e', '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: 18444110
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1f', '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: 18444111
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1g', '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: 18444112
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1h', '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: 18444113
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1i', '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: 18444093
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1j', '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: 18444094
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1k', '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: 18444095
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1l', '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: 18444096
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1m', '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: 18444097
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1n', '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: 18444098
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1o', '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: 18444099
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.1p', '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: 18444100
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18444101
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18444102
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18444104
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 18444105
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.4a', 'multiplicity': 1, 'nt': [8, 22], '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': 1}
  • id: 18444106
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '64.216', 'group_order': 64, 'image': None, 'label': '64.216.4b', 'multiplicity': 1, 'nt': [8, 22], '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': 1}
• gps_char •

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

  
  
  • id: 39673394
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 64, 'label': '64.216.1a', '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: 39673405
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 32, 'label': '64.216.1b', '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: 39673409
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.216.1c', '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: 39673410
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.216.1d', '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: 39673411
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.216.1e', '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: 39673412
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.216.1f', '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: 39673413
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 32, 'label': '64.216.1g', '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: 39673414
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 32, 'label': '64.216.1h', '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: 39673415
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 32, 'label': '64.216.1i', '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: 39673395
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 32, 'label': '64.216.1j', '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: 39673396
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 32, 'label': '64.216.1k', '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: 39673397
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 32, 'label': '64.216.1l', '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: 39673398
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 32, 'label': '64.216.1m', '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: 39673399
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 32, 'label': '64.216.1n', '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: 39673400
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 32, 'label': '64.216.1o', '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: 39673401
    {'center': '1.a1', 'center_index': 1, 'center_order': 64, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 32, 'label': '64.216.1p', '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: 39673402
    {'center': '4.c1', 'center_index': 4, 'center_order': 16, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 8, 'label': '64.216.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39673403
    {'center': '4.c1', 'center_index': 4, 'center_order': 16, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 8, 'label': '64.216.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39673404
    {'center': '4.c1', 'center_index': 4, 'center_order': 16, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 8, 'label': '64.216.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39673406
    {'center': '4.c1', 'center_index': 4, 'center_order': 16, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.h1', 'kernel_order': 8, 'label': '64.216.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 39673407
    {'center': '16.a1', 'center_index': 16, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1', 'kernel_order': 2, 'label': '64.216.4a', 'nt': [8, 22], '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: 39673408
    {'center': '16.a1', 'center_index': 16, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '64.216', 'group_counter': 216, 'group_order': 64, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1', 'kernel_order': 2, 'label': '64.216.4b', 'nt': [8, 22], '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: 273001314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '64.216.1.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': '64.216', 'subgroup_hash': 216, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 273001325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 273001336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 273001358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 273001368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.34', 'subgroup_hash': 34, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1', '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': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 273001371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 273001315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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: 273001316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': True, '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: 273001319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.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': 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: 273001321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': 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: 273001322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': [], 'split': True, '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: 273001323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1', '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 273001326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1', '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: 273001327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1', '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2: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': '64.216.4.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2: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': '64.216.4.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: 273001330
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 273001331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 273001332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 273001333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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': '8.5', '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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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: 273001335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001337
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.8.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': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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: 273001340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 273001346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 273001348
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.8.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.16.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': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 273001350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '64.216.16.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: 273001351
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.216.16.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: 273001352
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.216.16.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: 273001353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1', '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: 273001354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.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: 273001355
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.216.16.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 273001356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.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: 273001357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 273001359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 273001360
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.216.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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: 273001361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '64.216.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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: 273001362
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 2, 'counter': 53, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.216.32.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': '32.46', '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': ['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: 273001363
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '64.216.32.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': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 273001364
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2: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': '64.216.32.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: 273001365
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.216.32.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: 273001366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '64.216.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1', '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: 273001367
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '64.216', 'ambient_counter': 216, 'ambient_order': 64, 'ambient_tex': 'C_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '64.216.64.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': '64.216', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 216, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 273001314
    {'ambient': '64.216', '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', '2.g1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5188, 4230, 5251, 4290], 'generators': [39049, 39087, 13797, 23693], 'label': '64.216.1.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', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001315
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.a1', '8.c1', '8.g1', '8.j1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3174, 4372, 3182, 4434], 'generators': [39049, 54027, 28679], 'label': '64.216.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.a1', '8.c1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001316
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '4.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.a1', '8.d1', '8.e1', '8.h1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4426, 3468, 4438, 3516], 'generators': [39049, 23693, 28679], 'label': '64.216.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '8.d1', '8.e1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001317
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '8.f1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7904, 5652, 7926, 5732], 'generators': [39049, 13797], 'label': '64.216.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001318
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': ['16.l1'], 'conjugacy_class_count': 8, 'contained_in': ['2.a1', '2.e1', '2.f1'], 'contains': ['8.b1', '8.c1', '8.f1', '8.q1'], 'core': '4.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [9200, 8083, 9225, 8197], 'generators': [4135, 13797, 38921], 'label': '64.216.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.e1', '2.f1'], 'normal_contains': ['8.b1', '8.c1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001319
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '16.a1', 'complements': ['16.l1'], 'conjugacy_class_count': 8, 'contained_in': ['2.a1', '2.e1', '2.g1'], 'contains': ['8.b1', '8.f1', '8.g1'], 'core': '4.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [8520, 6347, 8543, 6437], 'generators': [4135, 54027], 'label': '64.216.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.e1', '2.g1'], 'normal_contains': ['8.b1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001320
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 32, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.f1', '2.g1'], 'contains': ['8.b1', '8.d1', '8.k1'], 'core': '4.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [5226, 2052, 5240, 2081], 'generators': [4135, 23693, 28679], 'label': '64.216.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.f1', '2.g1'], 'normal_contains': ['8.b1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001321
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 32, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.e1'], 'contains': ['8.b1', '8.e1', '8.l1'], 'core': '4.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [7224, 8926, 7244, 9052], 'generators': [54277, 39087, 28679], 'label': '64.216.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.b1', '2.e1'], 'normal_contains': ['8.b1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '16.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001322
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '4.i1', 'complements': ['16.l1'], 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '2.e1'], 'contains': ['8.c1', '8.e1', '8.g1', '8.m1'], 'core': '4.i1', 'coset_action_label': None, 'count': 2, 'diagramx': [2373, 7178, 2380, 7279], 'generators': [54277, 54027, 28679], 'label': '64.216.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.c1', '2.e1'], 'normal_contains': ['8.c1', '8.e1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001323
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.j1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 32, 'centralizer': '8.e1', 'complements': ['16.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.f1'], 'contains': ['8.c1', '8.d1', '8.n1'], 'core': '4.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [1573, 1209, 1578, 1226], 'generators': [21387, 23693, 28679], 'label': '64.216.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.c1', '2.f1'], 'normal_contains': ['8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001324
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '4.k1', 'complements': ['16.l1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.f1', '2.g1'], 'contains': ['8.d1', '8.f1'], 'core': '4.k1', 'coset_action_label': None, 'count': 2, 'diagramx': [3773, 2729, 3783, 2768], 'generators': [46437, 23693], 'label': '64.216.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.d1', '2.f1', '2.g1'], 'normal_contains': ['8.d1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001325
    {'ambient': '64.216', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 16, 'centralizer': '16.a1', 'complements': ['32.d1', '32.e1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.d1', '4.e1', '4.f1'], 'core': '2.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8264, 6347, 8079, 6437], 'generators': [39049, 39087, 13797], 'label': '64.216.2.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.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001326
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.l1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '64.138', 'aut_weyl_index': 32, 'centralizer': '8.e1', 'complements': ['16.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.g1'], 'contains': ['8.d1', '8.g1', '8.o1'], 'core': '4.l1', 'coset_action_label': None, 'count': 1, 'diagramx': [827, 367, 830, 371], 'generators': [54027, 23693, 28679], 'label': '64.216.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.c1', '2.g1'], 'normal_contains': ['8.d1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001327
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 64, 'centralizer': '8.d1', 'complements': ['16.l1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.e1'], 'contains': ['8.e1', '8.f1'], 'core': '4.m1', 'coset_action_label': None, 'count': 2, 'diagramx': [6598, 9633, 6616, 9769], 'generators': [54277, 13797], 'label': '64.216.4.m1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1', 'normal_contained_in': ['2.d1', '2.e1'], 'normal_contains': ['8.e1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001328
    {'ambient': '64.216', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.49', 'aut_weyl_index': 64, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1'], 'contains': ['8.h1', '8.i1', '8.k1', '8.l1'], 'core': '8.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [5972, -1, 5988, -1], 'generators': [39049, 39087, 23693], 'label': '64.216.4.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': '32.46', '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: 273001329
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['8.h1', '8.j1', '8.m1', '8.n1', '8.o1'], 'core': '8.h1', 'coset_action_label': None, 'count': 8, 'diagramx': [201, -1, 202, -1], 'generators': [39049, 54027, 23693], 'label': '64.216.4.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', '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: 273001330
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'contains': ['16.a1', '16.b1', '16.h1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6980, 4187, 6998, 4246], 'generators': [39049, 28679, 38921], 'label': '64.216.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normal_contains': ['16.a1', '16.b1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001331
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.e1', '4.f1', '4.g1', '4.h1'], 'contains': ['16.a1', '16.e1', '16.i1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8612, 6034, 8635, 6119], 'generators': [4135, 28679, 38921], 'label': '64.216.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.e1', '4.f1', '4.g1', '4.h1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001332
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '4.i1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.e1', '4.i1', '4.j1'], 'contains': ['16.a1', '16.f1', '16.j1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5009, 5529, 5022, 5607], 'generators': [21387, 28679, 38921], 'label': '64.216.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.e1', '4.i1', '4.j1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001333
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.g1', '4.j1', '4.k1', '4.l1'], 'contains': ['16.a1', '16.c1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3674, 2680, 3685, 2718], 'generators': [23693, 28679], 'label': '64.216.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.g1', '4.j1', '4.k1', '4.l1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001334
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '8.e1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.h1', '4.i1', '4.m1'], 'contains': ['16.a1', '16.d1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5994, 7541, 6010, 7647], 'generators': [54277, 28679], 'label': '64.216.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.c1', '4.h1', '4.i1', '4.m1'], 'normal_contains': ['16.a1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001335
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '8.f1', 'aut_quo_index': 84, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.k1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.e1', '4.f1', '4.k1', '4.m1'], 'contains': ['16.a1', '16.k1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [7573, 6704, 7593, 6799], 'generators': [46437, 38921], 'label': '64.216.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.d1', '4.e1', '4.f1', '4.k1', '4.m1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001336
    {'ambient': '64.216', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.6407070', 'aut_weyl_index': 4, 'centralizer': '8.a1', 'complements': ['32.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.g1', '4.h1', '4.n1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6102, 4230, 6168, 4290], 'generators': [39049, 39087, 23693, 28679], 'label': '64.216.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.g1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001337
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '8.g1', 'aut_quo_index': 42, 'aut_stab_index': 2, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '4.i1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.f1', '4.i1', '4.l1'], 'contains': ['16.a1', '16.g1'], 'core': '8.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [2935, 4858, 2942, 4927], 'generators': [54027, 28679], 'label': '64.216.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.b1', '4.f1', '4.i1', '4.l1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001338
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.c1', 'complements': ['8.q1'], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.n1', '4.o1'], 'contains': ['16.b1', '16.c1', '16.d1'], 'core': '8.h1', 'coset_action_label': None, 'count': 4, 'diagramx': [4415, 3516, 4427, 3566], 'generators': [39049, 23693], 'label': '64.216.8.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': ['4.c1'], 'normal_contains': ['16.b1', '16.c1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.h1', '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.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 273001339
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.n1'], 'contains': ['16.b1', '16.e1', '16.l1'], 'core': '16.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [8166, -1, 8188, -1], 'generators': [39049, 39087, 38921], 'label': '64.216.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.i1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001340
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.o1'], 'contains': ['16.b1', '16.f1', '16.g1'], 'core': '16.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2368, -1, 2375, -1], 'generators': [39049, 54027], 'label': '64.216.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.j1', 'projective_image': '32.46', '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': '4.2'}
  • id: 273001341
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '4.n1'], 'contains': ['16.c1', '16.e1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [5427, -1, 5442, -1], 'generators': [4135, 23693], 'label': '64.216.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.k1', 'projective_image': '32.46', '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': '4.2'}
  • id: 273001342
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.h1', '4.n1'], 'contains': ['16.d1', '16.e1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [6560, -1, 6578, -1], 'generators': [54277, 39087], 'label': '64.216.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.l1', 'projective_image': '32.46', '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': '4.2'}
  • id: 273001343
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '4.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.i1', '4.o1'], 'contains': ['16.d1', '16.f1', '16.g1'], 'core': '16.d1', 'coset_action_label': None, 'count': 8, 'diagramx': [1802, -1, 1807, -1], 'generators': [54277, 54027], 'label': '64.216.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', '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': '2.1'}
  • id: 273001344
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '4.o1'], 'contains': ['16.c1', '16.f1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1235, -1, 1239, -1], 'generators': [21387, 23693], 'label': '64.216.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', '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': '4.2'}
  • id: 273001345
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '4.o1'], 'contains': ['16.c1', '16.g1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [838, -1, 841, -1], 'generators': [54027, 23693], 'label': '64.216.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', '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': '4.2'}
  • id: 273001346
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['16.h1', '16.i1', '16.l1'], 'core': '32.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [9450, -1, 9476, -1], 'generators': [39049, 39087, 28679], 'label': '64.216.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.p1', 'projective_image': '32.49', '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': '1.1'}
  • id: 273001347
    {'ambient': '64.216', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 8, 'centralizer': '8.e1', 'complements': ['32.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.i1', '4.j1', '4.l1', '4.o1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2373, 2661, 2380, 2699], 'generators': [39049, 54027, 23693, 28679], 'label': '64.216.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.i1', '4.j1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001348
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.e1'], 'contains': ['16.i1', '16.j1', '16.k1'], 'core': '32.b1', 'coset_action_label': None, 'count': 32, 'diagramx': [9032, -1, 9056, -1], 'generators': [4135, 13797], 'label': '64.216.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '8.q1', 'projective_image': '32.49', '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: 273001349
    {'ambient': '64.216', 'aut_centralizer_order': 1024, 'aut_label': '16.a1', 'aut_quo_index': 2520, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'contains': ['32.a1', '32.b1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5988, 4858, 6005, 4927], 'generators': [28679, 38921], 'label': '64.216.16.a1', 'mobius_quo': 2, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '16.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 273001350
    {'ambient': '64.216', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.h1', '8.i1', '8.j1'], 'contains': ['32.a1', '32.c1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5542, 4187, 5557, 4246], 'generators': [39049, 38921], 'label': '64.216.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.h1'], 'normal_contains': ['32.a1'], '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: 273001351
    {'ambient': '64.216', 'aut_centralizer_order': 512, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.d1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.h1', '8.k1', '8.n1', '8.o1'], 'contains': ['32.a1'], 'core': '16.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4045, 3516, 4056, 3566], 'generators': [23693], 'label': '64.216.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.d1', '8.h1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', '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.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001352
    {'ambient': '64.216', 'aut_centralizer_order': 512, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.h1', '8.l1', '8.m1'], 'contains': ['32.a1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [5122, 5332, 5136, 5407], 'generators': [54277], 'label': '64.216.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.e1', '8.h1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.d1', '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.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001353
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.i1', '8.k1', '8.l1'], 'contains': ['32.a1', '32.d1'], 'core': '32.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6881, -1, 6900, -1], 'generators': [4135, 38921], 'label': '64.216.16.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.e1', 'projective_image': '32.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001354
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.j1', '8.m1', '8.n1'], 'contains': ['32.a1', '32.e1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3391, -1, 3401, -1], 'generators': [21387, 38921], 'label': '64.216.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.f1', 'projective_image': '32.46', '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': '2.1'}
  • id: 273001355
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '8.j1', '8.m1', '8.o1'], 'contains': ['32.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2368, -1, 2375, -1], 'generators': [54027], 'label': '64.216.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.g1', 'projective_image': '32.46', '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': '2.1'}
  • id: 273001356
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.p1'], 'contains': ['32.b1', '32.c1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7327, -1, 7347, -1], 'generators': [39049, 28679], 'label': '64.216.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.h1', 'projective_image': '32.49', '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': '1.1'}
  • id: 273001357
    {'ambient': '64.216', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.b1', '8.p1', '8.q1'], 'contains': ['32.b1', '32.d1'], 'core': '32.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [8612, -1, 8635, -1], 'generators': [4135, 28679], 'label': '64.216.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.i1', 'projective_image': '32.49', '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: 273001358
    {'ambient': '64.216', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 8, 'centralizer': '8.d1', 'complements': ['32.d1', '32.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.k1', '4.m1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5188, 5265, 5251, 5339], 'generators': [39049, 13797, 23693], 'label': '64.216.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.k1', '4.m1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 273001359
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.i1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.q1'], 'contains': ['32.b1', '32.e1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6435, -1, 6452, -1], 'generators': [21387, 28679], 'label': '64.216.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1', 'old_label': '16.j1', 'projective_image': '32.49', '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: 273001360
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '8.q1'], 'contains': ['32.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7747, -1, 7768, -1], 'generators': [46437], 'label': '64.216.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '16.k1', 'projective_image': '32.49', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 273001361
    {'ambient': '64.216', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.i1', '8.p1'], 'contains': ['32.c1', '32.d1'], 'core': '64.a1', 'coset_action_label': '16T73', 'count': 32, 'diagramx': [8166, -1, 8188, -1], 'generators': [39049, 39087], 'label': '64.216.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.l1', 'projective_image': '64.216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 273001362
    {'ambient': '64.216', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1'], 'contains': ['64.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5335, 4415, 5349, 4477], 'generators': [38921], 'label': '64.216.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1', '16.d1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', '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.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 273001363
    {'ambient': '64.216', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 18, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.h1', '16.i1', '16.j1', '16.k1'], 'contains': ['64.a1'], 'core': '32.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7327, 4858, 7347, 4927], 'generators': [28679], 'label': '64.216.32.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.49', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.49', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 273001364
    {'ambient': '64.216', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '16.h1', '16.l1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': '32T63', 'count': 4, 'diagramx': [6935, -1, 6954, -1], 'generators': [39049], 'label': '64.216.32.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': '64.216', '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: 273001365
    {'ambient': '64.216', 'aut_centralizer_order': 128, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.e1', '16.i1', '16.l1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': '32T62', 'count': 16, 'diagramx': [7943, -1, 7964, -1], 'generators': [4135], 'label': '64.216.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.d1', 'projective_image': '64.216', '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: 273001366
    {'ambient': '64.216', 'aut_centralizer_order': 256, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '4.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '16.j1'], 'contains': ['64.a1'], 'core': '64.a1', 'coset_action_label': '32T269', 'count': 8, 'diagramx': [6435, -1, 6452, -1], 'generators': [21387], 'label': '64.216.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1', 'old_label': '32.e1', 'projective_image': '64.216', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 273001367
    {'ambient': '64.216', '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', '32.e1'], 'contains': [], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6935, 4636, 6954, 4702], 'generators': [], 'label': '64.216.64.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': '64.216', '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: 273001368
    {'ambient': '64.216', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 16, 'centralizer': '16.a1', 'complements': ['32.c1', '32.d1', '32.e1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '4.h1', '4.i1', '4.m1'], 'core': '2.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [7099, 7658, 7091, 7766], 'generators': [54277, 39087, 13797], 'label': '64.216.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '4.h1', '4.i1', '4.m1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001369
    {'ambient': '64.216', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 8, 'centralizer': '16.a1', 'complements': ['32.d1', '32.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.g1', '4.j1', '4.k1'], 'core': '2.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [4453, 3461, 4514, 3510], 'generators': [4135, 13797, 23693], 'label': '64.216.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.g1', '4.j1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001370
    {'ambient': '64.216', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 8, 'centralizer': '16.a1', 'complements': ['32.e1', '32.d1', '32.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.k1', '4.l1'], 'core': '2.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [3952, 1861, 4012, 1888], 'generators': [4135, 54027, 23693], 'label': '64.216.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.k1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 273001371
    {'ambient': '64.216', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '64.138', 'aut_weyl_index': 32, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.i1', '8.p1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9799, 5049, 9825, 5120], 'generators': [39049, 39087, 28679, 38921], 'label': '64.216.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '16.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}