Abstract group data - 32.33

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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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 3, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8], [1, 22, 12], [1, 6, 24], [1, 26, 22], [17, 22, 24], [5, 6, 28], [17, 2, 8], [5, 2, 8]], 'aut_group': '192.1540', 'aut_hash': 1540, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 12, 'aut_perms': [143733964, 94586093, 314298665, 94560744, 14953955, 345943829, 98212372], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 4, 1, 1], [4, 2, 6, 1], [4, 4, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\wr C_3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 3, 'autcentquo_group': '3.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 3, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [4, 2, 6], [4, 4, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '8.5', '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'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 33, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [4, 2, 2, 3], [4, 4, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 56, 'exponent': 4, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '8.5', 'hash': 33, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 22, 12], [21, 2, 8], [5, 2, 8]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': True, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 6]], 'label': '32.33', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 3, 'linQ_dim': 8, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:C2', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 14, 'number_divisions': 11, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 30, 'number_subgroups': 42, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [0, 1, 0, 0], 'outer_gens': [[1, 6, 24], [1, 10, 2], [1, 2, 28], [1, 6, 28]], 'outer_group': '24.13', 'outer_hash': 13, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 6, 'outer_perms': [316, 181, 269, 314], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times A_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 3]], 'representations': {'PC': {'code': 2231959642, 'gens': [1, 2, 4], 'pres': [5, 2, 2, 2, 2, 2, 221, 26, 243, 58]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 30594431879, 40849247818, 30704310001, 61245322049]}, 'Perm': {'d': 16, 'gens': [40291223, 15316555121280, 8395940079936, 2789792421136, 1313941673647]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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', '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: 103763718
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 33, 'group_order': 32, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
  • id: 103763724
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 33, 'group_order': 32, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
  • id: 103763725
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 33, 'group_order': 32, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 4, 'size': 1}
  • id: 103763726
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 33, 'group_order': 32, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 20, 'size': 1}
  • id: 103763727
    {'aut_label': '2D', 'centralizer': '4.a1.a1', 'counter': 5, 'group_counter': 33, 'group_order': 32, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
  • id: 103763728
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 6, 'group_counter': 33, 'group_order': 32, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 8, 'size': 2}
  • id: 103763729
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 33, 'group_order': 32, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 24, 'size': 2}
  • id: 103763730
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 8, 'group_counter': 33, 'group_order': 32, 'label': '4B1', 'order': 4, 'powers': [3], 'representative': 2, 'size': 2}
  • id: 103763731
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 33, 'group_order': 32, 'label': '4B-1', 'order': 4, 'powers': [3], 'representative': 18, 'size': 2}
  • id: 103763719
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 10, 'group_counter': 33, 'group_order': 32, 'label': '4C1', 'order': 4, 'powers': [4], 'representative': 10, 'size': 2}
  • id: 103763720
    {'aut_label': '4A1', 'centralizer': '2.c1.a1', 'counter': 11, 'group_counter': 33, 'group_order': 32, 'label': '4C-1', 'order': 4, 'powers': [4], 'representative': 14, 'size': 2}
  • id: 103763721
    {'aut_label': '4D', 'centralizer': '4.c1.a1', 'counter': 12, 'group_counter': 33, 'group_order': 32, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 9, 'size': 4}
  • id: 103763722
    {'aut_label': '4D', 'centralizer': '4.c1.b1', 'counter': 13, 'group_counter': 33, 'group_order': 32, 'label': '4E', 'order': 4, 'powers': [2], 'representative': 3, 'size': 4}
  • id: 103763723
    {'aut_label': '4D', 'centralizer': '4.c1.c1', 'counter': 14, 'group_counter': 33, 'group_order': 32, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 11, 'size': 4}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 2464285
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2464288
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 2464289
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 2464290
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 2464291
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 2464292
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2464293
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 2464294
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 2464295
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.2a', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2464286
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.2b', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2464287
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '32.33', 'group_order': 32, 'image': None, 'label': '32.33.2c', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 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: 3169816
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 32, 'label': '32.33.1a', '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]]]}
  • id: 3169822
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 16, 'label': '32.33.1b', '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]]]}
  • id: 3169823
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.c1', 'kernel_order': 16, 'label': '32.33.1c', '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]]]}
  • id: 3169824
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 16, 'label': '32.33.1d', '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]]]}
  • id: 3169825
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 16, 'label': '32.33.1e', '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]]]}
  • id: 3169826
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 16, 'label': '32.33.1f', '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]]]}
  • id: 3169827
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.c1', 'kernel_order': 16, 'label': '32.33.1g', '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]]]}
  • id: 3169828
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 32, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 16, 'label': '32.33.1h', '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]]]}
  • id: 3169829
    {'center': '4.b1.b1', 'center_index': 4, 'center_order': 8, 'counter': 9, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.c1', 'kernel_order': 2, 'label': '32.33.2a1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3169817
    {'center': '4.b1.b1', 'center_index': 4, 'center_order': 8, 'counter': 10, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.c1', 'kernel_order': 2, 'label': '32.33.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3169818
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 8, 'counter': 11, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.b1', 'kernel_order': 2, 'label': '32.33.2b1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3169819
    {'center': '4.b1.a1', 'center_index': 4, 'center_order': 8, 'counter': 12, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.b1', 'kernel_order': 2, 'label': '32.33.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3169820
    {'center': '4.b1.c1', 'center_index': 4, 'center_order': 8, 'counter': 13, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.33.2c1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3169821
    {'center': '4.b1.c1', 'center_index': 4, 'center_order': 8, 'counter': 14, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '32.33', 'group_counter': 33, 'group_order': 32, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 2, 'label': '32.33.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[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: 51687428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 32, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '32.33.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 51687439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 51687450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 51687452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.a1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 51687453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], '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: 51687457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 8, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 51687429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], '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: 51687430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687431
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.4.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 4, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '32.33.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C3'], '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: 51687436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32.33.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 51687437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32.33.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51687438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32.33.8.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 51687440
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687441
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687442
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687443
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687444
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687445
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.8.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 51687446
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.33.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': True, 'solvable': True, 'special_labels': ['C4'], '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: 51687447
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.33.16.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': 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: 51687448
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '32.33.16.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': 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: 51687449
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '32.33.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, '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: 51687451
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '32.33', 'ambient_counter': 33, 'ambient_order': 32, 'ambient_tex': 'C_4^2:C_2', 'central': True, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '32.33.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '32.33', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 33, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C5'], '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: 51687428
    {'ambient': '32.33', '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': '8.a1.a1', 'complements': ['32.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.a1.c1', '2.b1.a1', '2.b1.b1', '2.b1.c1', '2.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3542, 6269, 4849, 5262, 3542, 6458, 4989, 5261], 'generators': [1, 2, 8], 'label': '32.33.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.a1.c1', '2.b1.a1', '2.b1.b1', '2.b1.c1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687429
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1757, 8682, 7673, 7784, 1756, 8244, 7895, 7784], 'generators': [8, 20], 'label': '32.33.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687430
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1757, 8682, 3437, 5307, 1756, 8244, 3536, 5307], 'generators': [2, 16], 'label': '32.33.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687431
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '2.b1.c1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.c1'], 'core': '4.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1757, 8682, 2025, 9330, 1756, 8244, 2083, 9330], 'generators': [10, 16], 'label': '32.33.4.b1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.c1', 'normal_contained_in': ['2.a1.c1', '2.b1.c1', '2.c1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.c1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687432
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.c1'], 'contains': ['8.a1.a1', '8.d1.c1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5804, 4420, 613, 3762, 5803, 4196, 630, 3761], 'generators': [9, 16], 'label': '32.33.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51687433
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '4.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.b1.c1'], 'contains': ['8.a1.a1', '8.d1.a1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5804, 4420, 6261, 670, 5803, 4196, 6442, 670], 'generators': [3, 20], 'label': '32.33.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.b1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51687434
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '4.c1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.c1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '8.d1.b1'], 'core': '4.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5804, 4420, 4849, 2215, 5803, 4196, 4989, 2216], 'generators': [11, 16], 'label': '32.33.4.c1.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.c1', 'normal_contained_in': ['2.a1.c1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.c1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51687435
    {'ambient': '32.33', 'aut_centralizer_order': 64, 'aut_label': '8.a1', 'aut_quo_index': 56, 'aut_stab_index': 1, 'aut_weyl_group': '3.1', 'aut_weyl_index': 64, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.c1.a1', '4.c1.b1', '4.c1.c1'], 'contains': ['16.a1.a1', '16.a1.b1', '16.a1.c1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4375, 4420, 5337, 5307, 4345, 4196, 5491, 5307], 'generators': [20, 16], 'label': '32.33.8.a1.a1', 'mobius_quo': 2, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.b1.c1', '4.c1.a1', '4.c1.b1', '4.c1.c1'], 'normal_contains': ['16.a1.b1', '16.a1.c1', '16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '8.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687436
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8958, -1, 9387, -1, 8929, -1, 9658, -1], 'generators': [1, 16], 'label': '32.33.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.c1', 'old_label': '8.b1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687437
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.b1', '16.b1.a1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8958, -1, 8535, -1, 8929, -1, 8782, -1], 'generators': [1, 4], 'label': '32.33.8.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687438
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.c1', '16.b1.a1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8958, -1, 7684, -1, 8929, -1, 7906, -1], 'generators': [1, 20], 'label': '32.33.8.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '8.b1.c1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687439
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6607, 3040, 8161, 6545, 6607, 3393, 8398, 6546], 'generators': [1, 8], 'label': '32.33.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687440
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1875, -1, 6884, -1, 1964, -1, 7083, -1], 'generators': [8], 'label': '32.33.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687441
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1875, -1, 3552, -1, 1964, -1, 3654, -1], 'generators': [2], 'label': '32.33.8.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.c1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687442
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.c1'], 'contains': ['16.a1.c1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [1875, -1, 2409, -1, 1964, -1, 2479, -1], 'generators': [10], 'label': '32.33.8.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.c1.c1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687443
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1'], 'contains': ['16.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6667, -1, 6137, -1, 6637, -1, 6314, -1], 'generators': [3], 'label': '32.33.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.c1', 'old_label': '8.d1.a1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687444
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.c1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.c1'], 'contains': ['16.a1.b1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6667, -1, 4538, -1, 6637, -1, 4669, -1], 'generators': [11], 'label': '32.33.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.b1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687445
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '4.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.a1.c1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6667, -1, 1329, -1, 6637, -1, 1368, -1], 'generators': [9], 'label': '32.33.8.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '8.d1.c1', 'projective_image': '16.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687446
    {'ambient': '32.33', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1'], 'contains': ['32.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 4420, 6137, 5307, 6637, 4196, 6314, 5307], 'generators': [16], 'label': '32.33.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687447
    {'ambient': '32.33', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.b1', '8.c1.b1', '8.d1.b1'], 'contains': ['32.a1.a1'], 'core': '16.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 4420, 5369, 6125, 6637, 4196, 5513, 6125], 'generators': [4], 'label': '32.33.16.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.b1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687448
    {'ambient': '32.33', 'aut_centralizer_order': 64, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.c1', '8.c1.c1', '8.d1.c1'], 'contains': ['32.a1.a1'], 'core': '16.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 4420, 4621, 4488, 6637, 4196, 4744, 4489], 'generators': [20], 'label': '32.33.16.a1.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.c1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.c1', 'projective_image': '16.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687449
    {'ambient': '32.33', 'aut_centralizer_order': 48, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.b1.b1', '8.b1.c1'], 'contains': ['32.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': '16T27', 'count': 4, 'diagramx': [8899, -1, 8109, -1, 8839, -1, 8344, -1], 'generators': [1], 'label': '32.33.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '32.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687450
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6607, 3040, 6988, 5262, 6607, 3393, 7190, 5261], 'generators': [1, 2], 'label': '32.33.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687451
    {'ambient': '32.33', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.b1', '16.a1.c1', '16.b1.a1'], 'contains': [], 'core': '32.a1.a1', 'coset_action_label': '32T13', 'count': 1, 'diagramx': [7798, 4420, 5752, 5307, 7708, 4196, 5919, 5307], 'generators': [], 'label': '32.33.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.b1', '16.a1.c1', '16.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.33', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51687452
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.c1', '4.c1.c1'], 'core': '2.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6607, 3040, 4849, 7830, 6607, 3393, 4989, 7830], 'generators': [1, 10], 'label': '32.33.2.a1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.c1', '4.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.c1', 'projective_image': '8.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687453
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': ['16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.b1', '4.c1.c1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3542, 6269, 5918, 2000, 3542, 6458, 6090, 2000], 'generators': [3, 8], 'label': '32.33.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687454
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': ['16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.c1.c1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3542, 6269, 2928, 3045, 3542, 6458, 3013, 3045], 'generators': [9, 2], 'label': '32.33.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.a1', '4.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687455
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 12, 'centralizer': '8.a1.a1', 'complements': ['16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.c1', '4.c1.a1', '4.c1.b1'], 'core': '2.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3542, 6269, 1973, 4091, 3542, 6458, 2030, 4091], 'generators': [9, 10], 'label': '32.33.2.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.c1', '4.c1.a1', '4.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.c1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 51687456
    {'ambient': '32.33', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.49', 'aut_weyl_index': 4, 'centralizer': '2.c1.a1', 'complements': ['16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.b1.c1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [953, 8996, 3831, 8943, 952, 9048, 3942, 8944], 'generators': [2, 8], 'label': '32.33.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51687457
    {'ambient': '32.33', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.3', 'aut_weyl_index': 16, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.a1.c1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.b1.c1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9047, 1004, 8805, 6545, 9048, 952, 9060, 6546], 'generators': [1, 20, 16], 'label': '32.33.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.a1.c1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '8.5', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}