Abstract group data - 1320.133

Formats: - HTML - YAML - JSON - 2026-02-24T23:04:01.957633

• 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': '2.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 660, 'aut_gen_orders': [10, 3], 'aut_gens': [[1333, 1231], [7512, 12560], [6258, 5502]], 'aut_group': '1320.133', 'aut_hash': 133, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1320, 'aut_permdeg': 66, 'aut_perms': [364519015743640424312551988223735814936800935493774972429567532336161042581209359002779908885, 73798632365460506396436749005781526678230026293185802997323265841890712174148871953336982216], 'aut_phi_ratio': 4.125, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 55, 1, 1], [2, 66, 1, 1], [3, 110, 1, 1], [4, 110, 1, 1], [5, 132, 1, 2], [6, 110, 1, 1], [10, 132, 1, 2], [11, 120, 1, 1], [12, 110, 1, 2]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,11)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '1320.133', 'autcentquo_hash': 133, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 55, 1], [2, 66, 1], [3, 110, 1], [4, 110, 1], [5, 132, 2], [6, 110, 1], [10, 132, 2], [11, 120, 1], [12, 110, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1320.133', 'commutator_count': 1, 'commutator_label': '660.13', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '660.13'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 133, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 55, 1, 1], [2, 66, 1, 1], [3, 110, 1, 1], [4, 110, 1, 1], [5, 132, 2, 1], [6, 110, 1, 1], [10, 132, 2, 1], [11, 120, 1, 1], [12, 110, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 876, 'exponent': 660, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 1, 5], [11, 1, 2], [12, 1, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1320.133', 'hash': 133, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 660, 'inner_gen_orders': [10, 3], 'inner_gens': [[1333, 1165], [3873, 1231]], 'inner_hash': 133, 'inner_nilpotent': False, 'inner_order': 1320, 'inner_split': True, 'inner_tex': '\\PGL(2,11)', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 10, 'irrQ_dim': 10, 'irrR_degree': 10, 'irrep_stats': [[1, 2], [10, 5], [11, 2], [12, 4]], 'label': '1320.133', 'linC_count': 5, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 3, 'linQ_dim': 10, 'linQ_dim_count': 3, 'linR_count': 5, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PGL(2,11)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 13, 'number_divisions': 10, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 29, 'number_subgroup_classes': 29, 'number_subgroups': 1624, 'old_label': None, 'order': 1320, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 121], [3, 110], [4, 110], [5, 264], [6, 110], [10, 264], [11, 120], [12, 220]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [10, 3], [11, 2], [20, 1], [24, 2]], 'representations': {'Lie': [{'d': 2, 'q': 11, 'gens': [1333, 1231], 'family': 'PGL'}, {'d': 3, 'q': 11, 'gens': [428732409, 17876563], 'family': 'SO'}, {'d': 3, 'q': 11, 'gens': [428732409, 17876563], 'family': 'PSO'}, {'d': 3, 'q': 11, 'gens': [17731461, 428732409, 17876563], 'family': 'PGO'}, {'d': 2, 'q': 11, 'gens': [116923037, 1126278], 'family': 'PGU'}, {'d': 3, 'q': 11, 'gens': [428732409, 17876563], 'family': 'CSO'}, {'d': 2, 'q': 11, 'gens': [1333, 1231], 'family': 'PGammaL'}, {'d': 2, 'q': 11, 'gens': [116923037, 1126278], 'family': 'PGammaU'}], 'GLFp': {'d': 3, 'p': 11, 'gens': [2043642619, 1675240484]}, 'Perm': {'d': 12, 'gens': [125614547, 377389185]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PGL(2,11)', 'transitive_degree': 12, '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: 171731922
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 133, 'group_order': 1320, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 1332, 'size': 1}
  • id: 171731927
    {'aut_label': '2A', 'centralizer': '55.b1.a1', 'counter': 2, 'group_counter': 133, 'group_order': 1320, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 9179, 'size': 55}
  • id: 171731928
    {'aut_label': '2B', 'centralizer': '66.a1.a1', 'counter': 3, 'group_counter': 133, 'group_order': 1320, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 1363, 'size': 66}
  • id: 171731929
    {'aut_label': '3A', 'centralizer': '110.b1.a1', 'counter': 4, 'group_counter': 133, 'group_order': 1320, 'label': '3A', 'order': 3, 'powers': [4, 1, 4, 4], 'representative': 1597, 'size': 110}
  • id: 171731930
    {'aut_label': '4A', 'centralizer': '110.b1.a1', 'counter': 5, 'group_counter': 133, 'group_order': 1320, 'label': '4A', 'order': 4, 'powers': [2, 5, 5, 5], 'representative': 3989, 'size': 110}
  • id: 171731931
    {'aut_label': '5A1', 'centralizer': '132.b1.a1', 'counter': 6, 'group_counter': 133, 'group_order': 1320, 'label': '5A1', 'order': 5, 'powers': [7, 7, 1, 6], 'representative': 4107, 'size': 132}
  • id: 171731932
    {'aut_label': '5A2', 'centralizer': '132.b1.a1', 'counter': 7, 'group_counter': 133, 'group_order': 1320, 'label': '5A2', 'order': 5, 'powers': [6, 6, 1, 7], 'representative': 5358, 'size': 132}
  • id: 171731933
    {'aut_label': '6A', 'centralizer': '110.b1.a1', 'counter': 8, 'group_counter': 133, 'group_order': 1320, 'label': '6A', 'order': 6, 'powers': [4, 2, 8, 8], 'representative': 5593, 'size': 110}
  • id: 171731934
    {'aut_label': '10A1', 'centralizer': '132.b1.a1', 'counter': 9, 'group_counter': 133, 'group_order': 1320, 'label': '10A1', 'order': 10, 'powers': [6, 10, 3, 9], 'representative': 4047, 'size': 132}
  • id: 171731923
    {'aut_label': '10A3', 'centralizer': '132.b1.a1', 'counter': 10, 'group_counter': 133, 'group_order': 1320, 'label': '10A3', 'order': 10, 'powers': [7, 9, 3, 10], 'representative': 12008, 'size': 132}
  • id: 171731924
    {'aut_label': '11A', 'centralizer': '120.a1.a1', 'counter': 11, 'group_counter': 133, 'group_order': 1320, 'label': '11A', 'order': 11, 'powers': [11, 11, 11, 1], 'representative': 8221, 'size': 120}
  • id: 171731925
    {'aut_label': '12A1', 'centralizer': '110.b1.a1', 'counter': 12, 'group_counter': 133, 'group_order': 1320, 'label': '12A1', 'order': 12, 'powers': [8, 5, 13, 12], 'representative': 10638, 'size': 110}
  • id: 171731926
    {'aut_label': '12A5', 'centralizer': '110.b1.a1', 'counter': 13, 'group_counter': 133, 'group_order': 1320, 'label': '12A5', 'order': 12, 'powers': [8, 5, 12, 13], 'representative': 2519, 'size': 110}
• 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: 17334052
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 17334054
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 17334055
    {'cdim': 10, 'counter': 3, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.10a', 'multiplicity': 1, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, -2, 0, 1, 2, 0, 0, 1, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 17334056
    {'cdim': 10, 'counter': 4, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.10b', 'multiplicity': 1, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, 2, 0, -2, 0, 0, 0, 2, 0, 0, -1, 0, 0], 'schur_index': 1}
  • id: 17334057
    {'cdim': 10, 'counter': 5, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.10c', 'multiplicity': 1, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, -2, 0, 1, -2, 0, 0, 1, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 17334059
    {'cdim': 11, 'counter': 7, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.11a', 'multiplicity': 1, 'nt': [12, 218], 'qdim': 11, 'qvalues': [11, -1, 1, -1, -1, 1, 1, -1, 1, 1, 0, -1, -1], 'schur_index': 1}
  • id: 17334060
    {'cdim': 11, 'counter': 8, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.11b', 'multiplicity': 1, 'nt': [24, 2949], 'qdim': 11, 'qvalues': [11, -1, -1, -1, 1, 1, 1, -1, -1, -1, 0, 1, 1], 'schur_index': 1}
  • id: 17334058
    {'cdim': 10, 'counter': 6, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.10d', 'multiplicity': 2, 'nt': [22, 14], 'qdim': 20, 'qvalues': [20, 4, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 17334061
    {'cdim': 12, 'counter': 9, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.12a', 'multiplicity': 2, 'nt': [55, 0], 'qdim': 24, 'qvalues': [24, 0, 4, 0, 0, -1, -1, 0, -1, -1, 2, 0, 0], 'schur_index': 1}
  • id: 17334053
    {'cdim': 12, 'counter': 10, 'faithful': True, 'group': '1320.133', 'group_order': 1320, 'image': None, 'label': '1320.133.12b', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 24, 'qvalues': [24, 0, -4, 0, 0, -1, -1, 0, 1, 1, 2, 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: 37957645
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1320, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1320, 'label': '1320.133.1a', '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]]]}
  • id: 37957650
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1320, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 660, 'label': '1320.133.1b', '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]]]}
  • id: 37957651
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 1, 'dim': 10, 'faithful': True, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.10a', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37957652
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 1, 'dim': 10, 'faithful': True, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.10b', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37957653
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 1, 'dim': 10, 'faithful': True, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.10c', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 37957654
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 12, 'dim': 10, 'faithful': True, 'field': [-3, 0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.10d1', 'nt': [22, 14], 'q_character': None, 'values': [[[10, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 37957655
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 12, 'dim': 10, 'faithful': True, 'field': [-3, 0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.10d2', 'nt': [22, 14], 'q_character': None, 'values': [[[10, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 37957656
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 1, 'dim': 11, 'faithful': True, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.11a', 'nt': [12, 218], 'q_character': None, 'values': [[[11, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 37957657
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 1, 'dim': 11, 'faithful': True, 'field': [0, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.11b', 'nt': [24, 2949], 'q_character': None, 'values': [[[11, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 37957646
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.12a1', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37957647
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.12a2', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37957648
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.12b1', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 37957649
    {'center': '1320.a1.a1', 'center_index': 1320, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1320.133', 'group_counter': 133, 'group_order': 1320, 'image': None, 'image_isoclass': '1320.133', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1.a1', 'kernel_order': 1, 'label': '1320.133.12b2', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 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: 262900742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1320, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 330, 'label': '1320.133.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': 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': None, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1320.133', 'subgroup_hash': 133, 'subgroup_order': 1320, 'subgroup_tex': '\\PGL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 262900753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 660, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1320.133.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': None, 'quotient_tex': 'C_2', 'simple': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L1', 'D1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '660.13', 'subgroup_hash': 13, 'subgroup_order': 660, 'subgroup_tex': '\\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 262900764
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.12.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 262900765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
  • id: 262900766
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 55, 'label': '1320.133.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 262900767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1320.133.55.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 262900768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1320.133.55.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 262900769
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 262900770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.66.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 262900743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 262900744
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 262900745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.110.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 262900746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.110.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.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': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 262900747
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 11, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '1320.133.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 262900748
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 262900749
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 262900750
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 262900751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1320.133.165.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '165.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 165, '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': 2}
  • id: 262900752
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 262900754
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.220.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 262900755
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.220.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 262900756
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1320.133.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 262900757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.330.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 330, '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: 262900758
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.330.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.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': 330, '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: 262900759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1320.133.330.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.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': 330, '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: 262900760
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '1320.133.440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 262900761
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.660.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, '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: 262900762
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1320.133.660.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.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': 660, '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: 262900763
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1320.133', 'ambient_counter': 133, 'ambient_order': 1320, 'ambient_tex': '\\PGL(2,11)', 'central': True, 'central_factor': False, 'centralizer_order': 1320, 'characteristic': True, 'core_order': 1, 'counter': 29, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1320.133.1320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1320.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1320.133', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 133, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1320, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': None, 'quotient_tex': '\\PGL(2,11)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C2'], '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: 262900742
    {'ambient': '1320.133', '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': '1320.a1.a1', 'complements': ['1320.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '12.a1.a1', '55.a1.a1', '55.b1.a1', '66.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5375, 5000, 3287, 5000, 5952, 5000, 5952, 5000], 'generators': [7499, 6837], 'label': '1320.133.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1320.133', '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': '1320.133'}
  • id: 262900743
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '110.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 110, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.a1.a1', '220.c1.a1', '330.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6219, -1, 7492, -1, 5872, -1, 5872, -1], 'generators': [9190, 8694, 14059], 'label': '1320.133.110.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 262900744
    {'ambient': '1320.133', 'aut_centralizer_order': 12, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1'], 'contains': ['220.a1.a1', '330.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [9584, -1, 9605, -1, 7610, -1, 7610, -1], 'generators': [8694, 14059, 3414], 'label': '1320.133.110.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900745
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '24.12', 'aut_weyl_index': 55, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '55.a1.a1'], 'contains': ['330.c1.a1', '440.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5375, -1, 5167, -1, 9348, -1, 9348, -1], 'generators': [14301, 594, 3851], 'label': '1320.133.110.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '110.c1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 262900746
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 110, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '55.b1.a1'], 'contains': ['220.a1.a1', '220.b1.a1', '330.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8201, -1, 8337, -1, 8525, -1, 8525, -1], 'generators': [8379, 12751, 10322], 'label': '1320.133.110.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.d1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 262900747
    {'ambient': '1320.133', 'aut_centralizer_order': 11, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '10.2', 'aut_weyl_index': 132, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.a1.a1'], 'contains': ['1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [874, -1, 684, -1, 1767, -1, 1767, -1], 'generators': [11903], 'label': '1320.133.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 262900748
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '10.1', 'aut_weyl_index': 132, 'centralizer': '660.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '66.a1.a1'], 'contains': ['264.a1.a1', '660.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [3394, -1, 3498, -1, 4523, -1, 4523, -1], 'generators': [7610, 13048], 'label': '1320.133.132.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 262900749
    {'ambient': '1320.133', 'aut_centralizer_order': 10, 'aut_label': '132.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '66.a1.a1'], 'contains': ['264.a1.a1', '660.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [874, -1, 1808, -1, 2784, -1, 2784, -1], 'generators': [3243, 7370], 'label': '1320.133.132.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900750
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '132.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '10.1', 'aut_weyl_index': 132, 'centralizer': '660.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.a1.a1'], 'contains': ['264.a1.a1', '660.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2550, -1, 2697, -1, 3699, -1, 3699, -1], 'generators': [5214, 8068], 'label': '1320.133.132.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '132.c1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 262900751
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '4.2', 'aut_weyl_index': 330, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.b1.a1'], 'contains': ['330.a1.a1', '330.b1.a1', '330.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8048, -1, 6412, -1, 6695, -1, 6695, -1], 'generators': [9190, 14059, 3414], 'label': '1320.133.165.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1.a1', 'old_label': '165.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 262900752
    {'ambient': '1320.133', 'aut_centralizer_order': 12, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '110.b1.a1', '110.d1.a1'], 'contains': ['440.a1.a1', '660.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [9385, -1, 9416, -1, 7930, -1, 7930, -1], 'generators': [8379, 12751], 'label': '1320.133.220.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '220.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900753
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1320.133', 'aut_weyl_index': 1, 'centralizer': '1320.a1.a1', 'complements': ['660.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '24.a1.a1', '110.d1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6279, 5000, 4755, 5000, 7804, 5000, 7804, 5000], 'generators': [8325, 10322], 'label': '1320.133.2.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['1320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1320.133'}
  • id: 262900754
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '6.1', 'aut_weyl_index': 220, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '110.d1.a1'], 'contains': ['440.a1.a1', '660.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [6712, -1, 8148, -1, 9691, -1, 9691, -1], 'generators': [3282, 10256], 'label': '1320.133.220.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.d1.a1', 'old_label': '220.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262900755
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '220.c1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '6.1', 'aut_weyl_index': 220, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '110.a1.a1'], 'contains': ['440.a1.a1', '660.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [4039, -1, 5177, -1, 6283, -1, 6283, -1], 'generators': [9190, 8694], 'label': '1320.133.220.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.a1.a1', 'old_label': '220.c1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262900756
    {'ambient': '1320.133', 'aut_centralizer_order': 10, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '132.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1'], 'contains': ['1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1647, -1, 1540, -1, 3288, -1, 3288, -1], 'generators': [7610], 'label': '1320.133.264.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900757
    {'ambient': '1320.133', 'aut_centralizer_order': 4, 'aut_label': '330.a1', 'aut_quo_index': None, 'aut_stab_index': 165, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '330.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.a1.a1', '110.a1.a1', '165.a1.a1'], 'contains': ['660.a1.a1', '660.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [5879, -1, 5133, -1, 5403, -1, 5403, -1], 'generators': [9190, 14059], 'label': '1320.133.330.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1.a1', 'old_label': '330.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900758
    {'ambient': '1320.133', 'aut_centralizer_order': 12, 'aut_label': '330.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.b1.a1', '165.a1.a1'], 'contains': ['660.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [9290, -1, 9371, -1, 7107, -1, 7107, -1], 'generators': [14059, 3414], 'label': '1320.133.330.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '330.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900759
    {'ambient': '1320.133', 'aut_centralizer_order': 4, 'aut_label': '330.c1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '6.1', 'aut_weyl_index': 220, 'centralizer': '330.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '110.d1.a1', '165.a1.a1'], 'contains': ['660.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8388, -1, 7068, -1, 8810, -1, 8810, -1], 'generators': [14301, 594], 'label': '1320.133.330.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '330.c1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 262900760
    {'ambient': '1320.133', 'aut_centralizer_order': 12, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '2.1', 'aut_weyl_index': 660, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '220.a1.a1', '220.b1.a1', '220.c1.a1'], 'contains': ['1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4730, -1, 6224, -1, 7930, -1, 7930, -1], 'generators': [3851], 'label': '1320.133.440.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '440.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 262900761
    {'ambient': '1320.133', 'aut_centralizer_order': 24, 'aut_label': '660.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1320, 'centralizer': '55.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.a1.a1', '220.a1.a1', '220.b1.a1', '330.a1.a1', '330.b1.a1', '330.c1.a1'], 'contains': ['1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6583, -1, 7068, -1, 7107, -1, 7107, -1], 'generators': [14301], 'label': '1320.133.660.a1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '660.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262900762
    {'ambient': '1320.133', 'aut_centralizer_order': 20, 'aut_label': '660.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1320, 'centralizer': '66.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '132.b1.a1', '132.c1.a1', '220.c1.a1', '330.a1.a1'], 'contains': ['1320.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2948, -1, 3231, -1, 4111, -1, 4111, -1], 'generators': [3243], 'label': '1320.133.660.b1.a1', 'mobius_quo': None, 'mobius_sub': -10, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '660.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262900763
    {'ambient': '1320.133', 'aut_centralizer_order': None, 'aut_label': '1320.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': ['120.a1.a1', '264.a1.a1', '440.a1.a1', '660.a1.a1', '660.b1.a1'], 'contains': [], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2948, 5000, 3231, 5000, 4111, 5000, 4111, 5000], 'generators': [], 'label': '1320.133.1320.a1.a1', 'mobius_quo': 1, 'mobius_sub': 660, 'normal_closure': '1320.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1320.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 262900764
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 12, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['24.a1.a1', '60.a1.a1', '132.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': '12T218', 'count': 12, 'diagramx': [897, -1, 1330, -1, 2418, -1, 2418, -1], 'generators': [3243, 7370, 834], 'label': '1320.133.12.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 262900765
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '60.5', 'aut_weyl_index': 22, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['110.c1.a1', '132.a1.a1', '220.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': '22T14', 'count': 22, 'diagramx': [6525, -1, 5144, -1, 9154, -1, 9154, -1], 'generators': [13285, 8519], 'label': '1320.133.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 262900766
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 12, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '12.a1.a1'], 'contains': ['120.a1.a1', '264.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': '24T2949', 'count': 12, 'diagramx': [1542, -1, 1985, -1, 577, -1, 577, -1], 'generators': [6779, 11903], 'label': '1320.133.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 262900767
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '24.12', 'aut_weyl_index': 55, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['110.c1.a1', '165.a1.a1', '220.c1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5375, -1, 4744, -1, 5952, -1, 5952, -1], 'generators': [10278, 11146, 3282, 594], 'label': '1320.133.55.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 262900768
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 55, 'aut_weyl_group': '12.4', 'aut_weyl_index': 110, 'centralizer': '660.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['110.a1.a1', '110.b1.a1', '110.d1.a1', '165.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8704, -1, 7492, -1, 6878, -1, 6878, -1], 'generators': [9190, 8694, 14059, 3414], 'label': '1320.133.55.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '55.b1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 262900769
    {'ambient': '1320.133', 'aut_centralizer_order': 1, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 12, 'centralizer': '1320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['120.a1.a1', '660.b1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [416, -1, 395, -1, 1767, -1, 1767, -1], 'generators': [3243, 834], 'label': '1320.133.60.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 262900770
    {'ambient': '1320.133', 'aut_centralizer_order': 2, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '10.1', 'aut_weyl_index': 132, 'centralizer': '660.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['132.a1.a1', '132.b1.a1', '132.c1.a1', '330.a1.a1'], 'core': '1320.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2995, -1, 2864, -1, 4077, -1, 4077, -1], 'generators': [5214, 10542, 8068], 'label': '1320.133.66.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '1320.133', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}