Abstract group data - 200.23

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [8, 10, 4], 'aut_gens': [[1, 2, 40], [10, 41, 24], [33, 182, 40], [13, 58, 120]], 'aut_group': '3200.w', 'aut_hash': 8298400542196966214, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3200, 'aut_permdeg': 14, 'aut_perms': [6395574383, 28740957841, 16421414521], 'aut_phi_ratio': 40.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 2, 1], [4, 5, 4, 1], [5, 2, 4, 1], [5, 4, 4, 1], [10, 2, 4, 1], [10, 4, 4, 1], [20, 10, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5^2:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '800.1191', 'autcentquo_hash': 1191, 'autcentquo_nilpotent': False, 'autcentquo_order': 800, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 25, 2], [4, 5, 4], [5, 2, 4], [5, 4, 4], [10, 2, 4], [10, 4, 4], [20, 10, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '100.13', 'commutator_count': 1, 'commutator_label': '25.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 23, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 1, 2], [4, 5, 2, 2], [5, 2, 2, 2], [5, 4, 2, 2], [10, 2, 2, 2], [10, 4, 2, 2], [20, 10, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 20, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[4, 1, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '100.13', 'hash': 23, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 10, 5], 'inner_gens': [[1, 18, 40], [25, 2, 160], [1, 82, 40]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 100, 'inner_split': False, 'inner_tex': 'D_5^2', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 16], [4, 8]], 'label': '200.23', 'linC_count': 52, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C10.D10', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 32, 'number_divisions': 16, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 23, 'number_subgroup_classes': 42, 'number_subgroups': 244, 'old_label': None, 'order': 200, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 51], [4, 20], [5, 24], [10, 24], [20, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [11, 1, 0, 11], 'outer_gens': [[21, 26, 80], [21, 26, 160], [21, 22, 40], [10, 141, 32]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [647, 265, 28003, 21700], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [8, 6]], 'representations': {'PC': {'code': 3302294325329197653007, 'gens': [1, 2, 5], 'pres': [5, -2, -2, -2, -5, -5, 100, 181, 26, 542, 42, 643, 2009]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [25977, 1565004, 1594376, 217061, 1027142]}, 'Perm': {'d': 14, 'gens': [50407, 482711760, 131760, 7188652800, 37]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}.D_{10}', 'transitive_degree': 20, '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: 109175229
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 23, 'group_order': 200, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 109175240
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 23, 'group_order': 200, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 20, 'size': 1}
  • id: 109175251
    {'aut_label': '2B', 'centralizer': '25.a1.a1', 'counter': 3, 'group_counter': 23, 'group_order': 200, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 35, 'size': 25}
  • id: 109175255
    {'aut_label': '2B', 'centralizer': '25.a1.a1', 'counter': 4, 'group_counter': 23, 'group_order': 200, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 79, 'size': 25}
  • id: 109175256
    {'aut_label': '4A1', 'centralizer': '5.a1.a1', 'counter': 5, 'group_counter': 23, 'group_order': 200, 'label': '4A1', 'order': 4, 'powers': [2, 5], 'representative': 10, 'size': 5}
  • id: 109175257
    {'aut_label': '4A1', 'centralizer': '5.a1.a1', 'counter': 6, 'group_counter': 23, 'group_order': 200, 'label': '4A-1', 'order': 4, 'powers': [2, 6], 'representative': 30, 'size': 5}
  • id: 109175258
    {'aut_label': '4A1', 'centralizer': '5.a1.b1', 'counter': 7, 'group_counter': 23, 'group_order': 200, 'label': '4B1', 'order': 4, 'powers': [2, 7], 'representative': 1, 'size': 5}
  • id: 109175259
    {'aut_label': '4A1', 'centralizer': '5.a1.b1', 'counter': 8, 'group_counter': 23, 'group_order': 200, 'label': '4B-1', 'order': 4, 'powers': [2, 8], 'representative': 21, 'size': 5}
  • id: 109175260
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 23, 'group_order': 200, 'label': '5A1', 'order': 5, 'powers': [10, 1], 'representative': 8, 'size': 2}
  • id: 109175230
    {'aut_label': '5A1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 23, 'group_order': 200, 'label': '5A2', 'order': 5, 'powers': [9, 1], 'representative': 16, 'size': 2}
  • id: 109175231
    {'aut_label': '5A1', 'centralizer': '2.b1.b1', 'counter': 11, 'group_counter': 23, 'group_order': 200, 'label': '5B1', 'order': 5, 'powers': [12, 1], 'representative': 160, 'size': 2}
  • id: 109175232
    {'aut_label': '5A1', 'centralizer': '2.b1.b1', 'counter': 12, 'group_counter': 23, 'group_order': 200, 'label': '5B2', 'order': 5, 'powers': [11, 1], 'representative': 120, 'size': 2}
  • id: 109175233
    {'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 23, 'group_order': 200, 'label': '5C1', 'order': 5, 'powers': [14, 1], 'representative': 88, 'size': 4}
  • id: 109175234
    {'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 23, 'group_order': 200, 'label': '5C2', 'order': 5, 'powers': [13, 1], 'representative': 176, 'size': 4}
  • id: 109175235
    {'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 15, 'group_counter': 23, 'group_order': 200, 'label': '5D1', 'order': 5, 'powers': [16, 1], 'representative': 168, 'size': 4}
  • id: 109175236
    {'aut_label': '5C1', 'centralizer': '4.a1.a1', 'counter': 16, 'group_counter': 23, 'group_order': 200, 'label': '5D2', 'order': 5, 'powers': [15, 1], 'representative': 136, 'size': 4}
  • id: 109175237
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 23, 'group_order': 200, 'label': '10A1', 'order': 10, 'powers': [9, 2], 'representative': 4, 'size': 2}
  • id: 109175238
    {'aut_label': '10A1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 23, 'group_order': 200, 'label': '10A3', 'order': 10, 'powers': [10, 2], 'representative': 12, 'size': 2}
  • id: 109175239
    {'aut_label': '10A1', 'centralizer': '2.b1.b1', 'counter': 19, 'group_counter': 23, 'group_order': 200, 'label': '10B1', 'order': 10, 'powers': [11, 2], 'representative': 100, 'size': 2}
  • id: 109175241
    {'aut_label': '10A1', 'centralizer': '2.b1.b1', 'counter': 20, 'group_counter': 23, 'group_order': 200, 'label': '10B3', 'order': 10, 'powers': [12, 2], 'representative': 60, 'size': 2}
  • id: 109175242
    {'aut_label': '10C1', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 23, 'group_order': 200, 'label': '10C1', 'order': 10, 'powers': [13, 2], 'representative': 44, 'size': 4}
  • id: 109175243
    {'aut_label': '10C1', 'centralizer': '4.a1.a1', 'counter': 22, 'group_counter': 23, 'group_order': 200, 'label': '10C3', 'order': 10, 'powers': [14, 2], 'representative': 92, 'size': 4}
  • id: 109175244
    {'aut_label': '10C1', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 23, 'group_order': 200, 'label': '10D1', 'order': 10, 'powers': [15, 2], 'representative': 84, 'size': 4}
  • id: 109175245
    {'aut_label': '10C1', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 23, 'group_order': 200, 'label': '10D3', 'order': 10, 'powers': [16, 2], 'representative': 52, 'size': 4}
  • id: 109175246
    {'aut_label': '20A1', 'centralizer': '10.d1.a1', 'counter': 25, 'group_counter': 23, 'group_order': 200, 'label': '20A1', 'order': 20, 'powers': [17, 5], 'representative': 2, 'size': 10}
  • id: 109175247
    {'aut_label': '20A1', 'centralizer': '10.d1.a1', 'counter': 26, 'group_counter': 23, 'group_order': 200, 'label': '20A-1', 'order': 20, 'powers': [17, 6], 'representative': 22, 'size': 10}
  • id: 109175248
    {'aut_label': '20A1', 'centralizer': '10.d1.a1', 'counter': 27, 'group_counter': 23, 'group_order': 200, 'label': '20A3', 'order': 20, 'powers': [18, 6], 'representative': 6, 'size': 10}
  • id: 109175249
    {'aut_label': '20A1', 'centralizer': '10.d1.a1', 'counter': 28, 'group_counter': 23, 'group_order': 200, 'label': '20A-3', 'order': 20, 'powers': [18, 5], 'representative': 26, 'size': 10}
  • id: 109175250
    {'aut_label': '20A1', 'centralizer': '10.d1.b1', 'counter': 29, 'group_counter': 23, 'group_order': 200, 'label': '20B1', 'order': 20, 'powers': [19, 7], 'representative': 41, 'size': 10}
  • id: 109175252
    {'aut_label': '20A1', 'centralizer': '10.d1.b1', 'counter': 30, 'group_counter': 23, 'group_order': 200, 'label': '20B-1', 'order': 20, 'powers': [19, 8], 'representative': 45, 'size': 10}
  • id: 109175253
    {'aut_label': '20A1', 'centralizer': '10.d1.b1', 'counter': 31, 'group_counter': 23, 'group_order': 200, 'label': '20B3', 'order': 20, 'powers': [20, 8], 'representative': 85, 'size': 10}
  • id: 109175254
    {'aut_label': '20A1', 'centralizer': '10.d1.b1', 'counter': 32, 'group_counter': 23, 'group_order': 200, 'label': '20B-3', 'order': 20, 'powers': [20, 7], 'representative': 81, 'size': 10}
• 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: 4171643
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4171651
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 4171652
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 4171653
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4171654
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171655
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171656
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2a', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 4, 4, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, 0, -1, 0, 0, -1, -1, 0], 'schur_index': 1}
  • id: 4171657
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2b', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, 0, -1, 0, -1, -1, 0, 0, -1], 'schur_index': 1}
  • id: 4171658
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2c', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, -4, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, 0, 1, 0, 1, 1, 0, 0, 1], 'schur_index': 1}
  • id: 4171644
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2d', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, -4, -4, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, 4, 4, -1, -1, -1, -1, 1, 0, 1, 0, 0, 1, 1, 0], 'schur_index': 1}
  • id: 4171645
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2e', 'multiplicity': 4, 'nt': [20, 6], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -2, -2, 8, 8, -2, -2, -2, -2, 2, 2, -8, -8, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171646
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.2f', 'multiplicity': 4, 'nt': [20, 6], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, -2, -2, -2, -2, -2, -2, -8, -8, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171647
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.4a', 'multiplicity': 2, 'nt': [10, 9], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 3, 3, -2, -2, -2, -2, -2, 3, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171648
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.4b', 'multiplicity': 2, 'nt': [10, 9], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, -2, -2, 3, -2, -2, -2, -2, -2, 3, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171649
    {'cdim': 4, 'counter': 15, 'faithful': True, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.4c', 'multiplicity': 2, 'nt': [20, 58], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 3, 3, -2, 2, 2, 2, 2, -3, 2, -3, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4171650
    {'cdim': 4, 'counter': 16, 'faithful': True, 'group': '200.23', 'group_order': 200, 'image': None, 'label': '200.23.4d', 'multiplicity': 2, 'nt': [20, 58], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, -2, -2, 3, 2, 2, 2, 2, 2, -3, 2, -3, 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: 6082926
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 200, 'label': '200.23.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6082937
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 100, 'label': '200.23.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 6082948
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 100, 'label': '200.23.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6082952
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 100, 'label': '200.23.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6082953
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 50, 'label': '200.23.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 6082954
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 50, 'label': '200.23.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 6082955
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 50, 'label': '200.23.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 6082956
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 200, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 50, 'label': '200.23.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 6082957
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 9, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 20, 'label': '200.23.2a1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]]]}
  • id: 6082927
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 10, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 20, 'label': '200.23.2a2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]]]}
  • id: 6082928
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 11, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.b1', 'kernel_order': 20, 'label': '200.23.2b1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]]]}
  • id: 6082929
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 12, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.b1', 'kernel_order': 20, 'label': '200.23.2b2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]]]}
  • id: 6082930
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 13, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 10, 'label': '200.23.2c1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]]]}
  • id: 6082931
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 14, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 10, 'label': '200.23.2c2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]]]}
  • id: 6082932
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 15, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.b1', 'kernel_order': 10, 'label': '200.23.2d1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 6082933
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 16, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.b1', 'kernel_order': 10, 'label': '200.23.2d2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[0, 0]]]}
  • id: 6082934
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 17, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.b1', 'kernel_order': 5, 'label': '200.23.2e1', 'nt': [20, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 3], [1, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]]]}
  • id: 6082935
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 18, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.b1', 'kernel_order': 5, 'label': '200.23.2e2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, 7]], [[0, 0]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]]]}
  • id: 6082936
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 19, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.b1', 'kernel_order': 5, 'label': '200.23.2e3', 'nt': [20, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]], [[1, 3], [1, 7]], [[0, 0]]]}
  • id: 6082938
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 20, 'counter': 20, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.b1', 'kernel_order': 5, 'label': '200.23.2e4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]], [[-1, 3], [-1, 7]], [[0, 0]]]}
  • id: 6082939
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 21, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 5, 'label': '200.23.2f1', 'nt': [20, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[-1, 3], [-1, 7]], [[0, 0]], [[1, 3], [1, 7]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]]]}
  • id: 6082940
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 22, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 5, 'label': '200.23.2f2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[1, 3], [1, 7]], [[0, 0]], [[-1, 3], [-1, 7]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]]]}
  • id: 6082941
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 23, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 5, 'label': '200.23.2f3', 'nt': [20, 6], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[-1, 3], [-1, 7]], [[0, 0]], [[0, 0]], [[1, 3], [1, 7]]]}
  • id: 6082942
    {'center': '10.a1.b1', 'center_index': 10, 'center_order': 20, 'counter': 24, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 3, 0, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '40.5', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 5, 'label': '200.23.2f4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[-1, 3], [1, 5], [-1, 7]], [[0, 0]], [[1, 3], [-1, 5], [1, 7]], [[1, 3], [1, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 7]]]}
  • id: 6082943
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 2, 'label': '200.23.4a1', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082944
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 2, 'label': '200.23.4a2', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082945
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 2, 'label': '200.23.4b1', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082946
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '100.13', 'image_order': 100, 'indicator': 1, 'kernel': '100.a1.a1', 'kernel_order': 2, 'label': '200.23.4b2', 'nt': [10, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082947
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '200.23', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 1, 'label': '200.23.4c1', 'nt': [20, 58], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082949
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '200.23', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 1, 'label': '200.23.4c2', 'nt': [20, 58], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082950
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '200.23', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 1, 'label': '200.23.4d1', 'nt': [20, 58], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0]], [[-1, 0]], [[1, 0], [-1, 2], [-1, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6082951
    {'center': '100.a1.a1', 'center_index': 100, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '200.23', 'group_counter': 23, 'group_order': 200, 'image': None, 'image_isoclass': '200.23', 'image_order': 200, 'indicator': 1, 'kernel': '200.a1.a1', 'kernel_order': 1, 'label': '200.23.4d2', 'nt': [20, 58], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[1, 0], [-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]], [[2, 0], [1, 2], [1, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[1, 0]], [[-2, 0], [-1, 2], [-1, -2]], [[1, 0]], [[-1, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 63654486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 200, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '200.23.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63654497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 100, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63654508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 100, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 63654519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 100, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 63654523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': True, 'core_order': 50, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': ['F', 'S', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63654524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.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': 5, '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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 20, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.5.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.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': 5, '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': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': True, 'core_order': 25, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '200.23.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 63654488
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63654489
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '200.23.10.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63654490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, '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: 63654491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, '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: 63654492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, '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: 63654493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, '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: 63654494
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 17, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.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': 10, '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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 63654495
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.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': 10, '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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 63654496
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 10, 'counter': 19, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '200.23.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63654498
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 10, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '200.23.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 63654499
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 20, '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: 63654500
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.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': 20, '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: 63654501
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654502
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654503
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654504
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, '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: 63654505
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654506
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654507
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, '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: 63654509
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.20.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, '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: 63654510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '200.23.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25.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': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 63654511
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 5, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '200.23.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654512
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 5, 'counter': 33, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '200.23.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_5', 'simple': True, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 63654513
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 40, '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': 0}
  • id: 63654514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 50, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.40.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 40, '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': 0}
  • id: 63654515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '200.23.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, '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: 63654516
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, '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: 63654517
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.50.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, '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: 63654518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 200, 'characteristic': True, 'core_order': 2, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '200.23.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '100.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '100.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63654520
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, '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: 63654521
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '200.23.100.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, '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: 63654522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '200.23', 'ambient_counter': 23, 'ambient_order': 200, 'ambient_tex': 'C_{10}.D_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 200, 'characteristic': True, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '200.23.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '200.23', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.D_{10}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', '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: 63654486
    {'ambient': '200.23', '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': '100.a1.a1', 'complements': ['200.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1', '5.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7511, 5031, 7966, 4754, 6475, 4970, 7001, 5507], 'generators': [1, 20, 8, 10, 40], 'label': '200.23.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '100.13', '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': '100.13'}
  • id: 63654487
    {'ambient': '200.23', 'aut_centralizer_order': 100, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 100, 'centralizer': '4.a1.a1', 'complements': ['25.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['40.a1.a1', '40.a1.b1', '40.b1.a1', '40.b1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3807, 5825, 3061, 6723, 1721, 6273, 2307, 3200], 'generators': [8, 40], 'label': '200.23.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['40.a1.b1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '200.23', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63654488
    {'ambient': '200.23', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '10.a1.b1', 'complements': ['20.c1.a1', '20.d1.b1', '20.d1.a1', '20.c1.c1', '20.d1.d1', '20.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.b1'], 'contains': ['20.a1.b1', '50.b1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9609, 1508, 9221, 5108, 8292, 1121, 6820, 7163], 'generators': [10, 40, 20], 'label': '200.23.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['20.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654489
    {'ambient': '200.23', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '10.a1.a1', 'complements': ['20.c1.b1', '20.d1.b1', '20.d1.a1', '20.c1.d1', '20.d1.d1', '20.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '50.b1.b1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9609, 1508, 8239, 1643, 8292, 1121, 9733, 8874], 'generators': [1, 8, 20], 'label': '200.23.10.a1.b1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.b1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.b1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654490
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '20.c1.c1', '50.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5557, -1, 5963, -1, 5191, -1, 4989, -1], 'generators': [3, 8, 20], 'label': '200.23.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654491
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '50.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.b1'], 'contains': ['20.a1.b1', '20.c1.b1', '20.c1.d1', '50.a1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [5557, -1, 6528, -1, 5191, -1, 4347, -1], 'generators': [3, 40, 20], 'label': '200.23.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.b1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654492
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['20.b1.a1', '20.d1.a1', '20.d1.c1', '50.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [912, -1, 4430, -1, 1749, -1, 3706, -1], 'generators': [3, 88, 20], 'label': '200.23.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '10.c1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654493
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 80, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['20.b1.b1', '20.d1.b1', '20.d1.d1', '50.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [912, -1, 729, -1, 1749, -1, 3064, -1], 'generators': [3, 48, 20], 'label': '200.23.10.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '10.c1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654494
    {'ambient': '200.23', 'aut_centralizer_order': 40, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 400, 'centralizer': '10.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '50.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8308, -1, 7624, -1, 9522, -1, 7469, -1], 'generators': [10, 20, 8], 'label': '200.23.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654495
    {'ambient': '200.23', 'aut_centralizer_order': 40, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.2', 'aut_weyl_index': 400, 'centralizer': '10.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.b1'], 'contains': ['20.a1.b1', '50.b1.b1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [8308, -1, 9791, -1, 9522, -1, 9084, -1], 'generators': [1, 20, 40], 'label': '200.23.10.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '10.d1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654496
    {'ambient': '200.23', 'aut_centralizer_order': 400, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.b1', '10.b1.a1', '10.d1.a1'], 'contains': ['40.a1.a1', '100.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 3825, 7263, 3160, 6188, 3697, 7491, 6419], 'generators': [20, 8], 'label': '200.23.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.b1'], 'normal_contains': ['40.a1.a1', '100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654497
    {'ambient': '200.23', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 2, 'centralizer': '100.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4588, 7665, 4835, 8042, 3470, 7515, 4030, 2400], 'generators': [3, 8, 40, 20], 'label': '200.23.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '100.13', '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': '100.13'}
  • id: 63654498
    {'ambient': '200.23', 'aut_centralizer_order': 400, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '2.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.b1', '10.d1.b1'], 'contains': ['40.a1.b1', '100.a1.a1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 3825, 7820, 4971, 6188, 3697, 6856, 4781], 'generators': [20, 40], 'label': '200.23.20.a1.b1', 'mobius_quo': 1, 'mobius_sub': -10, 'normal_closure': '20.a1.b1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.b1', '100.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.b1', 'projective_image': '100.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654499
    {'ambient': '200.23', 'aut_centralizer_order': 200, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.c1.a1'], 'contains': ['40.b1.a1', '100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2750, -1, 4854, -1, 3866, -1, 6222, -1], 'generators': [20, 88], 'label': '200.23.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654500
    {'ambient': '200.23', 'aut_centralizer_order': 200, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.c1.b1'], 'contains': ['40.b1.b1', '100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2750, -1, 1819, -1, 3866, -1, 5588, -1], 'generators': [20, 48], 'label': '200.23.20.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': '20.b1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654501
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.b1.a1'], 'contains': ['40.a1.a1', '100.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3908, -1, 5818, -1, 2773, -1, 4420, -1], 'generators': [3, 8], 'label': '200.23.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654502
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '50.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.b1.b1'], 'contains': ['40.a1.b1', '100.b1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3908, -1, 6273, -1, 2773, -1, 3900, -1], 'generators': [3, 40], 'label': '200.23.20.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '20.c1.b1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654503
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.b1.a1'], 'contains': ['40.a1.a1', '100.b1.b1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3908, -1, 3409, -1, 2773, -1, 1752, -1], 'generators': [23, 8], 'label': '200.23.20.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.c1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654504
    {'ambient': '200.23', 'aut_centralizer_order': 8, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '50.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.b1.b1'], 'contains': ['40.a1.b1', '100.b1.b1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [3908, -1, 5362, -1, 2773, -1, 1233, -1], 'generators': [23, 40], 'label': '200.23.20.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '20.c1.d1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654505
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.c1.a1'], 'contains': ['40.b1.a1', '100.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': '20T58', 'count': 10, 'diagramx': [391, -1, 3866, -1, 669, -1, 3381, -1], 'generators': [3, 88], 'label': '200.23.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '20.d1.a1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654506
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.c1.b1'], 'contains': ['40.b1.b1', '100.b1.a1'], 'core': '200.a1.a1', 'coset_action_label': '20T58', 'count': 10, 'diagramx': [391, -1, 957, -1, 669, -1, 2862, -1], 'generators': [3, 48], 'label': '200.23.20.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '20.d1.b1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654507
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.c1.a1'], 'contains': ['40.b1.a1', '100.b1.b1'], 'core': '200.a1.a1', 'coset_action_label': '20T58', 'count': 10, 'diagramx': [391, -1, 2472, -1, 669, -1, 714, -1], 'generators': [23, 88], 'label': '200.23.20.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '20.d1.c1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654508
    {'ambient': '200.23', 'aut_centralizer_order': 10, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '160.203', 'aut_weyl_index': 20, 'centralizer': '20.a1.a1', 'complements': ['100.b1.a1', '100.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.a1', '10.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8988, 2365, 7320, 4754, 8552, 2455, 5905, 5507], 'generators': [10, 20, 40, 8], 'label': '200.23.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '100.13', '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': '20.4'}
  • id: 63654509
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 160, 'centralizer': '100.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.c1.b1'], 'contains': ['40.b1.b1', '100.b1.b1'], 'core': '200.a1.a1', 'coset_action_label': '20T58', 'count': 10, 'diagramx': [391, -1, 171, -1, 669, -1, 195, -1], 'generators': [23, 48], 'label': '200.23.20.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.b1', 'old_label': '20.d1.d1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.d1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654510
    {'ambient': '200.23', 'aut_centralizer_order': 16, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '8.3', 'aut_weyl_index': 400, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.a1.b1'], 'contains': ['50.a1.a1', '50.b1.a1', '50.b1.b1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7613, -1, 9253, -1, 6735, -1, 8277, -1], 'generators': [1, 10], 'label': '200.23.25.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654511
    {'ambient': '200.23', 'aut_centralizer_order': 400, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '2.b1.a1', 'complements': ['5.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.c1.a1', '20.c1.c1'], 'contains': ['200.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4428, 5570, 4037, 6900, 3729, 5879, 3864, 4800], 'generators': [8], 'label': '200.23.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '200.23', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.1', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654512
    {'ambient': '200.23', 'aut_centralizer_order': 400, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '2.b1.b1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.b1', '20.c1.b1', '20.c1.d1'], 'contains': ['200.a1.a1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4428, 5570, 5577, 5482, 3729, 5879, 3345, 3460], 'generators': [40], 'label': '200.23.40.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.b1', 'normal_contained_in': ['8.a1.a1', '20.a1.b1'], 'normal_contains': ['200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.b1', 'projective_image': '200.23', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.1', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654513
    {'ambient': '200.23', 'aut_centralizer_order': 200, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.b1.a1', '20.d1.a1', '20.d1.c1'], 'contains': ['200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': '40T161', 'count': 2, 'diagramx': [1245, -1, 3168, -1, 1749, -1, 2826, -1], 'generators': [88], 'label': '200.23.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654514
    {'ambient': '200.23', 'aut_centralizer_order': 200, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 800, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.b1.b1', '20.d1.b1', '20.d1.d1'], 'contains': ['200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': '40T161', 'count': 2, 'diagramx': [1245, -1, 894, -1, 1749, -1, 2307, -1], 'generators': [48], 'label': '200.23.40.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.b1.b1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63654515
    {'ambient': '200.23', 'aut_centralizer_order': 64, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1600, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1', '25.a1.a1'], 'contains': ['100.a1.a1', '100.b1.a1', '100.b1.b1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5195, -1, 6579, -1, 5027, -1, 4975, -1], 'generators': [3, 20], 'label': '200.23.50.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654516
    {'ambient': '200.23', 'aut_centralizer_order': 160, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1600, 'centralizer': '5.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.d1.a1', '25.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8249, -1, 8391, -1, 7787, -1, 8068, -1], 'generators': [10], 'label': '200.23.50.b1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '50.b1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654517
    {'ambient': '200.23', 'aut_centralizer_order': 160, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1600, 'centralizer': '5.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.b1', '10.d1.b1', '25.a1.a1'], 'contains': ['100.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8249, -1, 9038, -1, 7787, -1, 8839, -1], 'generators': [1], 'label': '200.23.50.b1.b1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '50.b1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654518
    {'ambient': '200.23', 'aut_centralizer_order': 3200, 'aut_label': '100.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3200, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.a1.b1', '20.b1.a1', '20.b1.b1', '50.a1.a1', '50.b1.a1', '50.b1.b1'], 'contains': ['200.a1.a1'], 'core': '100.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5195, 3825, 7079, 4399, 5027, 3697, 6539, 6139], 'generators': [20], 'label': '200.23.100.a1.a1', 'mobius_quo': -1, 'mobius_sub': 50, 'normal_closure': '100.a1.a1', 'normal_contained_in': ['20.a1.b1', '20.a1.a1'], 'normal_contains': ['200.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '100.13', 'quotient_action_kernel_order': 100, 'quotient_fusion': None, 'short_label': '100.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654519
    {'ambient': '200.23', 'aut_centralizer_order': 10, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '160.203', 'aut_weyl_index': 20, 'centralizer': '20.a1.b1', 'complements': ['100.b1.a1', '100.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.b1', '10.d1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8988, 2365, 8612, 1466, 8552, 2455, 9084, 8614], 'generators': [1, 20, 8, 40], 'label': '200.23.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '100.13', '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': '20.4'}
  • id: 63654520
    {'ambient': '200.23', 'aut_centralizer_order': 64, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3200, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '20.c1.b1', '20.d1.a1', '20.d1.b1', '50.a1.a1'], 'contains': ['200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3256, -1, 5672, -1, 2746, -1, 4384, -1], 'generators': [3], 'label': '200.23.100.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.b1.a1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654521
    {'ambient': '200.23', 'aut_centralizer_order': 64, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3200, 'centralizer': '25.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.c1', '20.c1.d1', '20.d1.c1', '20.d1.d1', '50.a1.a1'], 'contains': ['200.a1.a1'], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3256, -1, 2231, -1, 2746, -1, 1492, -1], 'generators': [23], 'label': '200.23.100.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.b1.b1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654522
    {'ambient': '200.23', 'aut_centralizer_order': None, 'aut_label': '200.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': ['40.a1.a1', '40.a1.b1', '40.b1.a1', '40.b1.b1', '100.a1.a1', '100.b1.a1', '100.b1.b1'], 'contains': [], 'core': '200.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3661, 4714, 4037, 5482, 3238, 4788, 3345, 4800], 'generators': [], 'label': '200.23.200.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '200.a1.a1', 'normal_contained_in': ['40.a1.b1', '40.a1.a1', '100.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '200.a1.a1', 'projective_image': '200.23', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63654523
    {'ambient': '200.23', 'aut_centralizer_order': 100, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 100, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '20.a1.a1', '20.a1.b1', '20.b1.a1', '20.b1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6049, 4428, 6198, 3454, 3470, 5000, 5898, 4781], 'generators': [20, 40, 8], 'label': '200.23.4.a1.a1', 'mobius_quo': -1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '20.a1.b1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '100.13', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63654524
    {'ambient': '200.23', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 4, 'centralizer': '100.a1.a1', 'complements': ['50.b1.a1', '50.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '20.c1.a1', '20.c1.b1', '20.d1.a1', '20.d1.b1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1997, 8492, 3701, 6723, 505, 8879, 2408, 688], 'generators': [3, 40, 8], 'label': '200.23.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '200.23', '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': '100.13'}
  • id: 63654525
    {'ambient': '200.23', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 4, 'centralizer': '100.a1.a1', 'complements': ['50.b1.a1', '50.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '20.c1.c1', '20.c1.d1', '20.d1.c1', '20.d1.d1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1997, 8492, 3093, 8534, 505, 8879, 1500, 2400], 'generators': [23, 40, 8], 'label': '200.23.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '200.23', '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': '100.13'}
  • id: 63654526
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '80.50', 'aut_weyl_index': 40, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.b1', '10.b1.a1', '10.d1.a1', '25.a1.a1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [7583, -1, 7966, -1, 6475, -1, 7988, -1], 'generators': [1, 20, 8, 10], 'label': '200.23.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63654527
    {'ambient': '200.23', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '80.50', 'aut_weyl_index': 40, 'centralizer': '50.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.b1', '10.d1.b1', '25.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7583, -1, 9829, -1, 6475, -1, 7001, -1], 'generators': [1, 20, 40, 10], 'label': '200.23.5.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.b1', 'old_label': '5.a1.b1', 'projective_image': '100.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}