Abstract group data - 432.353

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 36, 'aut_gen_orders': [2, 2, 4, 6, 18], 'aut_gens': [[1, 4, 24], [1, 220, 24], [1, 4, 26], [217, 4, 26], [1, 4, 264], [1, 54, 24]], 'aut_group': '1728.18843', 'aut_hash': 18843, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 40, 'aut_perms': [714474905148784713374312773366038370745899399087, 81859832089678628806518962509858279501414526, 715038103652588251539616673122502831423852487751, 388102705555971552824479901992786710232073758958, 796066805284594632242951990333459993648811360781], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 9, 4, 1], [3, 2, 1, 1], [3, 3, 1, 2], [4, 1, 4, 1], [4, 9, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 1, 2], [6, 3, 2, 2], [6, 9, 4, 2], [9, 6, 1, 3], [12, 2, 4, 1], [12, 3, 4, 2], [12, 9, 4, 2], [18, 6, 1, 3], [18, 6, 2, 3], [36, 6, 4, 3]], 'aut_supersolvable': True, 'aut_tex': 'D_{18}:(C_6\\times D_4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '54.6', 'autcentquo_hash': 6, 'autcentquo_nilpotent': False, 'autcentquo_order': 54, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_9:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 9, 4], [3, 2, 1], [3, 3, 2], [4, 1, 4], [4, 9, 4], [6, 2, 3], [6, 3, 6], [6, 9, 8], [9, 6, 3], [12, 2, 4], [12, 3, 8], [12, 9, 8], [18, 6, 9], [36, 6, 12]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '54.6', 'commutator_count': 1, 'commutator_label': '9.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 353, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1], ['54.6', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 9, 1, 4], [3, 2, 1, 1], [3, 3, 2, 1], [4, 1, 2, 2], [4, 9, 2, 2], [6, 2, 1, 3], [6, 3, 2, 3], [6, 9, 2, 4], [9, 6, 1, 1], [9, 6, 2, 1], [12, 2, 2, 2], [12, 3, 4, 2], [12, 9, 4, 2], [18, 6, 1, 3], [18, 6, 2, 3], [36, 6, 2, 2], [36, 6, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 13104, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '72.48', 'hash': 353, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [1, 6, 9], 'inner_gens': [[1, 4, 24], [1, 4, 264], [1, 196, 24]], 'inner_hash': 6, 'inner_nilpotent': False, 'inner_order': 54, 'inner_split': True, 'inner_tex': 'C_9:C_6', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 24], [6, 8]], 'label': '432.353', 'linC_count': 144, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 24, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D18:C12', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 80, 'number_divisions': 42, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 170, 'number_subgroups': 574, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 39], [3, 8], [4, 40], [6, 96], [9, 18], [12, 104], [18, 54], [36, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[217, 6, 24], [217, 222, 24], [3, 4, 24], [217, 222, 26]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [55, 107, 5329, 40212], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 10], [6, 4], [8, 2], [12, 2]], 'representations': {'PC': {'code': 20936213688517764331987779197579, 'gens': [1, 3, 5], 'pres': [7, -2, -2, -2, -3, -2, -3, -3, 14, 58, 2328, 1390, 102, 1027, 1034, 166, 3548]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1089247, 478576, 793169, 46681, 70633, 47089, 638377]}, 'Perm': {'d': 15, 'gens': [14377673521, 127, 295, 19255587120, 126, 113527451520, 195128564400]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{18}:C_{12}', 'transitive_degree': 72, '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: 105199175
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 353, 'group_order': 432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 105199186
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 353, 'group_order': 432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 216, 'size': 1}
  • id: 105199197
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 353, 'group_order': 432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 218, 'size': 1}
  • id: 105199208
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 353, 'group_order': 432, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 2, 'size': 1}
  • id: 105199219
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 5, 'group_counter': 353, 'group_order': 432, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 12, 'size': 9}
  • id: 105199230
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 6, 'group_counter': 353, 'group_order': 432, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 180, 'size': 9}
  • id: 105199241
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 7, 'group_counter': 353, 'group_order': 432, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 14, 'size': 9}
  • id: 105199252
    {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 8, 'group_counter': 353, 'group_order': 432, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 182, 'size': 9}
  • id: 105199254
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 353, 'group_order': 432, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 144, 'size': 2}
  • id: 105199176
    {'aut_label': '3B1', 'centralizer': '3.b1.a1', 'counter': 10, 'group_counter': 353, 'group_order': 432, 'label': '3B1', 'order': 3, 'powers': [11, 1], 'representative': 160, 'size': 3}
  • id: 105199177
    {'aut_label': '3B-1', 'centralizer': '3.b1.a1', 'counter': 11, 'group_counter': 353, 'group_order': 432, 'label': '3B-1', 'order': 3, 'powers': [10, 1], 'representative': 296, 'size': 3}
  • id: 105199178
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 353, 'group_order': 432, 'label': '4A1', 'order': 4, 'powers': [4, 13], 'representative': 3, 'size': 1}
  • id: 105199179
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 353, 'group_order': 432, 'label': '4A-1', 'order': 4, 'powers': [4, 12], 'representative': 1, 'size': 1}
  • id: 105199180
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 353, 'group_order': 432, 'label': '4B1', 'order': 4, 'powers': [4, 15], 'representative': 219, 'size': 1}
  • id: 105199181
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 353, 'group_order': 432, 'label': '4B-1', 'order': 4, 'powers': [4, 14], 'representative': 217, 'size': 1}
  • id: 105199182
    {'aut_label': '4C1', 'centralizer': '9.a1.a1', 'counter': 16, 'group_counter': 353, 'group_order': 432, 'label': '4C1', 'order': 4, 'powers': [4, 17], 'representative': 15, 'size': 9}
  • id: 105199183
    {'aut_label': '4C1', 'centralizer': '9.a1.a1', 'counter': 17, 'group_counter': 353, 'group_order': 432, 'label': '4C-1', 'order': 4, 'powers': [4, 16], 'representative': 13, 'size': 9}
  • id: 105199184
    {'aut_label': '4C1', 'centralizer': '9.a1.a1', 'counter': 18, 'group_counter': 353, 'group_order': 432, 'label': '4D1', 'order': 4, 'powers': [4, 19], 'representative': 183, 'size': 9}
  • id: 105199185
    {'aut_label': '4C1', 'centralizer': '9.a1.a1', 'counter': 19, 'group_counter': 353, 'group_order': 432, 'label': '4D-1', 'order': 4, 'powers': [4, 18], 'representative': 181, 'size': 9}
  • id: 105199187
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 353, 'group_order': 432, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 72, 'size': 2}
  • id: 105199188
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 353, 'group_order': 432, 'label': '6B', 'order': 6, 'powers': [9, 3], 'representative': 74, 'size': 2}
  • id: 105199189
    {'aut_label': '6C', 'centralizer': '2.b1.a1', 'counter': 22, 'group_counter': 353, 'group_order': 432, 'label': '6C', 'order': 6, 'powers': [9, 4], 'representative': 290, 'size': 2}
  • id: 105199190
    {'aut_label': '6D1', 'centralizer': '3.b1.a1', 'counter': 23, 'group_counter': 353, 'group_order': 432, 'label': '6D1', 'order': 6, 'powers': [10, 2], 'representative': 80, 'size': 3}
  • id: 105199191
    {'aut_label': '6D-1', 'centralizer': '3.b1.a1', 'counter': 24, 'group_counter': 353, 'group_order': 432, 'label': '6D-1', 'order': 6, 'powers': [11, 2], 'representative': 88, 'size': 3}
  • id: 105199192
    {'aut_label': '6D1', 'centralizer': '3.b1.a1', 'counter': 25, 'group_counter': 353, 'group_order': 432, 'label': '6E1', 'order': 6, 'powers': [10, 3], 'representative': 82, 'size': 3}
  • id: 105199193
    {'aut_label': '6D-1', 'centralizer': '3.b1.a1', 'counter': 26, 'group_counter': 353, 'group_order': 432, 'label': '6E-1', 'order': 6, 'powers': [11, 3], 'representative': 90, 'size': 3}
  • id: 105199194
    {'aut_label': '6F1', 'centralizer': '3.b1.a1', 'counter': 27, 'group_counter': 353, 'group_order': 432, 'label': '6F1', 'order': 6, 'powers': [11, 4], 'representative': 18, 'size': 3}
  • id: 105199195
    {'aut_label': '6F-1', 'centralizer': '3.b1.a1', 'counter': 28, 'group_counter': 353, 'group_order': 432, 'label': '6F-1', 'order': 6, 'powers': [10, 4], 'representative': 10, 'size': 3}
  • id: 105199196
    {'aut_label': '6G1', 'centralizer': '9.a1.a1', 'counter': 29, 'group_counter': 353, 'group_order': 432, 'label': '6G1', 'order': 6, 'powers': [11, 5], 'representative': 4, 'size': 9}
  • id: 105199198
    {'aut_label': '6G-1', 'centralizer': '9.a1.a1', 'counter': 30, 'group_counter': 353, 'group_order': 432, 'label': '6G-1', 'order': 6, 'powers': [10, 5], 'representative': 20, 'size': 9}
  • id: 105199199
    {'aut_label': '6G1', 'centralizer': '9.a1.a1', 'counter': 31, 'group_counter': 353, 'group_order': 432, 'label': '6H1', 'order': 6, 'powers': [11, 6], 'representative': 28, 'size': 9}
  • id: 105199200
    {'aut_label': '6G-1', 'centralizer': '9.a1.a1', 'counter': 32, 'group_counter': 353, 'group_order': 432, 'label': '6H-1', 'order': 6, 'powers': [10, 6], 'representative': 44, 'size': 9}
  • id: 105199201
    {'aut_label': '6G1', 'centralizer': '9.a1.a1', 'counter': 33, 'group_counter': 353, 'group_order': 432, 'label': '6I1', 'order': 6, 'powers': [11, 7], 'representative': 6, 'size': 9}
  • id: 105199202
    {'aut_label': '6G-1', 'centralizer': '9.a1.a1', 'counter': 34, 'group_counter': 353, 'group_order': 432, 'label': '6I-1', 'order': 6, 'powers': [10, 7], 'representative': 22, 'size': 9}
  • id: 105199203
    {'aut_label': '6G1', 'centralizer': '9.a1.a1', 'counter': 35, 'group_counter': 353, 'group_order': 432, 'label': '6J1', 'order': 6, 'powers': [11, 8], 'representative': 30, 'size': 9}
  • id: 105199204
    {'aut_label': '6G-1', 'centralizer': '9.a1.a1', 'counter': 36, 'group_counter': 353, 'group_order': 432, 'label': '6J-1', 'order': 6, 'powers': [10, 8], 'representative': 46, 'size': 9}
  • id: 105199205
    {'aut_label': '9A', 'centralizer': '6.c1.a1', 'counter': 37, 'group_counter': 353, 'group_order': 432, 'label': '9A', 'order': 9, 'powers': [37, 9], 'representative': 48, 'size': 6}
  • id: 105199206
    {'aut_label': '9B1', 'centralizer': '6.h1.a1', 'counter': 38, 'group_counter': 353, 'group_order': 432, 'label': '9B1', 'order': 9, 'powers': [39, 9], 'representative': 352, 'size': 6}
  • id: 105199207
    {'aut_label': '9B-1', 'centralizer': '6.h1.a1', 'counter': 39, 'group_counter': 353, 'group_order': 432, 'label': '9B-1', 'order': 9, 'powers': [38, 9], 'representative': 392, 'size': 6}
  • id: 105199209
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 353, 'group_order': 432, 'label': '12A1', 'order': 12, 'powers': [22, 13], 'representative': 147, 'size': 2}
  • id: 105199210
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 353, 'group_order': 432, 'label': '12A-1', 'order': 12, 'powers': [22, 12], 'representative': 289, 'size': 2}
  • id: 105199211
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 42, 'group_counter': 353, 'group_order': 432, 'label': '12B1', 'order': 12, 'powers': [22, 15], 'representative': 75, 'size': 2}
  • id: 105199212
    {'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 353, 'group_order': 432, 'label': '12B-1', 'order': 12, 'powers': [22, 14], 'representative': 361, 'size': 2}
  • id: 105199213
    {'aut_label': '12C1', 'centralizer': '3.b1.a1', 'counter': 44, 'group_counter': 353, 'group_order': 432, 'label': '12C1', 'order': 12, 'powers': [27, 12], 'representative': 9, 'size': 3}
  • id: 105199214
    {'aut_label': '12C-1', 'centralizer': '3.b1.a1', 'counter': 45, 'group_counter': 353, 'group_order': 432, 'label': '12C-1', 'order': 12, 'powers': [28, 13], 'representative': 19, 'size': 3}
  • id: 105199215
    {'aut_label': '12C-1', 'centralizer': '3.b1.a1', 'counter': 46, 'group_counter': 353, 'group_order': 432, 'label': '12C5', 'order': 12, 'powers': [28, 12], 'representative': 17, 'size': 3}
  • id: 105199216
    {'aut_label': '12C1', 'centralizer': '3.b1.a1', 'counter': 47, 'group_counter': 353, 'group_order': 432, 'label': '12C-5', 'order': 12, 'powers': [27, 13], 'representative': 11, 'size': 3}
  • id: 105199217
    {'aut_label': '12C1', 'centralizer': '3.b1.a1', 'counter': 48, 'group_counter': 353, 'group_order': 432, 'label': '12D1', 'order': 12, 'powers': [27, 14], 'representative': 81, 'size': 3}
  • id: 105199218
    {'aut_label': '12C-1', 'centralizer': '3.b1.a1', 'counter': 49, 'group_counter': 353, 'group_order': 432, 'label': '12D-1', 'order': 12, 'powers': [28, 15], 'representative': 91, 'size': 3}
  • id: 105199220
    {'aut_label': '12C-1', 'centralizer': '3.b1.a1', 'counter': 50, 'group_counter': 353, 'group_order': 432, 'label': '12D5', 'order': 12, 'powers': [28, 14], 'representative': 89, 'size': 3}
  • id: 105199221
    {'aut_label': '12C1', 'centralizer': '3.b1.a1', 'counter': 51, 'group_counter': 353, 'group_order': 432, 'label': '12D-5', 'order': 12, 'powers': [27, 15], 'representative': 83, 'size': 3}
  • id: 105199222
    {'aut_label': '12E1', 'centralizer': '9.a1.a1', 'counter': 52, 'group_counter': 353, 'group_order': 432, 'label': '12E1', 'order': 12, 'powers': [28, 16], 'representative': 5, 'size': 9}
  • id: 105199223
    {'aut_label': '12E-1', 'centralizer': '9.a1.a1', 'counter': 53, 'group_counter': 353, 'group_order': 432, 'label': '12E-1', 'order': 12, 'powers': [27, 17], 'representative': 23, 'size': 9}
  • id: 105199224
    {'aut_label': '12E-1', 'centralizer': '9.a1.a1', 'counter': 54, 'group_counter': 353, 'group_order': 432, 'label': '12E5', 'order': 12, 'powers': [27, 16], 'representative': 21, 'size': 9}
  • id: 105199225
    {'aut_label': '12E1', 'centralizer': '9.a1.a1', 'counter': 55, 'group_counter': 353, 'group_order': 432, 'label': '12E-5', 'order': 12, 'powers': [28, 17], 'representative': 7, 'size': 9}
  • id: 105199226
    {'aut_label': '12E1', 'centralizer': '9.a1.a1', 'counter': 56, 'group_counter': 353, 'group_order': 432, 'label': '12F1', 'order': 12, 'powers': [28, 18], 'representative': 29, 'size': 9}
  • id: 105199227
    {'aut_label': '12E-1', 'centralizer': '9.a1.a1', 'counter': 57, 'group_counter': 353, 'group_order': 432, 'label': '12F-1', 'order': 12, 'powers': [27, 19], 'representative': 47, 'size': 9}
  • id: 105199228
    {'aut_label': '12E-1', 'centralizer': '9.a1.a1', 'counter': 58, 'group_counter': 353, 'group_order': 432, 'label': '12F5', 'order': 12, 'powers': [27, 18], 'representative': 45, 'size': 9}
  • id: 105199229
    {'aut_label': '12E1', 'centralizer': '9.a1.a1', 'counter': 59, 'group_counter': 353, 'group_order': 432, 'label': '12F-5', 'order': 12, 'powers': [28, 19], 'representative': 31, 'size': 9}
  • id: 105199231
    {'aut_label': '18A', 'centralizer': '6.c1.a1', 'counter': 60, 'group_counter': 353, 'group_order': 432, 'label': '18A', 'order': 18, 'powers': [37, 20], 'representative': 24, 'size': 6}
  • id: 105199232
    {'aut_label': '18A', 'centralizer': '6.c1.a1', 'counter': 61, 'group_counter': 353, 'group_order': 432, 'label': '18B', 'order': 18, 'powers': [37, 21], 'representative': 26, 'size': 6}
  • id: 105199233
    {'aut_label': '18C', 'centralizer': '6.c1.a1', 'counter': 62, 'group_counter': 353, 'group_order': 432, 'label': '18C', 'order': 18, 'powers': [37, 22], 'representative': 98, 'size': 6}
  • id: 105199234
    {'aut_label': '18D1', 'centralizer': '6.h1.a1', 'counter': 63, 'group_counter': 353, 'group_order': 432, 'label': '18D1', 'order': 18, 'powers': [38, 20], 'representative': 32, 'size': 6}
  • id: 105199235
    {'aut_label': '18D-1', 'centralizer': '6.h1.a1', 'counter': 64, 'group_counter': 353, 'group_order': 432, 'label': '18D-1', 'order': 18, 'powers': [39, 20], 'representative': 40, 'size': 6}
  • id: 105199236
    {'aut_label': '18D1', 'centralizer': '6.h1.a1', 'counter': 65, 'group_counter': 353, 'group_order': 432, 'label': '18E1', 'order': 18, 'powers': [38, 21], 'representative': 34, 'size': 6}
  • id: 105199237
    {'aut_label': '18D-1', 'centralizer': '6.h1.a1', 'counter': 66, 'group_counter': 353, 'group_order': 432, 'label': '18E-1', 'order': 18, 'powers': [39, 21], 'representative': 42, 'size': 6}
  • id: 105199238
    {'aut_label': '18F1', 'centralizer': '6.h1.a1', 'counter': 67, 'group_counter': 353, 'group_order': 432, 'label': '18F1', 'order': 18, 'powers': [39, 22], 'representative': 258, 'size': 6}
  • id: 105199239
    {'aut_label': '18F-1', 'centralizer': '6.h1.a1', 'counter': 68, 'group_counter': 353, 'group_order': 432, 'label': '18F-1', 'order': 18, 'powers': [38, 22], 'representative': 346, 'size': 6}
  • id: 105199240
    {'aut_label': '36A1', 'centralizer': '6.c1.a1', 'counter': 69, 'group_counter': 353, 'group_order': 432, 'label': '36A1', 'order': 36, 'powers': [62, 40], 'representative': 49, 'size': 6}
  • id: 105199242
    {'aut_label': '36A1', 'centralizer': '6.c1.a1', 'counter': 70, 'group_counter': 353, 'group_order': 432, 'label': '36A-1', 'order': 36, 'powers': [62, 41], 'representative': 51, 'size': 6}
  • id: 105199243
    {'aut_label': '36A1', 'centralizer': '6.c1.a1', 'counter': 71, 'group_counter': 353, 'group_order': 432, 'label': '36B1', 'order': 36, 'powers': [62, 42], 'representative': 25, 'size': 6}
  • id: 105199244
    {'aut_label': '36A1', 'centralizer': '6.c1.a1', 'counter': 72, 'group_counter': 353, 'group_order': 432, 'label': '36B-1', 'order': 36, 'powers': [62, 43], 'representative': 27, 'size': 6}
  • id: 105199245
    {'aut_label': '36C1', 'centralizer': '6.h1.a1', 'counter': 73, 'group_counter': 353, 'group_order': 432, 'label': '36C1', 'order': 36, 'powers': [67, 40], 'representative': 57, 'size': 6}
  • id: 105199246
    {'aut_label': '36C-1', 'centralizer': '6.h1.a1', 'counter': 74, 'group_counter': 353, 'group_order': 432, 'label': '36C-1', 'order': 36, 'powers': [68, 41], 'representative': 67, 'size': 6}
  • id: 105199247
    {'aut_label': '36C-1', 'centralizer': '6.h1.a1', 'counter': 75, 'group_counter': 353, 'group_order': 432, 'label': '36C5', 'order': 36, 'powers': [68, 40], 'representative': 65, 'size': 6}
  • id: 105199248
    {'aut_label': '36C1', 'centralizer': '6.h1.a1', 'counter': 76, 'group_counter': 353, 'group_order': 432, 'label': '36C-5', 'order': 36, 'powers': [67, 41], 'representative': 59, 'size': 6}
  • id: 105199249
    {'aut_label': '36C1', 'centralizer': '6.h1.a1', 'counter': 77, 'group_counter': 353, 'group_order': 432, 'label': '36D1', 'order': 36, 'powers': [67, 42], 'representative': 33, 'size': 6}
  • id: 105199250
    {'aut_label': '36C-1', 'centralizer': '6.h1.a1', 'counter': 78, 'group_counter': 353, 'group_order': 432, 'label': '36D-1', 'order': 36, 'powers': [68, 43], 'representative': 43, 'size': 6}
  • id: 105199251
    {'aut_label': '36C-1', 'centralizer': '6.h1.a1', 'counter': 79, 'group_counter': 353, 'group_order': 432, 'label': '36D5', 'order': 36, 'powers': [68, 42], 'representative': 41, 'size': 6}
  • id: 105199253
    {'aut_label': '36C1', 'centralizer': '6.h1.a1', 'counter': 80, 'group_counter': 353, 'group_order': 432, 'label': '36D-5', 'order': 36, 'powers': [67, 43], 'representative': 35, 'size': 6}
• 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: 3356146
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1a', '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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 3356157
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1b', '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, 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, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3356168
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1c', '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, 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, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 3356179
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1d', '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, -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, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 3356183
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -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, -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: 3356184
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 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, 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: 3356185
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 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, -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: 3356186
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 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, -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: 3356187
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3356147
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356148
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356149
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356150
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1m', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356151
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, 2, -1, -1, -2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 2, -1, -1, 2, -2, -2, 2, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -2, 1, -2, 1, 2, 1, -1, 1, -2, -1, -1, 1, -1, 2, 1, 2, -2, 1, 1, -1], 'schur_index': 1}
  • id: 3356152
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, 2, -1, -1, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 2, -1, -1, -2, 2, 2, -2, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -2, 1, -2, 1, 2, 1, -1, 1, 2, 1, 1, -1, 1, -2, -1, -2, 2, -1, -1, 1], 'schur_index': 1}
  • id: 3356153
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -1, -1, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 2, -1, -1, 2, -2, -2, 2, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -2, 1, -2, 1, 2, 1, -1, 1, -2, -1, -1, 1, -1, 2, 1, 2, -2, 1, 1, -1], 'schur_index': 1}
  • id: 3356154
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1q', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, -2, 2, -1, -1, 2, 2, -2, -2, 2, -2, -2, 2, -2, -2, 2, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 2, -1, -1, -2, 2, 2, -2, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -2, 1, -2, 1, 2, 1, -1, 1, 2, 1, 1, -1, 1, -2, -1, -2, 2, -1, -1, 1], 'schur_index': 1}
  • id: 3356155
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1r', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3356156
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1s', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, -1, -1, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3356158
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1t', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3356163
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -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: 3356164
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, -2, -2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -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: 3356165
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -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: 3356166
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -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: 3356159
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1u', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, -4, 2, -4, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356160
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1v', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, -4, 2, -4, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356161
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1w', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, -4, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 2, -2, -2, 2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -2, 4, -2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356162
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.1x', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -4, -4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -2, 4, -2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356167
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, -2, -2, 4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1], 'schur_index': 1}
  • id: 3356169
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2f', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356170
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2g', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356171
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2h', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, -2, -2, -4, -4, 4, 4, 0, 0, 0, 0, -4, -4, 4, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 4, -4, -4, 4, -2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, 2, -1, -2, -1, 1, -1, 2, 1, 1, -1, 1, -2, -1, -2, 2, -1, -1, 1], 'schur_index': 1}
  • id: 3356172
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2i', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, -2, -2, 4, 4, -4, -4, 0, 0, 0, 0, -4, -4, 4, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -4, 4, 4, -4, 2, 2, -2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, 2, -1, -2, -1, 1, -1, -2, -1, -1, 1, -1, 2, 1, 2, -2, 1, 1, -1], 'schur_index': 1}
  • id: 3356173
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2j', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, -2, -2, -4, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, -2, 1, 1, 1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1], 'schur_index': 1}
  • id: 3356176
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356177
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6b', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -3, 0, 0, -6, -6, 6, 6, 0, 0, 0, 0, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356178
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6c', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 0, 0, 0, 0, -3, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356180
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6d', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 0, -3, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356174
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2k', 'multiplicity': 4, 'nt': [24, 65], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -4, 4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, -2, 4, -2, 4, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356175
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.2l', 'multiplicity': 4, 'nt': [24, 65], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 2, -4, 2, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356181
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6e', 'multiplicity': 2, 'nt': [36, 214], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3356182
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '432.353', 'group_order': 432, 'image': None, 'label': '432.353.6f', 'multiplicity': 2, 'nt': [36, 214], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 4605273
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 432, 'label': '432.353.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 4605284
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 216, 'label': '432.353.1b', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 4605295
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 216, 'label': '432.353.1c', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 4605306
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 216, 'label': '432.353.1d', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 4605317
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 216, 'label': '432.353.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 4605328
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 216, 'label': '432.353.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 4605339
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 216, 'label': '432.353.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 4605350
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 216, 'label': '432.353.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 4605352
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.353.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 4605274
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.353.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 4605275
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.d1', 'kernel_order': 108, 'label': '432.353.1j1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[-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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4605276
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.d1', 'kernel_order': 108, 'label': '432.353.1j2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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]], [[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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605277
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.c1', 'kernel_order': 108, 'label': '432.353.1k1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4605278
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.c1', 'kernel_order': 108, 'label': '432.353.1k2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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]], [[-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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605279
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 108, 'label': '432.353.1l1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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]], [[-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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 4605280
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.b1', 'kernel_order': 108, 'label': '432.353.1l2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[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, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 4605281
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 17, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 108, 'label': '432.353.1m1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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]], [[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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 4605282
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 18, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 108, 'label': '432.353.1m2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[-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, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 4605283
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.c1', 'kernel_order': 72, 'label': '432.353.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]]]}
  • id: 4605285
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.c1', 'kernel_order': 72, 'label': '432.353.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]]]}
  • id: 4605286
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.d1', 'kernel_order': 72, 'label': '432.353.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]]]}
  • id: 4605287
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.d1', 'kernel_order': 72, 'label': '432.353.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]]]}
  • id: 4605288
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 72, 'label': '432.353.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]]]}
  • id: 4605289
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 72, 'label': '432.353.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]]]}
  • id: 4605290
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.b1', 'kernel_order': 72, 'label': '432.353.1q1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]]]}
  • id: 4605291
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.b1', 'kernel_order': 72, 'label': '432.353.1q2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-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]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]]]}
  • id: 4605292
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 27, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 72, 'label': '432.353.1r1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 4605293
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 28, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 72, 'label': '432.353.1r2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 4605294
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 29, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 72, 'label': '432.353.1s1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 4605296
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 30, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 72, 'label': '432.353.1s2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 4605297
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 31, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.353.1t1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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, -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, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 4605298
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 32, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.353.1t2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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, 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, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 4605299
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 33, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.d1', 'kernel_order': 36, 'label': '432.353.1u1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]]]}
  • id: 4605300
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 34, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.d1', 'kernel_order': 36, 'label': '432.353.1u2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]]]}
  • id: 4605301
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 35, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.d1', 'kernel_order': 36, 'label': '432.353.1u3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]]]}
  • id: 4605302
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 36, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.d1', 'kernel_order': 36, 'label': '432.353.1u4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]]]}
  • id: 4605303
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 37, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.c1', 'kernel_order': 36, 'label': '432.353.1v1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]]]}
  • id: 4605304
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 38, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.c1', 'kernel_order': 36, 'label': '432.353.1v2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]]]}
  • id: 4605305
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 39, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.c1', 'kernel_order': 36, 'label': '432.353.1v3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 4]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]]]}
  • id: 4605307
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 40, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.c1', 'kernel_order': 36, 'label': '432.353.1v4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]]]}
  • id: 4605308
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 41, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 36, 'label': '432.353.1w1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
  • id: 4605309
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 42, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 36, 'label': '432.353.1w2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
  • id: 4605310
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 43, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 36, 'label': '432.353.1w3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
  • id: 4605311
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 44, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.b1', 'kernel_order': 36, 'label': '432.353.1w4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[-1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
  • id: 4605312
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 45, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.353.1x1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
  • id: 4605313
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 46, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.353.1x2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
  • id: 4605314
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 47, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.353.1x3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[-1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
  • id: 4605315
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 48, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.353.1x4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
  • id: 4605316
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 49, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 72, 'label': '432.353.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 4605318
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 50, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 36, 'label': '432.353.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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: 4605319
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 51, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.b1', 'kernel_order': 36, 'label': '432.353.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 4605320
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 52, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 36, 'label': '432.353.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 4605321
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 53, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 24, 'label': '432.353.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 4605322
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 54, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 24, 'label': '432.353.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 4605323
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 55, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.b1', 'kernel_order': 18, 'label': '432.353.2f1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 4605324
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 56, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.b1', 'kernel_order': 18, 'label': '432.353.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 4605325
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 57, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.353.2g1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 4605326
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 58, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.353.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 4605327
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 59, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 12, 'label': '432.353.2h1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, -1]]]}
  • id: 4605329
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 60, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 12, 'label': '432.353.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[-1, 1]]]}
  • id: 4605330
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 61, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.b1', 'kernel_order': 12, 'label': '432.353.2i1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[2, -1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, -1]]]}
  • id: 4605331
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 62, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.b1', 'kernel_order': 12, 'label': '432.353.2i2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[2, 1]], [[-2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[1, 1]]]}
  • id: 4605332
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 63, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 12, 'label': '432.353.2j1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 4605333
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 64, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 12, 'label': '432.353.2j2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 4605334
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 65, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 6, 'label': '432.353.2k1', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[-2, 3]], [[2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 5]], [[-2, 5]], [[-2, 1]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 5]]]}
  • id: 4605335
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 66, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 6, 'label': '432.353.2k2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[2, 3]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[2, 1]], [[2, 5]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 1]]]}
  • id: 4605336
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 67, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 6, 'label': '432.353.2k3', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[2, 3]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 5]], [[2, 5]], [[2, 1]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[-1, 0]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 4]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 5]]]}
  • id: 4605337
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 68, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.b1', 'kernel_order': 6, 'label': '432.353.2k4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[-2, 3]], [[2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[-2, 5]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 1]]]}
  • id: 4605338
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 69, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 6, 'label': '432.353.2l1', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[2, 3]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[2, 1]], [[2, 5]], [[-2, 5]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
  • id: 4605340
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 70, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 6, 'label': '432.353.2l2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[2, 3]], [[2, 3]], [[-2, 3]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[-2, 1]], [[2, 1]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
  • id: 4605341
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 71, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 6, 'label': '432.353.2l3', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 2]], [[2, 4]], [[2, 3]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[2, 3]], [[2, 3]], [[-2, 3]], [[-2, 3]], [[2, 5]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[-2, 5]], [[2, 5]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
  • id: 4605342
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 72, 'counter': 72, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 6, 'label': '432.353.2l4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 4]], [[-2, 2]], [[-2, 3]], [[2, 3]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[2, 5]], [[2, 1]], [[-2, 1]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
  • id: 4605343
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 73, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1.a1', 'kernel_order': 8, 'label': '432.353.6a', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605344
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 74, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1.a1', 'kernel_order': 4, 'label': '432.353.6b', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605345
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 75, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1.b1', 'kernel_order': 4, 'label': '432.353.6c', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605346
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 76, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 4, 'label': '432.353.6d', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605347
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 77, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '216.53', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.b1', 'kernel_order': 2, 'label': '432.353.6e1', 'nt': [36, 214], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[6, 1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605348
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 78, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '216.53', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.b1', 'kernel_order': 2, 'label': '432.353.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[-6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605349
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 79, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '216.53', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.353.6f1', 'nt': [36, 214], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[-6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[-3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 4605351
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 8, 'counter': 80, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '432.353', 'group_counter': 353, 'group_order': 432, 'image': None, 'image_isoclass': '216.53', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.353.6f2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[6, 1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, 1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 58381634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.353.1.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': '432.353', 'subgroup_hash': 353, 'subgroup_order': 432, 'subgroup_tex': 'D_{18}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 216, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.2.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': '216.111', 'subgroup_hash': 111, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.75', 'subgroup_hash': 75, 'subgroup_order': 216, 'subgroup_tex': 'C_{18}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 216, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.61', 'subgroup_hash': 61, 'subgroup_order': 216, 'subgroup_tex': 'C_{18}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 216, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.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': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 216, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 216, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 216, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.d1', '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': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.38', 'subgroup_hash': 38, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, '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': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 12, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 13, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.4.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.c1', '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 14, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.4.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.d1', '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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 108, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 108, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 72, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 72, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.7', 'subgroup_hash': 7, 'subgroup_order': 72, 'subgroup_tex': 'C_{18}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381725
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381726
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.6.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.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': 6, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.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': 6, '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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.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': 6, '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': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.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': 6, '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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.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': 6, '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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.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': 6, '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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.6.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.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': 6, '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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 40, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 41, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 42, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.8.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.c1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.8.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.d1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9.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': 9, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, '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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381756
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381757
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 57, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381758
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381759
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381765
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381770
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381772
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 58381773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 27, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '432.353.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 58381774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.18.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381791
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 88, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381792
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 89, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381795
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381796
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381797
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381798
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381799
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.24.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381800
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381801
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381802
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 58381803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.24.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.24.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '432.353.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 58381640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 12, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381641
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 105, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381642
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 106, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381644
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381647
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381652
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381658
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381659
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381660
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381661
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381662
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.j1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381663
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.j1.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 58381664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381665
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 127, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.44', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381666
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, '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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 58381667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.353.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 58381670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.54.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381675
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 136, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381676
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 137, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381677
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 6, 'counter': 138, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381678
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381680
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381681
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381682
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381683
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381685
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.72.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 58381686
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381687
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381688
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.72.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381689
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.72.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.353.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 58381692
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.353.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381693
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.353.108.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 58381694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381697
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381698
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.353.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, '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: 58381700
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.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': 108, '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: 58381702
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.108.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.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': 108, '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: 58381703
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 3, 'counter': 161, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.159', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 159, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}\\times D_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381704
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 58381705
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.353.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.53', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 53, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58381706
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.353.216.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.53', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 53, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{36}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 58381707
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 2, 'counter': 165, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.353.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.111', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 111, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], '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: 58381708
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 58381709
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 58381710
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.216.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 58381711
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.353.216.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, '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: 58381713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.353', 'ambient_counter': 353, 'ambient_order': 432, 'ambient_tex': 'D_{18}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 1, 'counter': 170, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '432.353.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '432.353', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 353, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C7'], '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: 58381634
    {'ambient': '432.353', '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': '54.a1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '3.a1.a1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4091, 4097, 5701, 6096, 3195, 4744, 4608, 6025], 'generators': [1, 48, 2, 12, 144, 216, 8], 'label': '432.353.1.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.c1.a1', '2.d1.b1', '2.d1.a1', '2.d1.d1', '2.d1.c1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '54.6', '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': '54.6'}
  • id: 58381635
    {'ambient': '432.353', 'aut_centralizer_order': 3, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 9, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.f1.a1', '6.g1.a1', '6.i1.a1', '6.i1.b1', '6.i1.c1', '6.i1.d1', '9.a1.a1', '9.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2304, -1, 7753, -1, 6286, -1, 7060, -1], 'generators': [1, 144, 2, 12, 216, 8], 'label': '432.353.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381636
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.h1.a1', '12.h1.d1', '12.j1.b1'], 'contains': ['48.a1.a1', '72.e1.b1', '72.f1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7521, -1, 3050, -1, 3823, -1, 3391, -1], 'generators': [324, 8, 144], 'label': '432.353.24.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.b1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381637
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.c1', '12.h1.b1', '12.h1.d1', '12.j1.a1'], 'contains': ['48.a1.a1', '72.e1.c1', '72.f1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7521, -1, 2142, -1, 3823, -1, 2829, -1], 'generators': [14, 8, 144], 'label': '432.353.24.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.c1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381638
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.d1', '12.h1.b1', '12.h1.c1', '12.j1.b1'], 'contains': ['48.a1.a1', '72.e1.d1', '72.f1.d1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7521, -1, 2572, -1, 3823, -1, 2046, -1], 'generators': [326, 8, 144], 'label': '432.353.24.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.d1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381639
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 54, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.d1.b1', '54.d1.c1', '54.d1.d1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1289, -1, 9097, -1, 8800, -1, 9088, -1], 'generators': [1, 12, 216], 'label': '432.353.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381640
    {'ambient': '432.353', 'aut_centralizer_order': 432, 'aut_label': '36.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.i1.a1', '18.a1.a1', '18.c1.a1', '18.d1.a1'], 'contains': ['72.a1.a1', '72.a1.b1', '72.b1.a1', '108.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5655, 3734, 4954, 6776, 4867, 7529, 4789, 6586], 'generators': [2, 216, 144], 'label': '432.353.36.a1.a1', 'mobius_quo': -2, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.a1.a1'], 'normal_contains': ['72.b1.a1', '72.a1.b1', '72.a1.a1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381641
    {'ambient': '432.353', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '12.l1.a1', '18.a1.a1', '18.h1.a1', '18.h1.c1'], 'contains': ['72.b1.a1', '108.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4572, 2954, 6221, 8825, 5898, 8237, 6531, 7336], 'generators': [1, 144, 2], 'label': '432.353.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.e1.a1', '12.f1.a1', '18.a1.a1'], 'normal_contains': ['72.b1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381642
    {'ambient': '432.353', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.f1.b1', '12.l1.b1', '18.a1.a1', '18.h1.b1', '18.h1.d1'], 'contains': ['72.b1.a1', '108.b1.b1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4572, 2954, 7799, 7445, 5898, 8237, 6675, 7037], 'generators': [217, 144, 2], 'label': '432.353.36.b1.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.b1', 'normal_contained_in': ['12.e1.b1', '12.f1.b1', '18.a1.a1'], 'normal_contains': ['72.b1.a1', '108.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.b1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381643
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.b1.a1'], 'contains': ['72.c1.a1', '72.e1.a1', '72.e1.b1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5050, -1, 3833, -1, 6237, -1, 4057, -1], 'generators': [12, 216, 8], 'label': '432.353.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381644
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '18.b1.a1'], 'contains': ['72.c1.a1', '72.e1.c1', '72.e1.d1', '108.c1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5050, -1, 3413, -1, 6237, -1, 3613, -1], 'generators': [14, 216, 8], 'label': '432.353.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381645
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.c1', '18.b1.a1'], 'contains': ['72.c1.b1', '72.e1.a1', '72.e1.d1', '108.c1.c1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5050, -1, 4207, -1, 6237, -1, 3835, -1], 'generators': [218, 12, 8], 'label': '432.353.36.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.c1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381646
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.b1.a1', '108.b1.b1', '108.e1.a1', '108.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '12.a1.a1', '12.h1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8470, 8983, 1292, 903, 226, 472, 1298, 1387], 'generators': [12, 144, 216, 8, 48], 'label': '432.353.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381647
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.d1', '18.b1.a1'], 'contains': ['72.c1.b1', '72.e1.b1', '72.e1.c1', '108.c1.d1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5050, -1, 4737, -1, 6237, -1, 4280, -1], 'generators': [218, 324, 296], 'label': '432.353.36.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.d1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381648
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.h1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.f1.b1', '108.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7658, -1, 1604, -1, 3508, -1, 2438, -1], 'generators': [12, 216, 144], 'label': '432.353.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381649
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.h1.b1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.f1.c1', '72.f1.d1', '108.c1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7658, -1, 1182, -1, 3508, -1, 1759, -1], 'generators': [14, 216, 144], 'label': '432.353.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381650
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.c1', '12.h1.c1', '18.c1.a1'], 'contains': ['72.a1.b1', '72.f1.a1', '72.f1.d1', '108.c1.c1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7658, -1, 2868, -1, 3508, -1, 1876, -1], 'generators': [218, 12, 144], 'label': '432.353.36.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.c1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381651
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.d1', '12.h1.d1', '18.c1.a1'], 'contains': ['72.a1.b1', '72.f1.b1', '72.f1.c1', '108.c1.d1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7658, -1, 3118, -1, 3508, -1, 2999, -1], 'generators': [218, 324, 144], 'label': '432.353.36.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.d1.d1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381652
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.b1.a1', '18.e1.a1', '18.f1.a1'], 'contains': ['72.c1.a1', '72.c1.b1', '72.d1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2811, -1, 6823, -1, 7311, -1, 5603, -1], 'generators': [2, 216, 8], 'label': '432.353.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381653
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.b1.a1', '18.g1.a1', '18.g1.b1'], 'contains': ['72.d1.a1', '72.e1.a1', '72.e1.c1', '108.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4094, -1, 7057, -1, 6899, -1, 5825, -1], 'generators': [2, 12, 8], 'label': '432.353.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381654
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.b1.a1', '18.g1.c1', '18.g1.d1'], 'contains': ['72.d1.a1', '72.e1.b1', '72.e1.d1', '108.d1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4094, -1, 6400, -1, 6899, -1, 6047, -1], 'generators': [2, 324, 296], 'label': '432.353.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.f1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381655
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '18.c1.a1', '18.h1.a1', '18.h1.b1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.f1.c1', '108.d1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6260, -1, 5176, -1, 4551, -1, 4959, -1], 'generators': [2, 12, 144], 'label': '432.353.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381656
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.j1.b1', '18.c1.a1', '18.h1.c1', '18.h1.d1'], 'contains': ['72.b1.a1', '72.f1.b1', '72.f1.d1', '108.d1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6260, -1, 4572, -1, 4551, -1, 5077, -1], 'generators': [2, 324, 144], 'label': '432.353.36.g1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.g1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381657
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.b1.a1', '108.b1.b1', '108.e1.a1', '108.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.c1', '8.c1.d1', '12.a1.b1', '12.h1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8470, 8983, 985, 2151, 226, 472, 738, 820], 'generators': [14, 144, 216, 8, 48], 'label': '432.353.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.c1', '8.c1.d1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381658
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.k1.a1', '18.d1.a1', '18.h1.a1', '18.h1.d1'], 'contains': ['72.b1.a1', '108.e1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3173, -1, 6642, -1, 5625, -1, 6233, -1], 'generators': [15, 2, 144], 'label': '432.353.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.h1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381659
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.k1.b1', '18.d1.a1', '18.h1.b1', '18.h1.c1'], 'contains': ['72.b1.a1', '108.e1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3173, -1, 5795, -1, 5625, -1, 6384, -1], 'generators': [327, 2, 144], 'label': '432.353.36.h1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.h1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381660
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.e1.a1', '18.g1.a1', '18.g1.c1'], 'contains': ['72.d1.a1', '108.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2406, -1, 9374, -1, 9155, -1, 8217, -1], 'generators': [1, 8, 2], 'label': '432.353.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.i1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381661
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '18.e1.a1', '18.g1.b1', '18.g1.d1'], 'contains': ['72.d1.a1', '108.b1.b1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2406, -1, 9707, -1, 9155, -1, 8705, -1], 'generators': [217, 8, 2], 'label': '432.353.36.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.i1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381662
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.f1.a1', '18.g1.a1', '18.g1.d1'], 'contains': ['72.d1.a1', '108.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [919, -1, 8481, -1, 8063, -1, 6818, -1], 'generators': [15, 8, 2], 'label': '432.353.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381663
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '18.f1.a1', '18.g1.b1', '18.g1.c1'], 'contains': ['72.d1.a1', '108.e1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [919, -1, 7954, -1, 8063, -1, 7851, -1], 'generators': [327, 296, 2], 'label': '432.353.36.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.j1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381664
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.c1.a1', '24.h1.a1', '24.h1.b1', '24.h1.c1', '24.h1.d1'], 'contains': ['144.a1.a1', '144.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8178, 6074, 2296, 5658, 4257, 5820, 2922, 5363], 'generators': [8, 144], 'label': '432.353.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.c1.a1', '24.a1.b1', '24.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.353', 'quotient_action_image': '6.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381665
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '48.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.c1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.b1.b1', '24.d1.a1', '24.e1.a1', '24.e1.b1', '24.e1.c1', '24.e1.d1'], 'contains': ['144.a1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9165, 7409, 782, 2757, 2073, 4541, 1076, 3302], 'generators': [336], 'label': '432.353.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.d1.a1', '24.b1.b1', '24.b1.a1', '24.e1.a1', '24.e1.b1', '24.e1.c1', '24.e1.d1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.353', 'quotient_action_image': '6.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381666
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 576, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.f1.a1', '24.f1.b1', '24.g1.a1'], 'contains': ['144.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9769, -1, 2114, -1, 2725, -1, 1628, -1], 'generators': [344], 'label': '432.353.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381667
    {'ambient': '432.353', 'aut_centralizer_order': 216, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '1.a1.a1', 'complements': ['8.c1.a1', '8.c1.b1', '8.c1.c1', '8.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.b1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2371, 2372, 9235, 7770, 8816, 8946, 8400, 7716], 'generators': [1, 216], 'label': '432.353.54.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.a1.a1', '108.b1.b1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '54.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '54.6', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381668
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.b1.a1', '108.e1.a1', '108.b1.b1', '108.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.b1', '8.c1.a1', '8.c1.d1', '12.a1.c1', '12.h1.c1'], 'core': '4.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8470, 8983, 1595, 278, 226, 472, 1019, 253], 'generators': [218, 144, 12, 8, 48], 'label': '432.353.4.a1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.b1', '8.c1.a1', '8.c1.d1', '12.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.c1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381669
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.c1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.c1.b1', '108.c1.c1', '108.c1.d1', '108.d1.a1', '108.d1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4024, -1, 6166, -1, 6568, -1, 5425, -1], 'generators': [2, 12, 216], 'label': '432.353.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381670
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '108.e1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1696, -1, 8127, -1, 7724, -1, 7001, -1], 'generators': [15, 216], 'label': '432.353.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381671
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.h1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.a1', '108.e1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1262, -1, 9019, -1, 8403, -1, 7224, -1], 'generators': [1, 12], 'label': '432.353.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381672
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.b1', '18.h1.b1', '27.a1.a1'], 'contains': ['108.b1.b1', '108.d1.a1', '108.e1.b1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1262, -1, 8343, -1, 8403, -1, 8034, -1], 'generators': [217, 12], 'label': '432.353.54.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381673
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.c1', '18.h1.c1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.b1', '108.e1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1262, -1, 6728, -1, 8403, -1, 7668, -1], 'generators': [1, 324], 'label': '432.353.54.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.c1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381674
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.d1', '18.h1.d1', '27.a1.a1'], 'contains': ['108.b1.b1', '108.d1.b1', '108.e1.a1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1262, -1, 8803, -1, 8403, -1, 7446, -1], 'generators': [217, 324], 'label': '432.353.54.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.d1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381675
    {'ambient': '432.353', 'aut_centralizer_order': 432, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.f1.a1', '36.a1.a1', '36.d1.a1', '36.d1.b1'], 'contains': ['144.a1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8559, 5206, 1213, 5314, 4023, 6345, 2353, 5652], 'generators': [216, 144], 'label': '432.353.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.8', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381676
    {'ambient': '432.353', 'aut_centralizer_order': 432, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.b1.b1', '24.f1.b1', '36.a1.a1', '36.d1.c1', '36.d1.d1'], 'contains': ['144.a1.a1', '216.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8559, 5206, 2937, 6167, 4023, 6345, 2796, 5896], 'generators': [218, 144], 'label': '432.353.72.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1.b1', 'normal_contained_in': ['24.a1.b1', '24.b1.b1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.8', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381677
    {'ambient': '432.353', 'aut_centralizer_order': 864, 'aut_label': '72.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.g1.a1', '36.a1.a1', '36.b1.a1', '36.b1.b1', '36.g1.a1', '36.g1.b1', '36.h1.a1', '36.h1.b1'], 'contains': ['144.a1.a1', '216.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 4254, 5418, 6735, 4867, 6896, 5162, 6324], 'generators': [2, 144], 'label': '432.353.72.b1.a1', 'mobius_quo': 1, 'mobius_sub': -24, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.c1.a1', '24.d1.a1', '36.a1.a1', '36.b1.b1', '36.b1.a1'], 'normal_contains': ['144.a1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.14', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381678
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.c1.a1', '36.c1.b1', '36.e1.a1'], 'contains': ['144.b1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5546, -1, 3273, -1, 6395, -1, 3757, -1], 'generators': [216, 8], 'label': '432.353.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381679
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.b1.a1', '108.e1.b1', '108.b1.b1', '108.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.b1', '8.c1.b1', '8.c1.c1', '12.a1.d1', '12.h1.d1'], 'core': '4.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8470, 8983, 2008, 2776, 226, 472, 1628, 1954], 'generators': [218, 144, 324, 8, 48], 'label': '432.353.4.a1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.d1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.b1', '8.c1.b1', '8.c1.c1', '12.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.d1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381680
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '36.c1.c1', '36.c1.d1', '36.e1.a1'], 'contains': ['144.b1.a1', '216.a1.b1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5546, -1, 4630, -1, 6395, -1, 4378, -1], 'generators': [218, 8], 'label': '432.353.72.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.c1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381681
    {'ambient': '432.353', 'aut_centralizer_order': 576, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.e1.a1', '36.f1.a1', '36.f1.b1', '36.i1.a1', '36.i1.b1', '36.j1.a1', '36.j1.b1'], 'contains': ['144.b1.a1', '216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3591, -1, 7178, -1, 7111, -1, 5936, -1], 'generators': [2, 8], 'label': '432.353.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381682
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.c1.a1', '36.c1.c1', '36.f1.a1'], 'contains': ['144.b1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5305, -1, 4124, -1, 6177, -1, 4008, -1], 'generators': [12, 8], 'label': '432.353.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381683
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '36.c1.a1', '36.c1.d1', '36.f1.b1'], 'contains': ['144.b1.a1', '216.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5305, -1, 4416, -1, 6177, -1, 4495, -1], 'generators': [324, 296], 'label': '432.353.72.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.b1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381684
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.c1', '36.c1.b1', '36.c1.d1', '36.f1.a1'], 'contains': ['144.b1.a1', '216.c1.c1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5305, -1, 3951, -1, 6177, -1, 4126, -1], 'generators': [14, 8], 'label': '432.353.72.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.c1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381685
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.d1', '36.c1.b1', '36.c1.c1', '36.f1.b1'], 'contains': ['144.b1.a1', '216.c1.d1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5305, -1, 3810, -1, 6177, -1, 3639, -1], 'generators': [326, 296], 'label': '432.353.72.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.d1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381686
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.h1.a1', '36.d1.a1', '36.d1.c1', '36.g1.a1'], 'contains': ['144.a1.a1', '216.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 1908, -1, 3805, -1, 2561, -1], 'generators': [12, 144], 'label': '432.353.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381687
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.h1.b1', '36.d1.a1', '36.d1.d1', '36.g1.b1'], 'contains': ['144.a1.a1', '216.c1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 2546, -1, 3805, -1, 3048, -1], 'generators': [324, 144], 'label': '432.353.72.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.f1.b1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381688
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.c1', '24.h1.c1', '36.d1.b1', '36.d1.d1', '36.g1.a1'], 'contains': ['144.a1.a1', '216.c1.c1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 1666, -1, 3805, -1, 2679, -1], 'generators': [14, 144], 'label': '432.353.72.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.f1.c1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381689
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.d1', '24.h1.d1', '36.d1.b1', '36.d1.c1', '36.g1.b1'], 'contains': ['144.a1.a1', '216.c1.d1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7572, -1, 2238, -1, 3805, -1, 2046, -1], 'generators': [326, 144], 'label': '432.353.72.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.f1.d1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381690
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 48, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '12.b1.a1', '12.c1.a1', '12.i1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7871, 6294, 4120, 4219, 1755, 6339, 3046, 4232], 'generators': [2, 144, 216, 8, 336], 'label': '432.353.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.b1.a1', '8.a1.b1', '8.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381691
    {'ambient': '432.353', 'aut_centralizer_order': 864, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.e1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1', '216.a1.b1', '216.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3492, 3618, 6330, 6899, 6877, 7510, 5480, 6586], 'generators': [2, 216], 'label': '432.353.108.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '54.a1.a1'], 'normal_contains': ['216.b1.a1', '216.a1.b1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.26', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381692
    {'ambient': '432.353', 'aut_centralizer_order': 432, 'aut_label': '108.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['4.a1.a1', '4.a1.b1', '4.a1.c1', '4.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.i1.a1', '54.a1.a1', '54.d1.a1', '54.d1.c1'], 'contains': ['216.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2648, 2967, 8386, 7770, 8403, 8237, 7423, 7336], 'generators': [1], 'label': '432.353.108.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.b1.a1', '54.a1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.26', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381693
    {'ambient': '432.353', 'aut_centralizer_order': 432, 'aut_label': '108.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '1.a1.a1', 'complements': ['4.a1.a1', '4.a1.b1', '4.a1.c1', '4.a1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['36.b1.b1', '36.i1.b1', '54.a1.a1', '54.d1.b1', '54.d1.d1'], 'contains': ['216.b1.a1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2648, 2967, 8515, 7445, 8403, 8237, 7740, 7037], 'generators': [217], 'label': '432.353.108.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.b1.b1', 'normal_contained_in': ['36.b1.b1', '54.a1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.b1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.26', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381694
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.d1.a1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.c1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4941, -1, 3436, -1, 5943, -1, 3883, -1], 'generators': [12, 216], 'label': '432.353.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381695
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.d1.b1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.c1.c1', '216.c1.d1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4941, -1, 3213, -1, 5943, -1, 3379, -1], 'generators': [14, 216], 'label': '432.353.108.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381696
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.c1', '36.d1.c1', '54.b1.a1'], 'contains': ['216.a1.b1', '216.c1.a1', '216.c1.d1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4941, -1, 4321, -1, 5943, -1, 3513, -1], 'generators': [218, 12], 'label': '432.353.108.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.c1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381697
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.d1', '36.d1.d1', '54.b1.a1'], 'contains': ['216.a1.b1', '216.c1.b1', '216.c1.c1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4941, -1, 4524, -1, 5943, -1, 4252, -1], 'generators': [218, 324], 'label': '432.353.108.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.d1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381698
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.g1.a1', '54.b1.a1', '54.d1.a1', '54.d1.b1'], 'contains': ['216.b1.a1', '216.c1.a1', '216.c1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4151, -1, 6500, -1, 6629, -1, 5618, -1], 'generators': [2, 12], 'label': '432.353.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381699
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.b1', '36.g1.b1', '54.b1.a1', '54.d1.c1', '54.d1.d1'], 'contains': ['216.b1.a1', '216.c1.b1', '216.c1.d1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4151, -1, 6196, -1, 6629, -1, 5753, -1], 'generators': [2, 324], 'label': '432.353.108.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381700
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.j1.a1', '54.c1.a1', '54.d1.a1', '54.d1.d1'], 'contains': ['216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1610, -1, 8254, -1, 7724, -1, 6851, -1], 'generators': [15], 'label': '432.353.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.e1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381701
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.c1.c1', '12.d1.a1', '12.j1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7241, 7806, 3836, 3554, 1215, 1529, 2482, 2521], 'generators': [2, 144, 12, 8, 48], 'label': '432.353.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.b1', '2.d1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.c1.c1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381702
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.b1', '36.j1.b1', '54.c1.a1', '54.d1.b1', '54.d1.c1'], 'contains': ['216.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1610, -1, 6700, -1, 7724, -1, 7054, -1], 'generators': [327], 'label': '432.353.108.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.e1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381703
    {'ambient': '432.353', 'aut_centralizer_order': 864, 'aut_label': '144.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1', '72.a1.b1', '72.b1.a1', '72.f1.a1', '72.f1.b1', '72.f1.c1', '72.f1.d1'], 'contains': ['432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8384, 5206, 2151, 5905, 4023, 6345, 2679, 5682], 'generators': [144], 'label': '432.353.144.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.b1.a1', '72.a1.b1', '72.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.36', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381704
    {'ambient': '432.353', 'aut_centralizer_order': 576, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.c1.a1', '72.c1.b1', '72.d1.a1', '72.e1.a1', '72.e1.b1', '72.e1.c1', '72.e1.d1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5359, -1, 3991, -1, 6386, -1, 4180, -1], 'generators': [8], 'label': '432.353.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381765
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.h1.a1'], 'contains': ['24.f1.a1', '24.f1.b1', '24.g1.a1', '36.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8151, -1, 4301, -1, 2574, -1, 3564, -1], 'generators': [2, 216, 344, 144], 'label': '432.353.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381705
    {'ambient': '432.353', 'aut_centralizer_order': 864, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': ['2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.c1.a1', '108.a1.a1', '108.c1.a1', '108.c1.b1'], 'contains': ['432.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5534, 4617, 3242, 6324, 6168, 6959, 3709, 6039], 'generators': [216], 'label': '432.353.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '108.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.53', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381706
    {'ambient': '432.353', 'aut_centralizer_order': 864, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': ['2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '72.c1.b1', '108.a1.a1', '108.c1.c1', '108.c1.d1'], 'contains': ['432.a1.a1'], 'core': '216.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5534, 4617, 4540, 6735, 6168, 6959, 4062, 6283], 'generators': [218], 'label': '432.353.216.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.b1', 'normal_contained_in': ['72.a1.b1', '108.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.53', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381707
    {'ambient': '432.353', 'aut_centralizer_order': 1728, 'aut_label': '216.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '108.a1.a1', '108.b1.a1', '108.b1.b1', '108.d1.a1', '108.d1.b1', '108.e1.a1', '108.e1.b1'], 'contains': ['432.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3683, 3981, 6559, 7124, 6877, 7497, 5872, 6586], 'generators': [2], 'label': '432.353.216.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.b1.a1', '108.a1.a1', '108.b1.b1', '108.b1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '216.111', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.111', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381708
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '108.c1.a1', '108.c1.c1', '108.d1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5184, -1, 4169, -1, 5949, -1, 3827, -1], 'generators': [12], 'label': '432.353.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381709
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.b1', '72.f1.b1', '108.c1.a1', '108.c1.d1', '108.d1.b1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5184, -1, 4336, -1, 5949, -1, 4298, -1], 'generators': [324], 'label': '432.353.216.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.b1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381710
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.c1', '72.f1.c1', '108.c1.b1', '108.c1.d1', '108.d1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5184, -1, 3904, -1, 5949, -1, 3945, -1], 'generators': [14], 'label': '432.353.216.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.c1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381711
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.d1', '72.f1.d1', '108.c1.b1', '108.c1.c1', '108.d1.b1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5184, -1, 3787, -1, 5949, -1, 3575, -1], 'generators': [326], 'label': '432.353.216.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.d1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381712
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.b1.a1', '8.c1.b1', '8.c1.d1', '12.d1.b1', '12.j1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7241, 7806, 3483, 1527, 1215, 1529, 2755, 3628], 'generators': [2, 144, 324, 8, 48], 'label': '432.353.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.d1', '2.d1.c1'], 'normal_contains': ['8.b1.a1', '8.c1.b1', '8.c1.d1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381713
    {'ambient': '432.353', 'aut_centralizer_order': None, 'aut_label': '432.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': ['144.a1.a1', '144.b1.a1', '216.a1.a1', '216.a1.b1', '216.b1.a1', '216.c1.a1', '216.c1.b1', '216.c1.c1', '216.c1.d1'], 'contains': [], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5359, 4617, 3991, 6634, 6168, 6959, 3945, 6161], 'generators': [], 'label': '432.353.432.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.a1', '216.b1.a1', '216.a1.b1', '216.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381714
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 48, 'centralizer': '18.a1.a1', 'complements': ['108.c1.a1', '108.c1.b1', '108.c1.c1', '108.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.b1.a1', '12.e1.a1', '12.f1.a1', '12.l1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5814, 2427, 5997, 8765, 4072, 7465, 5503, 8640], 'generators': [1, 144, 8, 336, 2], 'label': '432.353.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'normal_contains': ['8.b1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381715
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 48, 'centralizer': '18.a1.a1', 'complements': ['108.c1.a1', '108.c1.b1', '108.c1.c1', '108.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.b1.a1', '12.e1.b1', '12.f1.b1', '12.l1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5814, 2427, 6815, 8141, 4072, 7465, 5776, 8073], 'generators': [217, 144, 8, 336, 2], 'label': '432.353.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'normal_contains': ['8.b1.a1', '12.e1.b1', '12.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381716
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 4, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.a1.c1', '4.a1.d1', '4.b1.a1', '4.c1.a1', '4.c1.b1', '6.a1.a1', '6.f1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7060, 7109, 3170, 2776, 1466, 2421, 2350, 2521], 'generators': [2, 144, 48, 12, 216, 8], 'label': '432.353.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.a1.c1', '4.a1.d1', '4.a1.a1', '4.a1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '108.26', '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': '54.6'}
  • id: 58381717
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.c1.a1', '108.c1.b1', '108.c1.c1', '108.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.b1.a1', '12.g1.a1', '12.k1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3358, 5240, 6345, 6227, 2728, 4307, 4137, 7122], 'generators': [15, 144, 8, 2, 48], 'label': '432.353.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'normal_contains': ['8.b1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381718
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['108.c1.a1', '108.c1.b1', '108.c1.c1', '108.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.b1.a1', '12.g1.b1', '12.k1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3358, 5240, 4955, 4794, 2728, 4307, 4779, 4755], 'generators': [327, 144, 8, 2, 48], 'label': '432.353.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'normal_contains': ['8.b1.a1', '12.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '216.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381719
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 4, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.a1.c1', '12.a1.d1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '18.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6891, 7143, 3093, 3143, 720, 2560, 2216, 3075], 'generators': [2, 144, 12, 216, 48], 'label': '432.353.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.d1.a1', '12.d1.b1', '12.a1.c1', '12.a1.d1', '12.a1.a1', '12.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381720
    {'ambient': '432.353', 'aut_centralizer_order': 36, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 36, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.e1.b1', '18.a1.a1', '18.e1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3744, 496, 8589, 9736, 7345, 9542, 7988, 9754], 'generators': [1, 2, 216, 8, 144], 'label': '432.353.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.b1.a1', '12.e1.b1', '12.e1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '54.6', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381721
    {'ambient': '432.353', 'aut_centralizer_order': 36, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.45', 'aut_weyl_index': 36, 'centralizer': '6.c1.a1', 'complements': ['72.e1.a1', '72.e1.b1', '72.e1.c1', '72.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.f1.b1', '18.a1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5493, 1879, 6045, 8697, 3571, 8510, 5234, 9200], 'generators': [1, 144, 216, 336, 2], 'label': '432.353.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.f1.b1', '12.f1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '54.6', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381722
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 4, 'centralizer': '54.a1.a1', 'complements': ['72.e1.a1', '72.e1.b1', '72.e1.c1', '72.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.g1.b1', '18.d1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3097, 4213, 5381, 6623, 2295, 5212, 3680, 5706], 'generators': [15, 144, 216, 2, 48], 'label': '432.353.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.g1.b1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381723
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['72.c1.a1', '72.e1.b1', '72.c1.b1', '72.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.g1.a1', '18.h1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 3173, 5683, 7991, 3116, 3497, 3928, 7557], 'generators': [1, 144, 12, 2, 48], 'label': '432.353.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.d1.a1', '12.f1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '108.26', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381724
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['72.c1.a1', '72.e1.b1', '72.c1.b1', '72.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.b1', '12.g1.b1', '18.h1.b1'], 'core': '6.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 3173, 5139, 6054, 3116, 3497, 4989, 5190], 'generators': [217, 144, 12, 2, 48], 'label': '432.353.6.e1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.b1', 'normal_contained_in': ['2.d1.b1', '3.a1.a1'], 'normal_contains': ['12.d1.a1', '12.f1.b1', '12.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '108.26', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381725
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['72.c1.a1', '72.e1.a1', '72.c1.b1', '72.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.f1.a1', '12.g1.b1', '18.h1.c1'], 'core': '6.e1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 3173, 3674, 5542, 3116, 3497, 4570, 6222], 'generators': [1, 144, 324, 2, 48], 'label': '432.353.6.e1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.c1', 'normal_contained_in': ['2.d1.c1', '3.a1.a1'], 'normal_contains': ['12.d1.b1', '12.f1.a1', '12.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.c1', 'projective_image': '108.26', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.e1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381726
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['72.c1.a1', '72.e1.a1', '72.c1.b1', '72.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '3.a1.a1'], 'contains': ['12.d1.b1', '12.f1.b1', '12.g1.a1', '18.h1.d1'], 'core': '6.e1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4222, 3173, 6284, 7333, 3116, 3497, 4346, 6688], 'generators': [217, 144, 324, 2, 48], 'label': '432.353.6.e1.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.d1', 'normal_contained_in': ['2.d1.d1', '3.a1.a1'], 'normal_contains': ['12.d1.b1', '12.f1.b1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.d1', 'projective_image': '108.26', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.e1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381727
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.162', 'aut_weyl_index': 12, 'centralizer': '18.a1.a1', 'complements': ['216.c1.a1', '216.c1.b1', '216.c1.c1', '216.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.d1.b1', '6.b1.a1', '6.c1.a1', '6.h1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5642, 2167, 6448, 8511, 4102, 7465, 5503, 8443], 'generators': [1, 144, 2, 216, 8, 336], 'label': '432.353.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.b1', '4.d1.a1', '6.b1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '54.6', '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': '18.3'}
  • id: 58381728
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 36, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.h1.a1', '12.h1.b1', '12.h1.c1', '12.h1.d1', '12.j1.a1', '12.j1.b1', '18.b1.a1', '18.c1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4897, -1, 4674, -1, 5140, -1, 3371, -1], 'generators': [2, 144, 12, 216, 8], 'label': '432.353.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381729
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 36, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.k1.a1', '12.k1.b1', '18.d1.a1', '18.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1686, -1, 6999, -1, 5713, -1, 6315, -1], 'generators': [15, 144, 216, 8, 2], 'label': '432.353.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381730
    {'ambient': '432.353', 'aut_centralizer_order': 36, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.10', 'aut_weyl_index': 72, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.i1.a1', '12.l1.a1', '12.l1.b1', '18.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6257, -1, 7641, -1, 4572, -1, 6046, -1], 'generators': [1, 144, 216, 344, 2], 'label': '432.353.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381731
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.j1.a1', '12.k1.a1', '18.g1.a1', '18.h1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2212, -1, 8014, -1, 6850, -1, 6928, -1], 'generators': [1, 144, 12, 8, 2], 'label': '432.353.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381732
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.b1.a1'], 'contains': ['12.e1.b1', '12.j1.a1', '12.k1.b1', '18.g1.b1', '18.h1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2212, -1, 7321, -1, 6850, -1, 7722, -1], 'generators': [217, 144, 12, 8, 2], 'label': '432.353.6.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381733
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.j1.b1', '12.k1.b1', '18.g1.c1', '18.h1.c1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2212, -1, 6523, -1, 6850, -1, 7457, -1], 'generators': [1, 144, 324, 8, 2], 'label': '432.353.6.i1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.c1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381734
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '3.b1.a1'], 'contains': ['12.e1.b1', '12.j1.b1', '12.k1.a1', '18.g1.d1', '18.h1.d1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2212, -1, 8849, -1, 6850, -1, 7192, -1], 'generators': [217, 144, 324, 8, 2], 'label': '432.353.6.i1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.d1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381735
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 96, 'centralizer': '18.a1.a1', 'complements': ['54.d1.a1', '54.d1.b1', '54.d1.c1', '54.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9310, 8361, 504, 1579, 802, 3478, 710, 2790], 'generators': [216, 8, 336, 144], 'label': '432.353.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.b1.a1', '4.a1.a1', '4.a1.b1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381736
    {'ambient': '432.353', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '18.3', 'aut_weyl_index': 96, 'centralizer': '18.a1.a1', 'complements': ['54.d1.a1', '54.d1.b1', '54.d1.c1', '54.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.c1', '4.a1.d1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.b1', '24.b1.b1', '24.f1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9310, 8361, 1844, 3965, 802, 3478, 1430, 3975], 'generators': [218, 8, 336, 144], 'label': '432.353.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.b1.a1', '4.a1.c1', '4.a1.d1'], 'normal_contains': ['16.a1.a1', '24.a1.b1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381737
    {'ambient': '432.353', 'aut_centralizer_order': 96, 'aut_label': '8.b1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 96, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '24.c1.a1', '24.d1.a1', '24.g1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7891, 6184, 4209, 4869, 2073, 5123, 3294, 5146], 'generators': [2, 8, 336, 144], 'label': '432.353.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.d1.b1', '4.d1.a1', '4.e1.b1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381738
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.362', 'aut_weyl_index': 4, 'centralizer': '54.a1.a1', 'complements': ['216.c1.a1', '216.c1.b1', '216.c1.c1', '216.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.e1.b1', '6.d1.a1', '6.g1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3355, 5328, 5516, 5232, 2295, 6029, 3695, 5095], 'generators': [15, 144, 48, 216, 8, 2], 'label': '432.353.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.b1', '4.e1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '108.26', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381739
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['54.a1.a1', '54.c1.a1', '54.d1.c1', '54.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.c1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.e1.a1', '24.h1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8677, 9504, 1103, 264, 408, 1529, 922, 1126], 'generators': [12, 8, 48, 144], 'label': '432.353.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1', '4.a1.c1', '4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381740
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['54.a1.a1', '54.c1.a1', '54.d1.a1', '54.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.d1', '4.c1.b1'], 'contains': ['16.a1.a1', '24.e1.b1', '24.h1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8677, 9504, 1637, 1094, 408, 1529, 1643, 3231], 'generators': [324, 8, 48, 144], 'label': '432.353.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.c1.b1', '4.a1.d1', '4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '432.353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381741
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['54.a1.a1', '54.c1.a1', '54.d1.c1', '54.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.a1.d1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.e1.c1', '24.h1.c1'], 'core': '8.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8677, 9504, 1249, 2346, 408, 1529, 1073, 1744], 'generators': [14, 8, 48, 144], 'label': '432.353.8.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.c1', 'normal_contained_in': ['4.c1.a1', '4.a1.d1', '4.a1.b1'], 'normal_contains': ['16.a1.a1', '24.e1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.c1', 'projective_image': '432.353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381742
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['54.a1.a1', '54.c1.a1', '54.d1.a1', '54.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.a1.c1', '4.c1.b1'], 'contains': ['16.a1.a1', '24.e1.d1', '24.h1.d1'], 'core': '8.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8677, 9504, 956, 750, 408, 1529, 207, 813], 'generators': [326, 8, 48, 144], 'label': '432.353.8.c1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.d1', 'normal_contained_in': ['4.c1.b1', '4.a1.c1', '4.a1.b1'], 'normal_contains': ['16.a1.a1', '24.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.d1', 'projective_image': '432.353', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381743
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.27', 'aut_weyl_index': 54, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.b1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '18.g1.b1', '18.g1.c1', '18.g1.d1', '27.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [747, -1, 9293, -1, 8558, -1, 8826, -1], 'generators': [1, 2, 12, 216, 8], 'label': '432.353.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381744
    {'ambient': '432.353', 'aut_centralizer_order': 3, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 9, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.c1.a1', '18.d1.a1', '18.h1.a1', '18.h1.b1', '18.h1.c1', '18.h1.d1', '27.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2728, -1, 7231, -1, 6286, -1, 6624, -1], 'generators': [1, 144, 12, 216, 2], 'label': '432.353.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381745
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.i1.a1', '36.i1.b1', '36.j1.a1', '36.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1', '36.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8919, 7896, 1205, 1467, 132, 2104, 501, 2355], 'generators': [12, 216, 48, 144], 'label': '432.353.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381746
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.i1.a1', '36.i1.b1', '36.j1.a1', '36.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.a1.a1'], 'contains': ['24.b1.a1', '24.e1.c1', '24.e1.d1', '36.d1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8919, 7896, 56, 2941, 132, 2104, 58, 2053], 'generators': [14, 216, 48, 144], 'label': '432.353.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.b1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.c1', '24.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381747
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.i1.a1', '36.j1.a1', '36.i1.b1', '36.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.c1', '6.a1.a1'], 'contains': ['24.b1.b1', '24.e1.a1', '24.e1.d1', '36.d1.c1'], 'core': '12.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8919, 7896, 1409, 989, 132, 2104, 355, 1435], 'generators': [218, 12, 48, 144], 'label': '432.353.12.a1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.c1', 'normal_contained_in': ['4.a1.c1', '6.a1.a1'], 'normal_contains': ['24.b1.b1', '24.e1.a1', '24.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.c1', 'projective_image': '216.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.a1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381748
    {'ambient': '432.353', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.i1.a1', '36.j1.b1', '36.i1.b1', '36.j1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.d1', '6.a1.a1'], 'contains': ['24.b1.b1', '24.e1.b1', '24.e1.c1', '36.d1.d1'], 'core': '12.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8919, 7896, 1625, 3796, 132, 2104, 1221, 3540], 'generators': [218, 324, 48, 144], 'label': '432.353.12.a1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.d1', 'normal_contained_in': ['4.a1.d1', '6.a1.a1'], 'normal_contains': ['24.b1.b1', '24.e1.b1', '24.e1.c1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.d1', 'projective_image': '216.53', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.a1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381749
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['216.a1.a1', '216.c1.b1', '216.a1.b1', '216.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '6.e1.a1', '6.i1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3928, 4097, 6035, 7291, 3483, 3548, 4335, 7557], 'generators': [1, 144, 48, 12, 8, 2], 'label': '432.353.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381750
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.c1.a1', '36.a1.a1', '36.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4413, 2940, 5329, 7613, 5058, 7503, 4020, 6124], 'generators': [2, 216, 8, 144], 'label': '432.353.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '24.a1.b1', '24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381751
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '12.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 144, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '24.b1.b1', '24.d1.a1', '36.a1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6674, 5273, 4042, 5218, 1573, 6168, 3025, 5706], 'generators': [2, 216, 336, 144], 'label': '432.353.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'normal_contains': ['24.d1.a1', '24.b1.b1', '24.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381752
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.e1.c1', '36.g1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7076, 6403, 3276, 4746, 1190, 2668, 2674, 4409], 'generators': [2, 12, 48, 144], 'label': '432.353.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1', '6.e1.b1', '6.e1.a1'], 'normal_contains': ['24.d1.a1', '24.e1.a1', '24.e1.c1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381753
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.a1.a1', '6.e1.c1', '6.e1.d1'], 'contains': ['24.d1.a1', '24.e1.b1', '24.e1.d1', '36.g1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7076, 6403, 3418, 3464, 1190, 2668, 2819, 4711], 'generators': [2, 324, 48, 144], 'label': '432.353.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.c1.b1', '6.a1.a1', '6.e1.d1', '6.e1.c1'], 'normal_contains': ['24.d1.a1', '24.e1.b1', '24.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381754
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.i1.a1', '6.i1.c1'], 'contains': ['24.c1.a1', '36.b1.a1', '36.i1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4021, 1208, 8095, 9359, 7345, 8282, 7761, 8317], 'generators': [1, 8, 144, 2], 'label': '432.353.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381755
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.b1.a1', '6.i1.b1', '6.i1.d1'], 'contains': ['24.c1.a1', '36.b1.b1', '36.i1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4021, 1208, 8739, 8463, 7345, 8282, 8027, 7764], 'generators': [217, 8, 144, 2], 'label': '432.353.12.e1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.d1.b1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '36.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '108.26', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381756
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 144, 'centralizer': '6.c1.a1', 'complements': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.e1.a1', '6.e1.c1'], 'contains': ['24.d1.a1', '36.b1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5502, 3522, 5171, 7991, 3235, 6965, 5158, 7336], 'generators': [1, 336, 2, 144], 'label': '432.353.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.d1.a1', '6.c1.a1', '6.e1.a1', '6.e1.c1'], 'normal_contains': ['24.d1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381757
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 144, 'centralizer': '6.c1.a1', 'complements': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.c1.a1', '6.e1.b1', '6.e1.d1'], 'contains': ['24.d1.a1', '36.b1.b1'], 'core': '12.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5502, 3522, 6100, 7240, 3235, 6965, 5302, 7037], 'generators': [217, 336, 2, 144], 'label': '432.353.12.f1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.b1', 'normal_contained_in': ['4.d1.b1', '6.c1.a1', '6.e1.b1', '6.e1.d1'], 'normal_contains': ['24.d1.a1', '36.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '108.26', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381758
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.d1.a1', '6.e1.a1', '6.e1.d1'], 'contains': ['24.d1.a1', '36.h1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3371, 4137, 5878, 6903, 2962, 4301, 4861, 6732], 'generators': [15, 2, 48, 144], 'label': '432.353.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.e1.a1', '6.d1.a1', '6.e1.a1', '6.e1.d1'], 'normal_contains': ['24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381759
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '12.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '108.26', 'aut_weyl_index': 16, 'centralizer': '54.a1.a1', 'complements': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.d1.a1', '6.e1.b1', '6.e1.c1'], 'contains': ['24.d1.a1', '36.h1.b1'], 'core': '12.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3371, 4137, 3838, 6402, 2962, 4301, 5011, 6419], 'generators': [327, 2, 48, 144], 'label': '432.353.12.g1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.g1.b1', 'normal_contained_in': ['4.e1.b1', '6.d1.a1', '6.e1.b1', '6.e1.c1'], 'normal_contains': ['24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.b1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381760
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['216.a1.a1', '216.c1.b1', '216.a1.b1', '216.c1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.b1', '4.e1.b1', '6.e1.b1', '6.i1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3928, 4097, 5229, 5905, 3483, 3548, 5154, 4484], 'generators': [217, 144, 48, 12, 8, 2], 'label': '432.353.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.b1', '4.e1.b1', '6.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381761
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.h1.b1', '36.c1.a1', '36.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7677, -1, 2416, -1, 3841, -1, 2270, -1], 'generators': [12, 216, 8, 144], 'label': '432.353.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381762
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.h1.c1', '24.h1.d1', '36.c1.b1', '36.d1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7677, -1, 2053, -1, 3841, -1, 1829, -1], 'generators': [14, 216, 8, 144], 'label': '432.353.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.h1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381763
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.c1', '6.f1.a1'], 'contains': ['24.a1.b1', '24.h1.a1', '24.h1.d1', '36.c1.c1', '36.d1.c1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7677, -1, 3098, -1, 3841, -1, 2050, -1], 'generators': [218, 12, 8, 144], 'label': '432.353.12.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.h1.c1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381764
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.d1', '6.f1.a1'], 'contains': ['24.a1.b1', '24.h1.b1', '24.h1.c1', '36.c1.d1', '36.d1.d1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7677, -1, 3596, -1, 3841, -1, 2491, -1], 'generators': [218, 324, 8, 144], 'label': '432.353.12.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.h1.d1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381766
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.f1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.c1.a1', '24.h1.a1', '24.h1.c1', '36.f1.a1', '36.g1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4881, -1, 5502, -1, 4727, -1, 4198, -1], 'generators': [2, 12, 8, 144], 'label': '432.353.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381767
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.f1.a1', '6.i1.c1', '6.i1.d1'], 'contains': ['24.c1.a1', '24.h1.b1', '24.h1.d1', '36.f1.b1', '36.g1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4881, -1, 4872, -1, 4727, -1, 4418, -1], 'generators': [2, 324, 8, 144], 'label': '432.353.12.j1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381768
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.g1.a1', '6.i1.a1', '6.i1.d1'], 'contains': ['24.c1.a1', '36.h1.a1', '36.j1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1767, -1, 7772, -1, 5940, -1, 6291, -1], 'generators': [15, 8, 2, 144], 'label': '432.353.12.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381769
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.g1.a1', '6.i1.b1', '6.i1.c1'], 'contains': ['24.c1.a1', '36.h1.b1', '36.j1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1767, -1, 6382, -1, 5940, -1, 7005, -1], 'generators': [327, 8, 2, 144], 'label': '432.353.12.k1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.k1.b1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381770
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.h1.a1'], 'contains': ['24.g1.a1', '36.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6273, -1, 6584, -1, 3502, -1, 5446, -1], 'generators': [1, 344, 2, 144], 'label': '432.353.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381771
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['216.a1.a1', '216.c1.a1', '216.a1.b1', '216.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.a1', '4.e1.b1', '6.e1.c1', '6.i1.c1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3928, 4097, 4897, 4560, 3483, 3548, 4881, 5706], 'generators': [1, 144, 48, 324, 8, 2], 'label': '432.353.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.d1.a1', '4.e1.b1', '6.e1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381772
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.h1.a1'], 'contains': ['24.g1.a1', '36.b1.b1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6273, -1, 8296, -1, 3502, -1, 5590, -1], 'generators': [217, 344, 2, 144], 'label': '432.353.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.l1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381773
    {'ambient': '432.353', 'aut_centralizer_order': 96, 'aut_label': '16.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '18.3', 'aut_weyl_index': 96, 'centralizer': '18.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '8.c1.b1', '8.c1.c1', '8.c1.d1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9769, 8464, 497, 2132, 2073, 3972, 1076, 2752], 'generators': [8, 336], 'label': '432.353.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1', '8.a1.b1', '8.a1.a1', '8.c1.a1', '8.c1.b1', '8.c1.c1', '8.c1.d1'], 'normal_contains': ['48.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.353', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 58381774
    {'ambient': '432.353', 'aut_centralizer_order': 108, 'aut_label': '18.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 108, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.h1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '54.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4957, 2249, 7896, 8981, 6850, 9314, 7495, 8871], 'generators': [1, 216, 144, 2], 'label': '432.353.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1', '36.b1.b1', '36.b1.a1', '54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '54.6', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 58381775
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.c1.b1', '36.c1.c1', '36.c1.d1', '36.e1.a1', '36.f1.a1', '36.f1.b1', '54.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3597, -1, 6304, -1, 7830, -1, 4657, -1], 'generators': [2, 12, 216, 8], 'label': '432.353.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381776
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 36, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.d1.a1', '36.d1.b1', '36.d1.c1', '36.d1.d1', '36.g1.a1', '36.g1.b1', '54.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5709, -1, 4627, -1, 4284, -1, 3825, -1], 'generators': [2, 12, 216, 144], 'label': '432.353.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.c1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381777
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 36, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.h1.a1', '36.h1.b1', '54.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2285, -1, 6804, -1, 5434, -1, 5797, -1], 'generators': [15, 216, 2, 144], 'label': '432.353.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381778
    {'ambient': '432.353', 'aut_centralizer_order': 72, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.i1.a1', '36.i1.b1', '54.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1639, -1, 9684, -1, 9780, -1, 9882, -1], 'generators': [1, 216, 8, 2], 'label': '432.353.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.e1.a1', 'projective_image': '54.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381779
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 216, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.j1.a1', '36.j1.b1', '54.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [231, -1, 8478, -1, 8315, -1, 8294, -1], 'generators': [15, 216, 8, 2], 'label': '432.353.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381780
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.i1.a1', '36.j1.a1', '54.d1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [874, -1, 9302, -1, 9286, -1, 8560, -1], 'generators': [1, 12, 8, 2], 'label': '432.353.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381781
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '9.a1.a1'], 'contains': ['36.f1.a1', '36.i1.b1', '36.j1.b1', '54.d1.b1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [874, -1, 8981, -1, 9286, -1, 9615, -1], 'generators': [217, 12, 8, 2], 'label': '432.353.18.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381782
    {'ambient': '432.353', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '216.111', 'aut_weyl_index': 8, 'centralizer': '54.a1.a1', 'complements': ['216.a1.a1', '216.c1.a1', '216.a1.b1', '216.c1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.b1', '4.e1.a1', '6.e1.d1', '6.i1.d1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3928, 4097, 6774, 6668, 3483, 3548, 4608, 6990], 'generators': [217, 144, 48, 324, 8, 2], 'label': '432.353.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.d1.b1', '4.e1.a1', '6.e1.d1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '108.26', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381783
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.c1', '9.a1.a1'], 'contains': ['36.f1.b1', '36.i1.a1', '36.j1.b1', '54.d1.c1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [874, -1, 8218, -1, 9286, -1, 9349, -1], 'generators': [1, 324, 296, 2], 'label': '432.353.18.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.c1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381784
    {'ambient': '432.353', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.d1', '9.a1.a1'], 'contains': ['36.f1.b1', '36.i1.b1', '36.j1.a1', '54.d1.d1'], 'core': '108.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [874, -1, 9944, -1, 9286, -1, 8826, -1], 'generators': [217, 324, 296, 2], 'label': '432.353.18.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.d1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 58381785
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.i1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.g1.a1', '36.h1.a1', '54.d1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2766, -1, 7382, -1, 6398, -1, 6044, -1], 'generators': [1, 12, 2, 144], 'label': '432.353.18.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381786
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.i1.b1', '9.b1.a1'], 'contains': ['36.b1.b1', '36.g1.a1', '36.h1.b1', '54.d1.b1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2766, -1, 7045, -1, 6398, -1, 7251, -1], 'generators': [217, 12, 2, 144], 'label': '432.353.18.h1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.b1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381787
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.c1', '6.i1.c1', '9.b1.a1'], 'contains': ['36.b1.a1', '36.g1.b1', '36.h1.b1', '54.d1.c1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2766, -1, 5162, -1, 6398, -1, 6758, -1], 'generators': [1, 324, 2, 144], 'label': '432.353.18.h1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.c1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381788
    {'ambient': '432.353', 'aut_centralizer_order': 6, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.d1', '6.i1.d1', '9.b1.a1'], 'contains': ['36.b1.b1', '36.g1.b1', '36.h1.a1', '54.d1.d1'], 'core': '36.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2766, -1, 7659, -1, 6398, -1, 6537, -1], 'generators': [217, 324, 2, 144], 'label': '432.353.18.h1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.d1', 'projective_image': '108.26', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381789
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.h1.a1', '12.h1.b1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8075, 5261, 1665, 5314, 4236, 5807, 2268, 4902], 'generators': [216, 8, 144], 'label': '432.353.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '216.53', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381790
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.b1.a1', '12.h1.c1', '12.h1.d1'], 'contains': ['48.a1.a1', '72.a1.b1', '72.c1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8075, 5261, 3326, 6156, 4236, 5807, 3169, 5363], 'generators': [218, 8, 144], 'label': '432.353.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.b1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '216.53', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381791
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.c1.a1', 'complements': ['18.g1.a1', '18.g1.b1', '18.g1.c1', '18.g1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.a1.b1', '12.c1.a1'], 'contains': ['48.b1.a1', '72.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9165, 7005, 56, 2791, 1573, 4541, 694, 3302], 'generators': [216, 336, 144], 'label': '432.353.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1', '12.a1.a1', '12.a1.b1'], 'normal_contains': ['48.b1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '216.53', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381792
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.c1.a1', 'complements': ['18.g1.a1', '18.g1.b1', '18.g1.c1', '18.g1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.a1.c1', '12.a1.d1', '12.c1.a1'], 'contains': ['48.b1.a1', '72.a1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9165, 7005, 1365, 4293, 1573, 4541, 1223, 3893], 'generators': [218, 336, 144], 'label': '432.353.24.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.a1.b1', '12.c1.a1', '12.a1.c1', '12.a1.d1'], 'normal_contains': ['48.b1.a1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': '216.53', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381793
    {'ambient': '432.353', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1728.18843', 'aut_weyl_index': 1, 'centralizer': '54.a1.a1', 'complements': ['144.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.e1.b1', '6.e1.c1', '6.e1.d1', '9.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 3283, 5593, 6835, 2910, 4744, 4026, 6348], 'generators': [1, 144, 48, 12, 216, 2], 'label': '432.353.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.c1.a1', '6.d1.a1', '6.e1.b1', '6.e1.a1', '6.e1.d1', '6.e1.c1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '54.6', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381794
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '24.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.a1', '12.e1.b1', '12.j1.a1', '12.j1.b1', '12.k1.a1', '12.k1.b1'], 'contains': ['48.a1.a1', '72.b1.a1', '72.d1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4307, 4070, 5657, 7359, 5279, 6668, 5247, 6124], 'generators': [2, 8, 144], 'label': '432.353.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1', '12.e1.b1', '12.e1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '216.111', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 58381795
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '24.d1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 288, 'centralizer': '6.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.f1.a1', '12.f1.b1', '12.g1.a1', '12.g1.b1'], 'contains': ['48.b1.a1', '72.b1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6801, 6027, 4029, 5736, 2725, 5098, 4463, 5744], 'generators': [2, 336, 144], 'label': '432.353.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1', '12.f1.b1', '12.f1.a1', '12.g1.b1', '12.g1.a1'], 'normal_contains': ['48.b1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '216.111', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 58381796
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['18.e1.a1', '18.f1.a1', '18.g1.c1', '18.g1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.a1.c1', '12.d1.a1'], 'contains': ['48.b1.a1', '72.f1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8807, 7985, 782, 802, 1190, 2389, 824, 2355], 'generators': [12, 48, 144], 'label': '432.353.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.c1.a1', '12.d1.a1', '12.a1.c1', '12.a1.a1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '432.353', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381797
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['18.e1.a1', '18.f1.a1', '18.g1.a1', '18.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.a1.a1', '12.a1.d1', '12.d1.b1'], 'contains': ['48.b1.a1', '72.f1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8807, 7985, 1085, 2234, 1190, 2389, 1354, 3574], 'generators': [324, 48, 144], 'label': '432.353.24.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.c1.b1', '12.d1.b1', '12.a1.d1', '12.a1.a1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '432.353', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381798
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['18.e1.a1', '18.f1.a1', '18.g1.c1', '18.g1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.c1', '12.a1.b1', '12.a1.d1', '12.d1.a1'], 'contains': ['48.b1.a1', '72.f1.c1'], 'core': '24.e1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8807, 7985, 529, 3513, 1190, 2389, 942, 3031], 'generators': [14, 48, 144], 'label': '432.353.24.e1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.c1', 'normal_contained_in': ['8.c1.c1', '12.d1.a1', '12.a1.d1', '12.a1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.c1', 'projective_image': '432.353', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.e1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381799
    {'ambient': '432.353', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 32, 'centralizer': '54.a1.a1', 'complements': ['18.e1.a1', '18.f1.a1', '18.g1.a1', '18.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.d1', '12.a1.b1', '12.a1.c1', '12.d1.b1'], 'contains': ['48.b1.a1', '72.f1.d1'], 'core': '24.e1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8807, 7985, 183, 1524, 1190, 2389, 458, 2053], 'generators': [326, 48, 144], 'label': '432.353.24.e1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.d1', 'normal_contained_in': ['8.c1.d1', '12.d1.b1', '12.a1.c1', '12.a1.b1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.d1', 'projective_image': '432.353', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.e1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 58381800
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3.1', 'aut_weyl_index': 576, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.i1.a1'], 'contains': ['48.c1.a1', '72.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9565, -1, 1843, -1, 2458, -1, 1484, -1], 'generators': [216, 344, 144], 'label': '432.353.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381801
    {'ambient': '432.353', 'aut_centralizer_order': 144, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3.1', 'aut_weyl_index': 576, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.i1.a1'], 'contains': ['48.c1.a1', '72.a1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9565, -1, 2871, -1, 2458, -1, 1628, -1], 'generators': [218, 344, 144], 'label': '432.353.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.b1', 'projective_image': '216.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381802
    {'ambient': '432.353', 'aut_centralizer_order': 288, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3.1', 'aut_weyl_index': 576, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.i1.a1', '12.l1.a1', '12.l1.b1'], 'contains': ['48.c1.a1', '72.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8432, -1, 5357, -1, 2992, -1, 4606, -1], 'generators': [2, 344, 144], 'label': '432.353.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '216.111', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 58381803
    {'ambient': '432.353', 'aut_centralizer_order': 24, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.h1.a1', '12.h1.c1', '12.j1.a1'], 'contains': ['48.a1.a1', '72.e1.a1', '72.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7521, -1, 2357, -1, 3823, -1, 2608, -1], 'generators': [12, 8, 144], 'label': '432.353.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '432.353', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}