Abstract group data - 324.166

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• gps_groups •

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

  
  {'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 6, 4, 4, 3, 4, 4, 3, 2], 'aut_gens': [[1, 6, 18, 108], [79, 12, 90, 108], [73, 6, 18, 108], [49, 12, 198, 108], [85, 84, 24, 108], [37, 48, 30, 108], [49, 6, 18, 108], [13, 72, 66, 216], [5, 78, 96, 108], [7, 6, 24, 108], [73, 6, 90, 108]], 'aut_group': '5184.qr', 'aut_hash': 8627901162325749137, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 14, 'aut_perms': [56567888771, 25517330398, 34180400329, 69023093998, 50338967290, 81717529188, 25391078837, 81848719572, 2546461, 3237814], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 2, 4, 1], [3, 2, 8, 1], [3, 4, 4, 1], [3, 4, 8, 1], [6, 3, 2, 1], [6, 6, 4, 1], [6, 6, 8, 1], [6, 9, 2, 1], [6, 18, 1, 1], [6, 18, 2, 1], [6, 27, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '2592.fv', 'autcentquo_hash': 9019849488891309561, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 9, 1], [2, 27, 1], [3, 1, 2], [3, 2, 15], [3, 4, 12], [6, 3, 2], [6, 6, 12], [6, 9, 2], [6, 18, 3], [6, 27, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '108.39', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 166, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 1], ['3.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [3, 1, 2, 1], [3, 2, 1, 5], [3, 2, 2, 5], [3, 4, 1, 4], [3, 4, 2, 4], [6, 3, 2, 1], [6, 6, 1, 4], [6, 6, 2, 4], [6, 9, 2, 1], [6, 18, 1, 1], [6, 18, 2, 1], [6, 27, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2184, 'exponent': 6, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '324.166', 'hash': 166, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 6, 3], 'inner_gens': [[1, 12, 90, 108], [13, 6, 18, 108], [37, 6, 18, 216], [1, 6, 234, 108]], 'inner_hash': 39, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': False, 'inner_tex': 'C_3:S_3^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 12], [2, 30], [4, 12]], 'label': '324.166', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:S3^2', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 54, 'number_divisions': 36, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 87, 'number_subgroup_classes': 224, 'number_subgroups': 1000, 'old_label': None, 'order': 324, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 39], [3, 80], [6, 204]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [0, 0, 1, 1, 1], 'outer_gens': [[1, 78, 90, 108], [5, 12, 90, 108], [1, 48, 90, 108], [1, 36, 60, 108], [1, 42, 102, 108]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [598, 719, 373, 639, 86], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 14], [4, 14], [8, 4]], 'representations': {'PC': {'code': 241842432640628585051, 'gens': [1, 3, 4, 6], 'pres': [6, -2, -3, -3, -2, -3, -3, 12, 218, 2163, 69, 2164, 455]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [24505, 40831, 6083, 5941, 96397, 5995]}, 'Perm': {'d': 12, 'gens': [136, 3633840, 325, 43590960, 45360, 435]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:S_3^2', 'transitive_degree': 36, '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: 103862967
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 166, 'group_order': 324, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 103862978
    {'aut_label': '2A', 'centralizer': '3.b1', 'counter': 2, 'group_counter': 166, 'group_order': 324, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 54, 'size': 3}
  • id: 103862989
    {'aut_label': '2B', 'centralizer': '9.c1', 'counter': 3, 'group_counter': 166, 'group_order': 324, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 3, 'size': 9}
  • id: 103863000
    {'aut_label': '2C', 'centralizer': '27.a1', 'counter': 4, 'group_counter': 166, 'group_order': 324, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 135, 'size': 27}
  • id: 103863011
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 166, 'group_order': 324, 'label': '3A1', 'order': 3, 'powers': [6, 1], 'representative': 4, 'size': 1}
  • id: 103863017
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 166, 'group_order': 324, 'label': '3A-1', 'order': 3, 'powers': [5, 1], 'representative': 2, 'size': 1}
  • id: 103863018
    {'aut_label': '3B', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 166, 'group_order': 324, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 36, 'size': 2}
  • id: 103863019
    {'aut_label': '3B', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 166, 'group_order': 324, 'label': '3C', 'order': 3, 'powers': [8, 1], 'representative': 48, 'size': 2}
  • id: 103863020
    {'aut_label': '3B', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 166, 'group_order': 324, 'label': '3D', 'order': 3, 'powers': [9, 1], 'representative': 42, 'size': 2}
  • id: 103862968
    {'aut_label': '3B', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 166, 'group_order': 324, 'label': '3E', 'order': 3, 'powers': [10, 1], 'representative': 12, 'size': 2}
  • id: 103862969
    {'aut_label': '3F', 'centralizer': '2.b1', 'counter': 11, 'group_counter': 166, 'group_order': 324, 'label': '3F', 'order': 3, 'powers': [11, 1], 'representative': 216, 'size': 2}
  • id: 103862970
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 166, 'group_order': 324, 'label': '3G1', 'order': 3, 'powers': [13, 1], 'representative': 40, 'size': 2}
  • id: 103862971
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 166, 'group_order': 324, 'label': '3G-1', 'order': 3, 'powers': [12, 1], 'representative': 74, 'size': 2}
  • id: 103862972
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 14, 'group_counter': 166, 'group_order': 324, 'label': '3H1', 'order': 3, 'powers': [15, 1], 'representative': 52, 'size': 2}
  • id: 103862973
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 15, 'group_counter': 166, 'group_order': 324, 'label': '3H-1', 'order': 3, 'powers': [14, 1], 'representative': 80, 'size': 2}
  • id: 103862974
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 16, 'group_counter': 166, 'group_order': 324, 'label': '3I1', 'order': 3, 'powers': [17, 1], 'representative': 46, 'size': 2}
  • id: 103862975
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 17, 'group_counter': 166, 'group_order': 324, 'label': '3I-1', 'order': 3, 'powers': [16, 1], 'representative': 86, 'size': 2}
  • id: 103862976
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 18, 'group_counter': 166, 'group_order': 324, 'label': '3J1', 'order': 3, 'powers': [19, 1], 'representative': 16, 'size': 2}
  • id: 103862977
    {'aut_label': '3G1', 'centralizer': '2.a1', 'counter': 19, 'group_counter': 166, 'group_order': 324, 'label': '3J-1', 'order': 3, 'powers': [18, 1], 'representative': 8, 'size': 2}
  • id: 103862979
    {'aut_label': '3K1', 'centralizer': '2.b1', 'counter': 20, 'group_counter': 166, 'group_order': 324, 'label': '3K1', 'order': 3, 'powers': [21, 1], 'representative': 218, 'size': 2}
  • id: 103862980
    {'aut_label': '3K1', 'centralizer': '2.b1', 'counter': 21, 'group_counter': 166, 'group_order': 324, 'label': '3K-1', 'order': 3, 'powers': [20, 1], 'representative': 112, 'size': 2}
  • id: 103862981
    {'aut_label': '3L', 'centralizer': '4.a1', 'counter': 22, 'group_counter': 166, 'group_order': 324, 'label': '3L', 'order': 3, 'powers': [22, 1], 'representative': 144, 'size': 4}
  • id: 103862982
    {'aut_label': '3L', 'centralizer': '4.a1', 'counter': 23, 'group_counter': 166, 'group_order': 324, 'label': '3M', 'order': 3, 'powers': [23, 1], 'representative': 114, 'size': 4}
  • id: 103862983
    {'aut_label': '3L', 'centralizer': '4.a1', 'counter': 24, 'group_counter': 166, 'group_order': 324, 'label': '3N', 'order': 3, 'powers': [24, 1], 'representative': 150, 'size': 4}
  • id: 103862984
    {'aut_label': '3L', 'centralizer': '4.a1', 'counter': 25, 'group_counter': 166, 'group_order': 324, 'label': '3O', 'order': 3, 'powers': [25, 1], 'representative': 186, 'size': 4}
  • id: 103862985
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 26, 'group_counter': 166, 'group_order': 324, 'label': '3P1', 'order': 3, 'powers': [27, 1], 'representative': 146, 'size': 4}
  • id: 103862986
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 27, 'group_counter': 166, 'group_order': 324, 'label': '3P-1', 'order': 3, 'powers': [26, 1], 'representative': 148, 'size': 4}
  • id: 103862987
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 28, 'group_counter': 166, 'group_order': 324, 'label': '3Q1', 'order': 3, 'powers': [29, 1], 'representative': 116, 'size': 4}
  • id: 103862988
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 29, 'group_counter': 166, 'group_order': 324, 'label': '3Q-1', 'order': 3, 'powers': [28, 1], 'representative': 118, 'size': 4}
  • id: 103862990
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 30, 'group_counter': 166, 'group_order': 324, 'label': '3R1', 'order': 3, 'powers': [31, 1], 'representative': 152, 'size': 4}
  • id: 103862991
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 31, 'group_counter': 166, 'group_order': 324, 'label': '3R-1', 'order': 3, 'powers': [30, 1], 'representative': 154, 'size': 4}
  • id: 103862992
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 32, 'group_counter': 166, 'group_order': 324, 'label': '3S1', 'order': 3, 'powers': [33, 1], 'representative': 188, 'size': 4}
  • id: 103862993
    {'aut_label': '3P1', 'centralizer': '4.a1', 'counter': 33, 'group_counter': 166, 'group_order': 324, 'label': '3S-1', 'order': 3, 'powers': [32, 1], 'representative': 190, 'size': 4}
  • id: 103862994
    {'aut_label': '6A1', 'centralizer': '3.b1', 'counter': 34, 'group_counter': 166, 'group_order': 324, 'label': '6A1', 'order': 6, 'powers': [5, 2], 'representative': 56, 'size': 3}
  • id: 103862995
    {'aut_label': '6A1', 'centralizer': '3.b1', 'counter': 35, 'group_counter': 166, 'group_order': 324, 'label': '6A-1', 'order': 6, 'powers': [6, 2], 'representative': 58, 'size': 3}
  • id: 103862996
    {'aut_label': '6B', 'centralizer': '6.f1', 'counter': 36, 'group_counter': 166, 'group_order': 324, 'label': '6B', 'order': 6, 'powers': [7, 2], 'representative': 18, 'size': 6}
  • id: 103862997
    {'aut_label': '6B', 'centralizer': '6.f1', 'counter': 37, 'group_counter': 166, 'group_order': 324, 'label': '6C', 'order': 6, 'powers': [8, 2], 'representative': 24, 'size': 6}
  • id: 103862998
    {'aut_label': '6B', 'centralizer': '6.f1', 'counter': 38, 'group_counter': 166, 'group_order': 324, 'label': '6D', 'order': 6, 'powers': [9, 2], 'representative': 30, 'size': 6}
  • id: 103862999
    {'aut_label': '6B', 'centralizer': '6.f1', 'counter': 39, 'group_counter': 166, 'group_order': 324, 'label': '6E', 'order': 6, 'powers': [10, 2], 'representative': 60, 'size': 6}
  • id: 103863001
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 40, 'group_counter': 166, 'group_order': 324, 'label': '6F1', 'order': 6, 'powers': [12, 2], 'representative': 20, 'size': 6}
  • id: 103863002
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 41, 'group_counter': 166, 'group_order': 324, 'label': '6F-1', 'order': 6, 'powers': [13, 2], 'representative': 22, 'size': 6}
  • id: 103863003
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 42, 'group_counter': 166, 'group_order': 324, 'label': '6G1', 'order': 6, 'powers': [14, 2], 'representative': 26, 'size': 6}
  • id: 103863004
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 43, 'group_counter': 166, 'group_order': 324, 'label': '6G-1', 'order': 6, 'powers': [15, 2], 'representative': 28, 'size': 6}
  • id: 103863005
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 44, 'group_counter': 166, 'group_order': 324, 'label': '6H1', 'order': 6, 'powers': [16, 2], 'representative': 32, 'size': 6}
  • id: 103863006
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 45, 'group_counter': 166, 'group_order': 324, 'label': '6H-1', 'order': 6, 'powers': [17, 2], 'representative': 34, 'size': 6}
  • id: 103863007
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 46, 'group_counter': 166, 'group_order': 324, 'label': '6I1', 'order': 6, 'powers': [18, 2], 'representative': 62, 'size': 6}
  • id: 103863008
    {'aut_label': '6F1', 'centralizer': '6.f1', 'counter': 47, 'group_counter': 166, 'group_order': 324, 'label': '6I-1', 'order': 6, 'powers': [19, 2], 'representative': 64, 'size': 6}
  • id: 103863009
    {'aut_label': '6J1', 'centralizer': '9.c1', 'counter': 48, 'group_counter': 166, 'group_order': 324, 'label': '6J1', 'order': 6, 'powers': [6, 3], 'representative': 1, 'size': 9}
  • id: 103863010
    {'aut_label': '6J1', 'centralizer': '9.c1', 'counter': 49, 'group_counter': 166, 'group_order': 324, 'label': '6J-1', 'order': 6, 'powers': [5, 3], 'representative': 5, 'size': 9}
  • id: 103863012
    {'aut_label': '6K', 'centralizer': '18.h1', 'counter': 50, 'group_counter': 166, 'group_order': 324, 'label': '6K', 'order': 6, 'powers': [11, 3], 'representative': 111, 'size': 18}
  • id: 103863013
    {'aut_label': '6L1', 'centralizer': '18.h1', 'counter': 51, 'group_counter': 166, 'group_order': 324, 'label': '6L1', 'order': 6, 'powers': [20, 3], 'representative': 109, 'size': 18}
  • id: 103863014
    {'aut_label': '6L1', 'centralizer': '18.h1', 'counter': 52, 'group_counter': 166, 'group_order': 324, 'label': '6L-1', 'order': 6, 'powers': [21, 3], 'representative': 113, 'size': 18}
  • id: 103863015
    {'aut_label': '6M1', 'centralizer': '27.a1', 'counter': 53, 'group_counter': 166, 'group_order': 324, 'label': '6M1', 'order': 6, 'powers': [5, 4], 'representative': 137, 'size': 27}
  • id: 103863016
    {'aut_label': '6M1', 'centralizer': '27.a1', 'counter': 54, 'group_counter': 166, 'group_order': 324, 'label': '6M-1', 'order': 6, 'powers': [6, 4], 'representative': 133, 'size': 27}
• 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: 2508325
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1a', '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], 'schur_index': 1}
  • id: 2508336
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1b', '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], 'schur_index': 1}
  • id: 2508347
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1c', '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], 'schur_index': 1}
  • id: 2508355
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1d', '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], 'schur_index': 1}
  • id: 2508356
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 2508357
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, -2, 1, 1, -1, -1], 'schur_index': 1}
  • id: 2508358
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, -1, -1, 2, -1, -1, 1, 1], 'schur_index': 1}
  • id: 2508359
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
  • id: 2508360
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, 2, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 2508326
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508327
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, -1, 2, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508328
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508329
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2e', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508330
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -2, -2, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508331
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, -1, 2, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508332
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -2, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508333
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508334
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 0, 2, 2, 2, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 2508335
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2k', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 4, 0, -2, -2, -2, 4, 1, -2, -2, -2, 1, 4, -2, 4, -2, -2, -2, 4, -2, -2, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, 0, 0], 'schur_index': 1}
  • id: 2508337
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2l', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -2, 4, 4, -2, 1, 1, -2, -2, 1, 4, 1, 1, -2, 1, 1, -2, -2, 1, 1, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, -2, 1, 4, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508338
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2m', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -2, -2, 1, -2, -2, -2, -2, 1, -2, -2, 4, -2, 1, 1, 1, 4, 1, -2, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508339
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2n', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -2, -2, 1, -2, -2, 1, 1, -2, -2, -2, 4, 4, 1, -2, 1, -2, 1, -2, -2, -2, -2, 1, 1, -2, 4, 1, 1, 1, 1, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, 4, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508340
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2o', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -2, -2, 1, 4, -2, 1, 1, 1, -2, -2, 4, -2, -2, 1, 1, -2, -2, -2, 1, 1, -2, 1, 1, 4, -2, -2, -2, 1, 1, -2, -2, 4, 1, 1, 1, 1, -2, 1, -2, -2, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508341
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2p', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -2, 4, 4, -2, 1, 1, -2, -2, 1, 4, 1, 1, -2, 1, 1, -2, -2, 1, 1, -2, -2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -4, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508342
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2q', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, 1, -2, -2, -2, -2, 1, -2, -2, 4, -2, 1, 1, 1, 4, 1, -2, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508343
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2r', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, 1, -2, -2, 1, 1, -2, -2, -2, 4, 4, 1, -2, 1, -2, 1, -2, -2, -2, -2, 1, 1, -2, 4, 1, 1, 1, 1, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, -4, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508344
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2s', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, 1, 4, -2, 1, 1, 1, -2, -2, 4, -2, -2, 1, 1, -2, -2, -2, 1, 1, -2, 1, 1, 4, -2, -2, -2, 1, 1, 2, 2, -4, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 2508345
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.2t', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 0, -4, 0, -2, -2, -2, 4, 1, -2, -2, -2, 1, 4, -2, 4, -2, -2, -2, 4, -2, -2, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 0, 0], 'schur_index': 1}
  • id: 2508346
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, -2, 4, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, 1, 1, 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: 2508348
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 4, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 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: 2508349
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, -2, 4, -2, -2, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, 4, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 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: 2508350
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4d', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, -2, 4, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 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: 2508351
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4e', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, -4, -4, 2, 2, 2, 2, 2, 8, -4, -4, 2, 2, -4, -4, 2, -4, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, 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: 2508352
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4f', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, 2, -4, 2, -4, -4, 2, 2, -4, -4, -4, 2, 2, 2, 8, 2, 2, -1, -1, -4, 2, 2, 2, 2, -1, -1, -1, -1, 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: 2508353
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4g', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, 2, -4, 2, 2, 2, -4, 2, -4, -4, 8, 2, -4, 2, -4, 2, 2, 2, 2, 2, -1, -1, 2, -4, -1, -1, -1, -1, 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: 2508354
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '324.166', 'group_order': 324, 'image': None, 'label': '324.166.4h', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 0, 0, 0, -4, -4, 2, 8, 2, 2, 2, 2, 2, -4, -4, -4, -4, 2, 2, -4, -4, 2, -1, -1, 2, -1, -1, -4, 2, 2, 2, -1, -1, 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: 3269065
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 324, 'label': '324.166.1a', '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]]]}
  • id: 3269076
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 162, 'label': '324.166.1b', '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]]]}
  • id: 3269087
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 162, 'label': '324.166.1c', '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]]]}
  • id: 3269098
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 162, 'label': '324.166.1d', '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]]]}
  • id: 3269109
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 108, 'label': '324.166.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 3269115
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 108, 'label': '324.166.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 3269116
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 54, 'label': '324.166.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 3269117
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 54, 'label': '324.166.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 3269118
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 54, 'label': '324.166.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 3269066
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 54, 'label': '324.166.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 3269067
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 54, 'label': '324.166.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 3269068
    {'center': '1.a1', 'center_index': 1, 'center_order': 324, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 54, 'label': '324.166.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 3269069
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1', 'kernel_order': 54, 'label': '324.166.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269070
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 54, 'label': '324.166.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269071
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 54, 'label': '324.166.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269072
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 54, 'label': '324.166.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269073
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 54, 'label': '324.166.2e', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269074
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 27, 'label': '324.166.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269075
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 27, 'label': '324.166.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269077
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 27, 'label': '324.166.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269078
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 27, 'label': '324.166.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269079
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 27, 'label': '324.166.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269080
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 18, 'label': '324.166.2k1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -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]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 3269081
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 18, 'label': '324.166.2k2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 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]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3269082
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2l1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269083
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2l2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269084
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2m1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269085
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2m2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269086
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2n1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269088
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2n2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269089
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2o1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269090
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 18, 'label': '324.166.2o2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269091
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2p1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269092
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2p2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269093
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2q1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269094
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2q2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269095
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 37, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2r1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269096
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2r2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269097
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2s1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269099
    {'center': '6.a1', 'center_index': 6, 'center_order': 54, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 9, 'label': '324.166.2s2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 3269100
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1', 'kernel_order': 9, 'label': '324.166.2t1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -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]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 3269101
    {'center': '6.c1', 'center_index': 6, 'center_order': 54, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.d1', 'kernel_order': 9, 'label': '324.166.2t2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 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]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 3269102
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 9, 'label': '324.166.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]]]}
  • id: 3269103
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 9, 'label': '324.166.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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]]]}
  • id: 3269104
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 9, 'label': '324.166.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[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]]]}
  • id: 3269105
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 9, 'label': '324.166.4d', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 3269106
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4e1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[4, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -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]]]}
  • id: 3269107
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 48, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4e2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 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]]]}
  • id: 3269108
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 49, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4f1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[4, 0]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -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]]]}
  • id: 3269110
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 50, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4f2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[4, 0]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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]]]}
  • id: 3269111
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 51, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4g1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[4, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -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]]]}
  • id: 3269112
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 52, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4g2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[4, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 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]]]}
  • id: 3269113
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 53, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4h1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 1]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[4, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -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]]]}
  • id: 3269114
    {'center': '36.a1', 'center_index': 36, 'center_order': 9, 'counter': 54, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '324.166', 'group_counter': 166, 'group_order': 324, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1', 'kernel_order': 3, 'label': '324.166.4h2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, -1]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[4, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 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]]]}
• 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: 51860075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 324, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '324.166.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 162, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 162, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 51860108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 162, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': True, 'core_order': 108, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '324.166.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.3.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860152
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '324.166.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
  • id: 51860161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 54, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 54, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, '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': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 18, 'characteristic': True, 'core_order': 54, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '324.166.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 54, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 54, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, '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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 18, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860093
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 27, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, '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': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860096
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860099
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 51860100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 54, 'characteristic': True, 'core_order': 18, 'counter': 32, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '324.166.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 51860101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 18, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, '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': ['C3'], 'split': True, '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: 51860102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 18, 'characteristic': True, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '324.166.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860104
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860105
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 6, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860118
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860122
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860124
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1', 'outer_equivalence': True, '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': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '324.166.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.d1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860126
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860129
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860132
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 51860135
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 54, 'characteristic': True, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '324.166.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860136
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860137
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860138
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860139
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860140
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860142
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860143
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860144
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 51860145
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860146
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860147
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324.166.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '324.166.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': 2}
  • id: 51860149
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 77, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '324.166.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.39', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860150
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.166.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860151
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 3, 'counter': 79, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '324.166.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.43', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 51860153
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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: 51860154
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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: 51860155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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: 51860156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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: 51860157
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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: 51860158
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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: 51860159
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '324.166.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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: 51860160
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '324.166', 'ambient_counter': 166, 'ambient_order': 324, 'ambient_tex': 'C_3^2:S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 1, 'counter': 87, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '324.166.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '324.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 51860154
    {'ambient': '324.166', 'aut_centralizer_order': 1296, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.g1', '36.k1', '54.g1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8900, -1, 5132, -1], 'generators': [110], 'label': '324.166.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '108.e1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860091
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '3.c1'], 'contains': ['18.b1', '18.j1', '18.o1', '27.b1', '27.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [4017, -1, 7494, -1], 'generators': [3, 54, 6, 108], 'label': '324.166.9.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '9.d1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51860075
    {'ambient': '324.166', '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': '108.a1', 'complements': ['324.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '3.b1', '3.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4145, 4240, 4417, 5255], 'generators': [3, 108, 36, 54, 2, 6], 'label': '324.166.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 51860076
    {'ambient': '324.166', 'aut_centralizer_order': 18, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.851', 'aut_weyl_index': 18, 'centralizer': '12.b1', 'complements': ['54.e1', '54.g1', '54.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.c1', '18.b1', '18.f1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [898, 2650, 1839, 2737], 'generators': [54, 6, 36, 108], 'label': '324.166.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.c1', '18.b1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51860077
    {'ambient': '324.166', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 6, 'centralizer': '18.a1', 'complements': ['54.a1', '54.k1', '54.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.b1', '18.c1', '18.i1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2665, 9188, 2942, 9100], 'generators': [3, 2, 6, 36], 'label': '324.166.6.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.b1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '108.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860078
    {'ambient': '324.166', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 6, 'centralizer': '36.b1', 'complements': ['54.b1', '54.d1', '54.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.c1', '18.c1', '18.j1'], 'core': '6.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1451, 7233, 3503, 7080], 'generators': [3, 108, 6, 36], 'label': '324.166.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.c1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 51860079
    {'ambient': '324.166', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 2, 'centralizer': '108.a1', 'complements': ['54.b1', '54.d1', '54.e1', '54.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.c1', '18.o1', '18.p1', '18.q1'], 'core': '6.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [2275, 4240, 5622, 5377], 'generators': [21, 6, 36, 108], 'label': '324.166.6.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': ['2.c1', '3.a1'], 'normal_contains': ['12.c1'], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 51860080
    {'ambient': '324.166', 'aut_centralizer_order': 18, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.189', 'aut_weyl_index': 54, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.b1', '18.d1', '18.e1', '18.f1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1900, -1, 1309, -1], 'generators': [54, 2, 6, 36], 'label': '324.166.6.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.f1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860081
    {'ambient': '324.166', 'aut_centralizer_order': 9, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 72, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['12.e1', '18.b1', '18.e1', '18.g1'], 'core': '18.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [3218, -1, 779, -1], 'generators': [54, 38, 6, 108], 'label': '324.166.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860082
    {'ambient': '324.166', 'aut_centralizer_order': 18, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.c1'], 'contains': ['12.a1', '18.h1', '18.i1', '18.j1', '18.k1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7069, -1, 6637, -1], 'generators': [3, 2, 108, 6], 'label': '324.166.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.h1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51860083
    {'ambient': '324.166', 'aut_centralizer_order': 3, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 6, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['12.g1', '18.c1', '18.k1'], 'core': '18.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5515, -1, 2382, -1], 'generators': [3, 218, 6, 36], 'label': '324.166.6.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '6.i1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860084
    {'ambient': '324.166', 'aut_centralizer_order': 6, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 72, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.c1'], 'contains': ['12.a1', '18.l1', '18.m1', '18.n1', '18.o1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7515, -1, 7913, -1], 'generators': [21, 2, 6, 108], 'label': '324.166.6.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.j1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51860085
    {'ambient': '324.166', 'aut_centralizer_order': 1, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '216.102', 'aut_weyl_index': 24, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1'], 'contains': ['12.d1', '18.l1', '18.n1', '18.p1'], 'core': '36.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6621, -1, 6094, -1], 'generators': [21, 2, 6, 144], 'label': '324.166.6.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '6.k1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860086
    {'ambient': '324.166', 'aut_centralizer_order': 9, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 9, 'centralizer': '12.b1', 'complements': ['162.b1', '162.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1', '6.b1', '6.f1', '6.g1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3723, 2144, 1576, 2092], 'generators': [54, 108, 2, 6, 36], 'label': '324.166.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51860087
    {'ambient': '324.166', 'aut_centralizer_order': 2, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 6, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.b1', '18.l1', '18.q1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3770, -1, 5149, -1], 'generators': [21, 2, 6, 36], 'label': '324.166.6.l1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.l1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860088
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.b1', '3.c1'], 'contains': ['18.d1', '18.i1', '18.l1', '27.a1', '27.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4532, -1, 7130, -1], 'generators': [3, 54, 2, 6], 'label': '324.166.9.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860089
    {'ambient': '324.166', 'aut_centralizer_order': 4, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.734', 'aut_weyl_index': 12, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.c1', '18.f1', '18.q1', '27.b1'], 'core': '18.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [614, -1, 4589, -1], 'generators': [3, 54, 6, 36], 'label': '324.166.9.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.b1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860090
    {'ambient': '324.166', 'aut_centralizer_order': 48, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1'], 'contains': ['18.a1', '18.h1', '18.m1', '27.a1', '27.c1'], 'core': '18.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8821, -1, 8871, -1], 'generators': [3, 54, 2, 108], 'label': '324.166.9.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '9.c1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860092
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 648, 'centralizer': '4.a1', 'complements': ['27.b1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.a1', '6.h1', '6.j1'], 'contains': ['36.a1', '36.b1', '36.c1', '36.e1', '36.g1', '36.j1', '36.k1'], 'core': '12.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7449, 4028, 3455, 3917], 'generators': [2, 6, 108], 'label': '324.166.12.a1', 'mobius_quo': -1, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['36.a1', '36.b1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '108.39', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51860093
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.189', 'aut_weyl_index': 54, 'centralizer': '2.a1', 'complements': ['27.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.c1', '6.f1', '6.l1'], 'contains': ['36.a1', '36.d1', '36.f1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2945, 6184, 1674, 5912], 'generators': [2, 6, 36], 'label': '324.166.12.b1', 'mobius_quo': -3, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.c1'], 'normal_contains': ['36.a1', '36.d1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860094
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.189', 'aut_weyl_index': 54, 'centralizer': '4.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1', '6.d1', '6.e1'], 'contains': ['36.c1', '36.d1', '36.h1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1747, 5148, 2409, 4915], 'generators': [6, 36, 108], 'label': '324.166.12.c1', 'mobius_quo': -3, 'mobius_sub': -2, 'normal_closure': '12.c1', 'normal_contained_in': ['4.a1', '6.b1', '6.d1', '6.e1'], 'normal_contains': ['36.c1', '36.d1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '324.166', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51860095
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.k1'], 'contains': ['36.a1', '36.e1', '36.h1', '36.i1', '36.l1'], 'core': '36.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6138, -1, 938, -1], 'generators': [2, 6, 144], 'label': '324.166.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '12.d1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860096
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.g1'], 'contains': ['36.c1', '36.f1', '36.i1', '36.j1', '36.l1'], 'core': '36.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [3595, -1, 108, -1], 'generators': [38, 6, 108], 'label': '324.166.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.e1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860097
    {'ambient': '324.166', 'aut_centralizer_order': 3, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47845', 'aut_weyl_index': 3, 'centralizer': '36.b1', 'complements': ['162.a1', '162.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.c1', '6.d1', '6.h1', '6.i1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4384, 7150, 3223, 8479], 'generators': [3, 36, 2, 108, 6], 'label': '324.166.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.c1', '6.d1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 51860098
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['36.f1', '36.g1', '36.h1', '36.i1', '36.k1', '36.l1'], 'core': '108.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [5470, -1, 385, -1], 'generators': [218, 6, 144], 'label': '324.166.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.f1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860099
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.189', 'aut_weyl_index': 54, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.i1'], 'contains': ['36.d1', '36.g1', '36.i1'], 'core': '36.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [5804, -1, 661, -1], 'generators': [110, 6, 36], 'label': '324.166.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860100
    {'ambient': '324.166', 'aut_centralizer_order': 432, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '6.c1', 'complements': ['18.c1', '18.q1', '18.p1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.c1'], 'contains': ['36.b1', '54.a1', '54.b1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9079, 966, 8183, 949], 'generators': [54, 2, 108], 'label': '324.166.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['36.b1', '54.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '108.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860101
    {'ambient': '324.166', 'aut_centralizer_order': 108, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '12.b1', 'complements': ['18.i1', '18.k1', '18.l1', '18.n1'], 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '6.b1', '6.g1', '9.d1'], 'contains': ['36.c1', '54.a1', '54.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1959, 2556, 4282, 2591], 'generators': [54, 6, 108], 'label': '324.166.18.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1', '6.b1'], 'normal_contains': ['36.c1', '54.a1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51860102
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 12, 'centralizer': '18.a1', 'complements': ['18.a1', '18.g1', '18.m1', '18.n1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.d1', '6.i1', '9.b1'], 'contains': ['36.d1', '54.h1'], 'core': '18.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [586, 7233, 3162, 7080], 'generators': [3, 6, 36], 'label': '324.166.18.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1', 'normal_contained_in': ['6.c1', '6.d1'], 'normal_contains': ['36.d1'], 'normalizer': '1.a1', 'old_label': '18.c1', 'projective_image': '324.166', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860103
    {'ambient': '324.166', 'aut_centralizer_order': 108, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '6.f1', '9.a1'], 'contains': ['36.a1', '54.b1', '54.c1', '54.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4068, -1, 3823, -1], 'generators': [54, 2, 6], 'label': '324.166.18.d1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.d1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860104
    {'ambient': '324.166', 'aut_centralizer_order': 18, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.f1', '6.g1'], 'contains': ['36.f1', '54.c1', '54.d1'], 'core': '108.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1370, -1, 1306, -1], 'generators': [54, 38, 6], 'label': '324.166.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '18.e1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860105
    {'ambient': '324.166', 'aut_centralizer_order': 36, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.29', 'aut_weyl_index': 108, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.f1', '9.b1'], 'contains': ['36.d1', '54.c1'], 'core': '36.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [164, -1, 2777, -1], 'generators': [54, 6, 36], 'label': '324.166.18.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.f1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860106
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '6.g1'], 'contains': ['36.j1', '54.a1', '54.d1'], 'core': '54.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4551, -1, 2041, -1], 'generators': [54, 8, 108], 'label': '324.166.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '18.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860107
    {'ambient': '324.166', 'aut_centralizer_order': 144, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '18.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.c1'], 'contains': ['36.b1', '54.e1', '54.f1', '54.g1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9458, -1, 8642, -1], 'generators': [3, 2, 108], 'label': '324.166.18.h1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.h1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860108
    {'ambient': '324.166', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 1, 'centralizer': '108.a1', 'complements': ['162.a1', '162.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.e1', '6.j1', '6.k1', '6.l1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5220, 4900, 5510, 4185], 'generators': [21, 108, 2, 6, 36], 'label': '324.166.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.e1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 51860109
    {'ambient': '324.166', 'aut_centralizer_order': 36, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '6.h1', '9.a1'], 'contains': ['36.a1', '54.e1', '54.h1'], 'core': '36.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5246, -1, 5807, -1], 'generators': [3, 2, 6], 'label': '324.166.18.i1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.i1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860110
    {'ambient': '324.166', 'aut_centralizer_order': 36, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '6.h1', '9.d1'], 'contains': ['36.c1', '54.f1', '54.h1'], 'core': '36.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [2653, -1, 6263, -1], 'generators': [3, 108, 6], 'label': '324.166.18.j1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.j1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 51860111
    {'ambient': '324.166', 'aut_centralizer_order': 18, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.h1', '6.i1'], 'contains': ['36.g1', '54.g1', '54.h1'], 'core': '108.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7691, -1, 4738, -1], 'generators': [3, 218, 6], 'label': '324.166.18.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '18.k1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860112
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.j1', '6.k1', '6.l1', '9.a1'], 'contains': ['36.a1', '54.i1', '54.j1'], 'core': '36.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6996, -1, 6965, -1], 'generators': [21, 2, 6], 'label': '324.166.18.l1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.l1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860113
    {'ambient': '324.166', 'aut_centralizer_order': 48, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.c1'], 'contains': ['36.b1', '54.i1', '54.k1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9836, -1, 9802, -1], 'generators': [21, 2, 108], 'label': '324.166.18.m1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.m1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860114
    {'ambient': '324.166', 'aut_centralizer_order': 6, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.j1', '6.k1'], 'contains': ['36.e1', '54.i1', '54.l1'], 'core': '108.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8490, -1, 7420, -1], 'generators': [21, 2, 114], 'label': '324.166.18.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '18.n1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860115
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 144, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1', '6.j1', '9.d1'], 'contains': ['36.c1', '54.j1', '54.k1', '54.l1'], 'core': '36.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [3181, -1, 7802, -1], 'generators': [21, 6, 108], 'label': '324.166.18.o1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.o1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51860116
    {'ambient': '324.166', 'aut_centralizer_order': 2, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '108.17', 'aut_weyl_index': 48, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.e1', '6.k1'], 'contains': ['36.h1', '54.j1', '54.l1'], 'core': '108.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [3435, -1, 5426, -1], 'generators': [21, 6, 144], 'label': '324.166.18.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '18.p1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860117
    {'ambient': '324.166', 'aut_centralizer_order': 4, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.734', 'aut_weyl_index': 12, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.l1', '9.b1'], 'contains': ['36.d1', '54.j1'], 'core': '36.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [948, -1, 5119, -1], 'generators': [21, 6, 36], 'label': '324.166.18.q1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.q1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860118
    {'ambient': '324.166', 'aut_centralizer_order': 96, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.c1'], 'contains': ['54.b1', '54.e1', '54.i1', '81.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8589, -1, 9101, -1], 'generators': [3, 54, 2], 'label': '324.166.27.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860119
    {'ambient': '324.166', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 2, 'centralizer': '108.a1', 'complements': ['108.a1', '108.e1', '108.d1', '108.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.d1', '6.e1', '9.b1', '9.d1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 3251, 4697, 6338], 'generators': [3, 108, 54, 6, 36], 'label': '324.166.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.b1', '6.d1', '6.e1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '324.166', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 51860120
    {'ambient': '324.166', 'aut_centralizer_order': 24, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.a1', '9.b1', '9.d1'], 'contains': ['54.c1', '54.h1', '54.j1', '81.a1'], 'core': '108.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [2609, -1, 6614, -1], 'generators': [3, 54, 6], 'label': '324.166.27.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.b1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860121
    {'ambient': '324.166', 'aut_centralizer_order': 96, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1', '9.d1'], 'contains': ['54.a1', '54.f1', '54.k1', '81.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6821, -1, 9452, -1], 'generators': [3, 54, 108], 'label': '324.166.27.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '27.c1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860122
    {'ambient': '324.166', 'aut_centralizer_order': 324, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '2.a1', 'complements': ['9.d1'], 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.b1', '12.d1', '18.d1', '18.i1', '18.l1'], 'contains': ['108.a1', '108.b1', '108.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5613, 5266, 3749, 4915], 'generators': [2, 6], 'label': '324.166.36.a1', 'mobius_quo': 1, 'mobius_sub': 18, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1'], 'normal_contains': ['108.a1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860123
    {'ambient': '324.166', 'aut_centralizer_order': 1296, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '2.b1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.a1', '18.h1', '18.m1'], 'contains': ['108.a1', '108.c1', '108.e1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9313, 3075, 6121, 2920], 'generators': [2, 108], 'label': '324.166.36.b1', 'mobius_quo': 1, 'mobius_sub': 54, 'normal_closure': '36.b1', 'normal_contained_in': ['12.a1', '18.a1'], 'normal_contains': ['108.a1', '108.c1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860124
    {'ambient': '324.166', 'aut_centralizer_order': 324, 'aut_label': '36.c1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1', 'complements': ['9.a1'], 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.c1', '12.e1', '18.b1', '18.j1', '18.o1'], 'contains': ['108.b1', '108.c1', '108.f1'], 'core': '36.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2245, 4041, 4268, 3917], 'generators': [6, 108], 'label': '324.166.36.c1', 'mobius_quo': 1, 'mobius_sub': 6, 'normal_closure': '36.c1', 'normal_contained_in': ['12.a1', '12.c1', '18.b1'], 'normal_contains': ['108.b1', '108.c1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '324.166', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51860125
    {'ambient': '324.166', 'aut_centralizer_order': 108, 'aut_label': '36.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 108, 'centralizer': '2.a1', 'complements': ['9.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.c1', '12.g1', '18.c1', '18.f1', '18.q1'], 'contains': ['108.b1'], 'core': '36.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [917, 6244, 3196, 5912], 'generators': [6, 36], 'label': '324.166.36.d1', 'mobius_quo': 3, 'mobius_sub': 6, 'normal_closure': '36.d1', 'normal_contained_in': ['12.b1', '12.c1', '18.c1'], 'normal_contains': ['108.b1'], 'normalizer': '1.a1', 'old_label': '36.d1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860126
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.d1', '18.n1'], 'contains': ['108.a1', '108.f1', '108.g1'], 'core': '108.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8135, -1, 3472, -1], 'generators': [2, 114], 'label': '324.166.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '36.e1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860127
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.e1', '12.f1', '18.e1'], 'contains': ['108.b1', '108.d1'], 'core': '108.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [1973, -1, 1421, -1], 'generators': [38, 6], 'label': '324.166.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.f1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860128
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.f1', '12.g1', '18.k1'], 'contains': ['108.b1', '108.e1', '108.g1'], 'core': '108.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [7185, -1, 2399, -1], 'generators': [110, 6], 'label': '324.166.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '36.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860129
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1', '12.d1', '12.f1', '18.p1'], 'contains': ['108.b1', '108.f1'], 'core': '108.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4328, -1, 2676, -1], 'generators': [6, 144], 'label': '324.166.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '36.h1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860130
    {'ambient': '324.166', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 6, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.c1', '6.f1', '6.l1', '9.a1', '9.b1'], 'core': '6.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [2998, -1, 4137, -1], 'generators': [3, 36, 54, 2, 6], 'label': '324.166.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 51860131
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 432, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '12.e1', '12.f1', '12.g1'], 'contains': ['108.b1', '108.g1'], 'core': '108.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [6052, -1, 1100, -1], 'generators': [146, 6], 'label': '324.166.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.i1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860132
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.e1', '18.g1'], 'contains': ['108.c1', '108.d1', '108.g1'], 'core': '108.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4585, -1, 1846, -1], 'generators': [8, 108], 'label': '324.166.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.j1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860133
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '12.f1'], 'contains': ['108.d1', '108.e1', '108.f1', '108.g1'], 'core': '324.a1', 'coset_action_label': '36T522', 'count': 16, 'diagramx': [7908, -1, 2122, -1], 'generators': [8, 114], 'label': '324.166.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.k1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860134
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1296, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.d1', '12.e1', '12.f1'], 'contains': ['108.d1', '108.f1', '108.g1'], 'core': '324.a1', 'coset_action_label': '36T531', 'count': 48, 'diagramx': [4812, -1, 823, -1], 'generators': [38, 114], 'label': '324.166.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.l1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860135
    {'ambient': '324.166', 'aut_centralizer_order': 864, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '6.c1', 'complements': ['6.c1', '6.i1', '6.l1', '6.k1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.g1', '27.c1'], 'contains': ['108.c1', '162.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5970, 2368, 5375, 1983], 'generators': [54, 108], 'label': '324.166.54.a1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1', '18.b1'], 'normal_contains': ['108.c1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '324.166', 'quotient_action_image': '1.1', 'quotient_action_kernel': '54.13', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860136
    {'ambient': '324.166', 'aut_centralizer_order': 864, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.d1', '27.a1'], 'contains': ['108.a1', '162.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7865, -1, 5861, -1], 'generators': [54, 2], 'label': '324.166.54.b1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.b1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860137
    {'ambient': '324.166', 'aut_centralizer_order': 216, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.b1', '18.d1', '18.e1', '18.f1', '27.b1'], 'contains': ['108.b1', '162.a1'], 'core': '108.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2412, -1, 4009, -1], 'generators': [54, 6], 'label': '324.166.54.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.c1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860138
    {'ambient': '324.166', 'aut_centralizer_order': 108, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.d1', '18.e1', '18.g1'], 'contains': ['108.d1', '162.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3748, -1, 2936, -1], 'generators': [54, 8], 'label': '324.166.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '54.d1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860139
    {'ambient': '324.166', 'aut_centralizer_order': 288, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '9.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.i1', '27.a1'], 'contains': ['108.a1', '162.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8066, -1, 6624, -1], 'generators': [3, 2], 'label': '324.166.54.e1', 'mobius_quo': None, 'mobius_sub': 9, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.e1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860140
    {'ambient': '324.166', 'aut_centralizer_order': 288, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.j1', '27.c1'], 'contains': ['108.c1', '162.b1'], 'core': '108.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6588, -1, 6867, -1], 'generators': [3, 108], 'label': '324.166.54.f1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.f1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860141
    {'ambient': '324.166', 'aut_centralizer_order': 6, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 72, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.h1', '6.j1', '9.a1', '9.c1', '9.d1'], 'core': '6.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6174, -1, 7130, -1], 'generators': [3, 108, 54, 2, 6], 'label': '324.166.3.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '3.c1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 51860142
    {'ambient': '324.166', 'aut_centralizer_order': 144, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '18.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.k1'], 'contains': ['108.e1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9168, -1, 6381, -1], 'generators': [3, 218], 'label': '324.166.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '54.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860143
    {'ambient': '324.166', 'aut_centralizer_order': 72, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '18.i1', '18.j1', '18.k1', '27.b1'], 'contains': ['108.b1', '162.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [3348, -1, 4889, -1], 'generators': [3, 6], 'label': '324.166.54.h1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '54.h1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860144
    {'ambient': '324.166', 'aut_centralizer_order': 96, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '18.m1', '18.n1', '27.a1'], 'contains': ['108.a1', '162.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8735, -1, 7410, -1], 'generators': [21, 2], 'label': '324.166.54.i1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.i1', 'projective_image': '108.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860145
    {'ambient': '324.166', 'aut_centralizer_order': 24, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.l1', '18.o1', '18.p1', '18.q1', '27.b1'], 'contains': ['108.b1', '162.c1'], 'core': '108.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [3548, -1, 5132, -1], 'generators': [21, 6], 'label': '324.166.54.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.j1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860146
    {'ambient': '324.166', 'aut_centralizer_order': 96, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '54.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '18.o1', '27.c1'], 'contains': ['108.c1', '162.c1'], 'core': '108.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6177, -1, 7802, -1], 'generators': [21, 108], 'label': '324.166.54.k1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.k1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860147
    {'ambient': '324.166', 'aut_centralizer_order': 12, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 864, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.n1', '18.o1', '18.p1'], 'contains': ['108.f1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4429, -1, 5618, -1], 'generators': [21, 114], 'label': '324.166.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1', 'old_label': '54.l1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 51860148
    {'ambient': '324.166', 'aut_centralizer_order': 192, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.c1'], 'contains': ['162.a1', '162.b1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6659, -1, 7127, -1], 'generators': [3, 54], 'label': '324.166.81.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '81.a1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860149
    {'ambient': '324.166', 'aut_centralizer_order': 2592, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '1.a1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.e1', '54.b1', '54.e1', '54.i1'], 'contains': ['324.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8113, 4088, 5740, 3978], 'generators': [2], 'label': '324.166.108.a1', 'mobius_quo': -1, 'mobius_sub': -162, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1', '36.b1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '108.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.39', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860150
    {'ambient': '324.166', 'aut_centralizer_order': 648, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1', 'complements': ['3.c1'], 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.c1', '36.d1', '36.f1', '36.g1', '36.h1', '36.i1', '54.c1', '54.h1', '54.j1'], 'contains': ['324.a1'], 'core': '108.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3479, 5007, 3749, 4878], 'generators': [6], 'label': '324.166.108.b1', 'mobius_quo': -1, 'mobius_sub': -18, 'normal_closure': '108.b1', 'normal_contained_in': ['36.a1', '36.c1', '36.d1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '108.b1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.12', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860151
    {'ambient': '324.166', 'aut_centralizer_order': 2592, 'aut_label': '108.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.b1', 'complements': ['3.b1'], 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.c1', '36.j1', '54.a1', '54.f1', '54.k1'], 'contains': ['324.a1'], 'core': '108.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6177, 3110, 5983, 3041], 'generators': [108], 'label': '324.166.108.c1', 'mobius_quo': -1, 'mobius_sub': -54, 'normal_closure': '108.c1', 'normal_contained_in': ['36.b1', '36.c1', '54.a1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '108.c1', 'projective_image': '324.166', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.13', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860152
    {'ambient': '324.166', 'aut_centralizer_order': 27, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1475', 'aut_weyl_index': 27, 'centralizer': '4.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['12.a1', '12.b1', '12.c1', '12.d1', '12.e1', '12.f1', '12.g1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4854, 6031, 378, 4185], 'generators': [2, 6, 36, 108], 'label': '324.166.4.a1', 'mobius_quo': 3, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '108.39', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 51860153
    {'ambient': '324.166', 'aut_centralizer_order': 324, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.f1', '36.j1', '36.k1', '36.l1', '54.d1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5226, -1, 2244, -1], 'generators': [8], 'label': '324.166.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '108.d1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860155
    {'ambient': '324.166', 'aut_centralizer_order': 324, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c1', '36.e1', '36.h1', '36.k1', '36.l1', '54.l1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5542, -1, 3472, -1], 'generators': [114], 'label': '324.166.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '108.f1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 51860156
    {'ambient': '324.166', 'aut_centralizer_order': 162, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2592, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.e1', '36.g1', '36.i1', '36.j1', '36.k1', '36.l1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7038, -1, 2001, -1], 'generators': [116], 'label': '324.166.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '108.g1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860157
    {'ambient': '324.166', 'aut_centralizer_order': 1728, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.b1', '54.c1', '54.d1', '81.a1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5993, -1, 5375, -1], 'generators': [54], 'label': '324.166.162.a1', 'mobius_quo': None, 'mobius_sub': -27, 'normal_closure': '54.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '162.a1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860158
    {'ambient': '324.166', 'aut_centralizer_order': 576, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '9.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1', '54.f1', '54.g1', '54.h1', '81.a1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7335, -1, 6502, -1], 'generators': [3], 'label': '324.166.162.b1', 'mobius_quo': None, 'mobius_sub': -9, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '162.b1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860159
    {'ambient': '324.166', 'aut_centralizer_order': 192, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5184, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1', '54.j1', '54.k1', '54.l1', '81.a1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6465, -1, 6995, -1], 'generators': [21], 'label': '324.166.162.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.c1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860160
    {'ambient': '324.166', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '108.e1', '108.f1', '108.g1', '162.a1', '162.b1', '162.c1'], 'contains': [], 'core': '324.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6363, 4088, 5254, 3978], 'generators': [], 'label': '324.166.324.a1', 'mobius_quo': 1, 'mobius_sub': 162, 'normal_closure': '324.a1', 'normal_contained_in': ['108.a1', '108.b1', '108.c1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '324.166', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 51860161
    {'ambient': '324.166', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 216, 'centralizer': '12.b1', 'complements': ['54.h1', '54.j1', '54.l1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '3.c1'], 'contains': ['12.a1', '18.a1', '18.b1', '18.d1', '18.g1'], 'core': '6.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6174, 812, 4046, 839], 'generators': [54, 2, 6, 108], 'label': '324.166.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '18.a1', '18.b1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '108.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}